vol i, pars i

CLAUDII PTOLEMAE(BOPERA aUAE EXSTANT OMNIA

VOLUMEN I.

SYNTAXIS MATHEMATICA

EDIDIT

J. L. HEIBERG,PBOFESSOR HAUNIENSIS.

PARS I

LIBROS I VI CONTINENS.

LIPSIAEIN AEDIBUS B. G. TEUBNERL

MDCCCLXXXXVIII.

PA/4-H-OH"

ft*

LIPSIAE : TYPIS B. G. TEUBNEEI

PRAEFATIO.

Ad Ptolemaeum edendum adcessi aBibliopola hone-stissimo rogatus, nee inuitus obsecutus sum, cum id

maxime opus esse uiderem, quod praestare me posse puta-

bam, ut codicibus denuo collatis aestimatisque fundamen-

tum quoddam recensionis iaceretur. nam editio princepsSyntaxis (Basileae 1538), ut mos erat illorum temporum,uno nee eo bono codice nititur, et Halma, abbas Pari-

sinus, qui delude solus Graecam editionem curauit (Parisiis

1813sqq.) hodie rarissimam, ut optimum codicem Parisi-

num adhibuit, ita neque negotii critici neque sermonis

Graeci satis peritus fuit. mihi igitur incipiendum erat a

codicibus conquirendis, inspiciendis, conferendis, ubi opusesse uisum erat. quern laborem ut per annos 1893 et

1894 profligare possem, effectum est ope et liberalitate

summi Ministerii, quod cultui scholisque Daniae

praeest, maximeque Instituti Carlsbergici, bonarumavtium in rebus angustis adminiculi locupletissimi ,

cuius

praesidibus hoc loco ex animi sententia maximas ago gratias.

Inspectis examinatisque codicibus, qui quidem innotuis-

sent, omnibus, de quibus in Prolegomenis partis\ poste-

rioris agam, hos elegi ut recensioni et utiles et sufficientes:

A codex Parisinus Graecus 2389, membranaceus in

folio, litteris uncialibus binis columnis scriptus s. IX

(u. Omont, Inventaire II p. 251), charactere, ut Henrico

Omont uidetur, Aegyptio. constat foliis 376, quorumprimum ad extremum libruni XIII pertinet et paenedetritum est, foil. 207210, 255 270, 374 375

IV PRAEFATIO.

suppleta sunt s. XV (a); post fol. 68 quattuor folia

desunt (u. p. 200, 7 et p. 209, 21), ut ex quaternionumratione colligitur. scriptus est codex omnium praestan-tissimus duabus manibus eiusdem temporis, quarum una

(A sine A2

) atramento rauo, altera (A1

) badio utiturj

A1, quae a fol. 175 (p. 487, 17) incipit, sed iam in

priore parte nonnulla correxit, litteras inclinatiores habet,i adscriptum interdum ab A2

semper fere omittit, ad-

centus uero spiritusque plures adponit quam A2, spe-

cimen exstat apud Omont Facsimiles des plus anciens

Manuscrits Grecs en onciale et en minuscule de la Biblio-

theque Nationale tab. IX. correctiones paucae manibus

recentiori (A3

)et recentissimae (A

4,

s. XVI) debentur.

contuli ipse Parisiis 1893. spiritus adcentusque hie ut

semper in adparatu neglexi.B - - codex Uaticanus Graecus 1594, membranaceus in

folio s. IX, quo nullum pulchriorem elegantioremque

unquam uidi. constat foliis 284, sed olim plura habuit^nam fol. 284V legitur: j\ fitfikog amy rrjg peydKrig 6vv-

rd^ecog k'%i cpvkXcc TIE nctl dvo slg tr^v (XQ%r}v rov fiifiXlov

aTtokvTK. post fol. 65 unum folium excidit, cui manusrecens s XV duo substituit (u. p. 224, 14 et p. 228, 20).eontin codex: fol. 1 8 Prolegomena anonyma adPtole-

maeum. fol. 9 263 Ptolemaei Syntaxin cum scholiis,

fol. 264 272 r Ptolemaeum de apparentiis, fol. 272V

276 Pt^lemaeum Ttegl x^tr^^tov, fol. 277r tabulam cate-

goriarum (fol. 277V uacat), fol. 278 283r Ptolemaei

hypotheses, fol. 283V 284 notasuarias. inde a folio 271V

extreme duabus columnis uti desinit. - -inuestigaui

ipse et, quoad potui, contuli Romae 1894. P. 232, 4

p. 546, 20 mea causa contulit loannes Tschiedel.C - codex Marcianus Graecus 313, membranaceus in folio

s. X, ab imperito librario pulcherrime scriptus non sine

compendiis maxime uersus finem. correctus est duabus

manibus recentioribus (C2

s. XIV XV) et una recen-

tissima (C3

,fortasse ipsius Halmae; nam fuit Parisiis

initio huius saeculi). continet: fol. 1 30r

Prolegomena

PRAEFATIO. V

ad Ptolemaeum ab initio mutila, fol. 30V 370 Ptole-

maei Syntaxin cum scholiis. ex archetype codicis Bdescriptus est. - - contuli ipse Uenetiis 1893.

D codex Uaticamis Graecus 180, membranaceus in

quarto s. XII, compluribus manibus eiusdem temporis

scriptus, saltim alio alibi calamo atramentoque, et dua-

bus minimum manibus antiquis (D2 D 3

),una recentiore

(D4)correctus. continet: fol. 1 2 notas quasdam astro-

nomicas a manu recenti, fol. 3 280r Ptolemaei Syn-taxin cum scholiis, fol. 280V notas uarias manuurn

recentium, in imo mg. opov gjiUAor a 8do(Jii]KOvrcc ema

(debuit computari 278). deriuatus est ab exemplari

optimo et uetustissimo, quod saepe cum codice A con-

sentiebat contra BC, saepe etiam solum ueram scriptu-

ram seruabat, sed ab hornine rerum perito audacter

interpolatum erat siue ipsum siue aliquod eius apo-

graphum; nam imperitis librariis codicis D interpola-

tiones illae adtribui minime possunt. quorum errores

incredibiles,

ex itacismo et ex compendiis male intel-

lectis plerumque ortos, saepe omisi, sed numquam nisi

monito lectore (u.ad p. 4, 3; 12, 20; 27, 2; 29, 23;

cfr. p. 40, 20). compendiorum usum significaui, quiaad aetatem genusque archetypi definienda uiflia sunt.

contuli ipse Romae 1893 94.

E - - codex Marcianus Graecus 310, chartdceus s. XV.continet: fol. 1 13 r

Prolegomena ad Ptolemaeum,fol. 13V 151 Ptolemaei Syntaxin cum scholiis (fol. 152

uacat), fol. 153 261 Theonis commentaria in Syntaxin

(fol. 262 264 uacant), fol. 265286 alia manu Ca-

basilae commentaria aliaque eius opera, fol. 287 288Barlaami quaedam. adcedit ad BC. inspexi paucislocis Uenetiis 1893.

F codex Parisinus Graecus 2390, bombycinus s. XIII,de quo u. Omont Inventaire II p. 251. arte cohaeret

cum BC. hie illic inspexi Parisiis 1893.

Horum codicum ope uerba Ptolemaei talia restitui

posse 'confido, qualia a uiris doctis Alexandriae anno cir-

VI PRAEFATIO.

citer 500 legerentur. interpretationibus commentariisqueArabum uti non potui, Latinis nolui. interpretationemmeam siue Latinam siue linguae recentioris in tanta rerum

difficultate addere ausus non sum; de ea re uideant astro-

nomi, si interpretationem desiderauerint.

In adparatu ad p. 227, 10 et p. 481, 15 pro Halma

reponendum ed. Basil, ad p. 522, 49 delendum <?'] // A1?;

nam etiam in A est $', ut ab Henrico Omont posteacertior factus sum. ad p. 539, 7 haec adnotatio addatur:

7. inrog] scripsi, Ivrog A1 BCD.In plagulis corrigendis opem peritam diligentemque

beneuolenter mihi praestitit Henricus Menge amicus.

Scr. Hauniae mense Maio MDCCCLXXXXVIII.

J. L. Heiberg.

KAATAIOT IITOAEMAIOT

MA<H)HMATIKHS

Ptolemaeus, ed. Heiberg.

A'.

Tads V6riv v TGJ jrpcjTtp r^g IIroA,[iciiov

a.

$' . 3t$i rrls rcc&as rcbv

y'. on <J<jpcctpOfcd\ 6 OVQCCVOQ

d'. cm xlij yij 6<pcuQOidris 6nv n$bs afafrqew cog

. on p6r] rov

$'. on 6r][iiov Adyov %ei icgos ra OVQKVLCC ij yij. 10

f. ort ovdc xivyGiv twee nBraftatLKriv noisltut,r\ yij.

if . on dvo dicupOQal T&V XQ&TCOV xivtfte&v i6iv iv

TfiJ OVQCIV&.

&'. 7t$l r&v Kara ptgos KccraA.r)t}>G)v.

i . 7tQl r?\<s Ttrjfa^Trjros tcbv v Ttp KVK&G) sv&ei&v. 15

W. XCCVOVIOV XG)V SV

ngo-A, v-^avSiov nrol8(jLaiov ^ctd-rj^KTiKfjs Gvvtd&cos fiiptiov

TIQ&XOV B, om. CD. 2 p. 4, 5. om. A. 2. rads] corr. exrdd' D 8

. TT^COTOT 3. avvrd&mg] a D. 4. a'] om. D, et

sic deinceps. fr/*cf$00f] D, 0WTa|fcog BC. 6. orqoatpoet^ws 6

ov^iavog] ccpttiQOSLSrjs 6 ovquvbg nod GcpaiQOSidobs fpsgsrui D.

7. jtat 8. /*^>7]] GcpuLQOi8'r]g v.a.1 i] yfj D. 10. |JUA} postras. 2 litt. B, 8^fi 17 yf) D. ra yrf} rbv OVQKVOV D. 11.

noisiTui iLtxafiKTwriv D, noisltKi corr. ex noifixui m. 1. 12.

ffotv] om. D. 15. xfjs srrj/ltxdrTjTog] om. D. rc5] om. B.16. ta'] al B, et similiter deinceps. xavdvtov ebfrsuov]

xal Eot-d'fCts xarortx^ D. KCCVOVIOV p. 4, 1. TCBQI] in ras.

m. 1 B.

4 KAATAIOT HTOAEMAIOT

ift'. 7tQi rrjs iiTct%v tibv

id'. 7tql rcbv fisra^v TOV

if

. xccvoviov Aojco<?0).

5 is'. TtSQi T&V in dQ&ijs rife 6<pcciQccs

a .

Ildvv xaA&s Oi yvrjGicas (pi%o6o(piJ6avTS) d) 2/up,tf /not x%a)()iXvai TO &coQrjTixbv Tils cptAotfogptag

aitb TOV TtgaxTiXOv. xccl ydg i &v^^x xal TW

10 TCQaXTlXG) 1tQOTQOV CiVTOV TOVTOV &O)Qr)Tt,X(p TVy%KVl,V,

ovdev fjTTov av Tis VQOt, iifydhrjv ov0ccv iv

OV [IOVOV did TO T&V [lV YJîXK)V

WvaG&ai rtoMots xccl %&QiS

Tijs $ Tfbv oAcw fa&Qias ddvvaTOV dvau rv^lv avzv

15 didaGxccMccS) AA xal TK> Trjv jtfaidTrjv cocpefaictv Xt

[lV X T^S V CCVTOiS TOiS 3lQdy[ia6i 6VV%OVS VQ-8' X TilS W TOiS

1. TteQKpSQBiag] corr. ex Treptqpf^tag D 3. 2. fo/êtg] corr.

ex Sethis D 3. 3. TOV] post ras. 3 litt. D. x-yx/Lov] corr. ex

Y.OV D 8. itEQicpfQti&v] corr. ex 7iQi(pfQLfbv D 3

;similes eiTores,

quibus scatet D, posthac non notabo. 4. uavoviovom. D. 5. KvatpoQ&v] TOV dice psccov ncci TOV

D (a supra scr. D 3). Seq. old' on &vr}Tog scpvv

KCtl S(pd[l8QOS' &M,' OTUV CC6TQCOV \ 1%VV(O Y.UTO. VOVV CC}lCpt.dQ6(lOVg'

sitnpava) yafyg TIOGLV,&Ma TCKQ' O.VT&I

\ r]vi

itlaiicu d/nôatrjg CD (idem in mg. inf. B, sed6. a'~\ om. A, mg. B, -nJLavdtov 7tTote[iaLov iia&ir]-

, 7tTOlE[LClloV GVVTCcl$ D. 7tQOOi^,LOv] Om. A.8. x%co^r]>tfVat D, sed corr. 9. na (alt.)] del. D. 10.

TrpaxrtHw] corr. ex TIQCCKTMOV C 3. CCVTOV TOVTOV] mut. in

CIVTO TOVTO C 2. 14. cc8vvccTov\ corr. ex SVVCITOV A 3

. 16.

D. 18. nciQccyCvsGQ'cii, yi- in ras., D 3.

MA0HMATIKHS 2TNTABE&S A'. 5

tag [iV ngaêig iv rats ai)ro3V rcbv tpavratfiav iiti-

oit&s pyd' iv rots rv%ov6iv BTCI-

a rrjs ngbs rrjv xaAqv xal evraxrov xard-

') rtf de 6%oAfi %aQLt>e6%'cci rb jttettirov

noM&v xai KK^COV ovr&v 5

ds slg r^v rcbv tdicsg

[icc&rj[iccrMG)v. xal yap av xccl rb

6 'AQiGrordKris Jtdvv fftftfAcog Big ryCa, ra itQ&ra ysvrj

dicuQst r6 re <pv6i,xbv xccl rb iia&r}[iarixbv xccl rb ftso-

hoyixov. Ttdvrov yap rcov '6vrov rr\v vitccQ%iv fyovrcw 10

sx re vlris xccl effiovs xccl xwt]6eG)s %coQlg per exddrov

rovr&v xccra rb {jxoxeipevov fteaQetd&cu pr} dwccpevov,

voelGftcti de povov., xccl ccvev r&v Aotjrrav, rb [lev rr^g

r&v oAcdv TtQcbryg xwtJGe&s rtg&rov ccl'riov, el' rig xccra

rb ccitAovv ^xAaiiftdvoi,) &ebv d6ârov xal axiwiyrov av 15

fjyiJGairo xal rb rovrov fyjvrjTixbv eldog fteokoyiKov

area nov negl ra pere&Qorara rov x66{iov rj]g roiavrrj$

vorj&efarjs av povov xal xa&dita% xeôQi&ê-

r&v afa&rjrav ovGicbv rb de rijg tifoxris xal atel

itoioryrog dieQevvrjnxbv eldo$ itegi re rb 20

Aevxbv xal rb ftegiibv xal rb ykvKv xccl rb ccTtahbv

xal ra roiavra xarayi/

yv6^tevov (pvtiixbv av xcckdtieie

rr\g roiccvrrig ovtiiag ev rots tp&agrots cos snl tb itohv

xal V7toxdro3 rijg G^yviaxiis 6<pcciQK$ dva6rQ(poiievrjs'

rb $ rr^g xccra ra d'drj xal ras perafiarixas xivriGeig 25

2. indctv&ccvcopEQ'u] snda\ fruvaiieofa* A, v add. A 2

. 3.

Tijc] corr. ex xr\ D 3. 4. An rr)g ^8 aô^g? cfr. Boll, Studien

viber Cl. Ptolemaus p. 68 not. 3. 8. 'AQLCXOTE^S] Metaph. E 1;

cfr. Boll p. 71. 9. re] om. D. jtta^Ttxdv D, corr. D 2.

15. Klcc[ipdvi D, corr. D 2. KV.LVT]XOV xal CCOQCCTOV D. 17.

ufTfto^toTaTa C, sed corr. 19. afoi'] &fi CD. 20. TB\ om. D.22. tiKTccyivo^fvov C et corr. ex naTayivofitvaiv D. 23. Ante

tTfc del. s" D. 24. xai] om. D.

jtoiorytog [i(pavi,6nxbv sidog 6%ijiiKt6g rs xccl

rrjros xal 7trjA,ix6rr]ros en TE roitov xal %$6vov xocl

rcbv bîOLCDV fyrynxov vndgôv dtg iia&rjiianxbv civ

K<pOQi6Ei rils roLccvrys ovGfas HETCC^V &6itSQ EKEIVGW

5 rcbv dvo TtinrovGrjS ov povov r& xccl di afad"iJ6Ci)g

ftri<5G) dvvaG&ui voftât, aM.K xal r&

rols ovtii tivppefit]xevtb KK\ ftvyrots xal

rots V&v afel pBtufittM<ov6i Kara TO sldog

rb Ki&QiGrov 6viJi[iei;a(laM,oiievriv, rots ds uidioi$ xal

10 i% cct&Q(bdovs (pvcte&s GwtrjQOvGccv axivyTov rb rov

si'dovg cîsrK^rjrov. % d>v diavori&Bvres, on r& psv

dvo ysvy rov ftscoQrjnxov paMov KV n<s

Ttt^rrjôviKrjv sfaoi, rb {LEV

dia rb 3tavrsA.K>s oupavss avrov xal avsTtttrjTtrov ,rb

15 ds <pv6ixbv dia rb rrjs vAqs atirarov xal

dia rovro iiqdEitore av iKitfaui TtEQi avr&v

rovs cpihoGocpovvTaS) povov d rb iia&rjiiccnxoV) el' ng

%era6nxG)s avrtp 7tQo6EQ%oiTO, ^Kiav xal a

rotg iieitt%siQi,oiivois tyv fi'drjGi

20 rrls ajtodffef&s 8i>' ccvaî^^r^rov od&v

xara vvcc[ii,v r]s roiavrrjs

7t()l XGi &ttt Xtt.1 OVQKVICC

rccvrrjs 7tgl rfjv r&v aiel

25 xa

3. HK&rjiiamov B. 5. 81,'] 810. BC. 8. rots] suprascr. D 3

. octet] A, &et BCD. [u-zapdUovcl A. TO elSos]

mg. add. D 3. 9. Se] S' D. 13. efaoi] corr. ex efasv D.

14. Ttavxtk&g] -06- in ras. B. nut] ncti 8C C. ccvsni^riTttov]a- in ras. 2 litt. C, post -rjras. 2 litt. D. 16. ^dsnor' D.

18. ccfifrccTiLarov] mut. in apsraneiGTov D 3. 19. Mg. y$.

Gvvidi6Lv D 2. 20. yivofievn? CD. 22. iidJLiara] supra

scr. D 3. 24. alst] A, &et BCD. aiel V.KI ma-] in ras. D 3

.

MA0HMATIKH2 STNTABE&S A'.

rovr6 re dvvarrjg ovGrjs xal avrijg itgl psv rr\v

oixeCav xardArjifrw ovts adyhov ovrs draxrov ovdav

atei xal cadavrcog fysw, ojto 6rlv I'diov fjutfrifp??,

itgbg $ rag aMag ov% tfrrov avr&v dxuv&v Gwegyetv.ro re yaQ fteokoyiKov eldog avxr] ^dh6r' av jtQoodo- 5

axivijrov xal %a)QL6rils VQyiccs djcb r

rcav it()l rag afa&rjtccs pv xal xivovtiag t xal xivov-

aidiovg df xal aTtaftfig ovGiag 6v^^x6r(Dvi t rag tpogag xal rag rd&ig r&v xt,vrj6G)v' itgog 10

r rb (pvGixov ov rb ivyjbv av GviifidMoiro' 6%$bv

yag rb xaO-oAou rijg vfaxijg ovGiag i'diov anb rijg xard

rv\v iifrafiarixrjv XLV^LV tdiorgoytiag xarayatvfrai,

<og rb pv tp&agrbv avrb xal rb acp&agrov aitb ryg

v&i'ag xal rr^g fyxvxMov, rb $ flagy xal rb xovtpov 15

^ rb itu&rirLxbv xal rb noirjrixbv dnb rrjg iitl rb [i6ov

xal ri\g ditb rov p&ov. TtQog y /LM)V rqv xara rag

xal rb rj&og xakoxaya&iav Ttdvrcov av avrrj

dioganxovg xara6xvd<jiv aitb ri\g itQ\ ra

G)QOVfivr]g oftotdr^rog xal fvra&ag xal 6vp- 20

xal arvyiag fyatirag plv noiovtia rovg

xoAov&ovvrag rov &LOV rovrov xdMovg,81 xal &6itQ tpvGiovGa Jtgbg rtfv bpoiav rr\g

xara6ra6iv.

rovrov dy xal avrol rbv Ho&ra rrjg rcbv aid xal 25

fotiavrcog tyovr&v &G)aiag xard rb 0vv%sg av&iv

1. Tt] corr. ex 8 D. rifv] mut. in TOLV C. 3. ccki] AB,afi CD. Post Y.KL del. cb(j{ D. 7. ^oo^tar^g] corr. ex %COQIS

TI~]$ C 2. 8. Tf] supra ras. 3 litt. D 3

. 11. ro qpvfftxov] corr.

ex T&V (pv6i*.a)v C. 14. avrd] -6 e corr. D 3. 15.

in f-v&efas D. 16. ano] corrigere uoluit C 2. 18.

in ras. D 3. 19. ite^i ra] bis C. 25. ccsi D. 26.

pr. v ins. A 2.

TtsiQcjps&a iiav&dvovrfg [ilv ret ijdq xart,^rj^va r&v

rotovrcov [iad"T][idrG)v vjtb r&v yvr}6(X)$ xal fyrrjnx&s

avrotg 3tQo6sA.&6vTG)v , 7tQoat,QOV[ivoi ds xal avrol

roGavrfjV TCQOti&riXriV 6VVl6V'yXtV 5 00r]V 6%$bv 6

5 JtQoGys'yovcos an sxsivcw %QOVOS p%Qi tov xa&' rtficcs

dvvaw' av TtegiitoiYiGai. xal o6a ye dr} voôîsv in\

rov jtagovTOs sis <p&S Wtv cAÂv^fVat, TCeiQciGoiifd'a

8ia PQCC%G)V &s BVI iidAiGra, xal &s av 01 r^dri xal

ejtl Jtotibv 7tQOXXO(p6rS dvvccwto TtaQaxoAovd'flv, VTCO-

10 iivrjiiarfaae&at, rov [iv rsfoiov ri}g 7tQay[iari

aTcavra ra ^^Lâ itgbs rrjv r&v ovgavicwKara, r^v oiKefav raîv xn,&iivot,, dia $ rb p

7toiiv rbv Aoyov ra plv vnb r&v nahaicbv

a di(>%6nvoi ii6vov, ra $r) nqd* oAog xara-

15 Arjy&wra ij ^ &s vrjv v%Qifi6rG)$, ravra df xara

IIspl rrjs rd$(os rCov &&()r][idra)v.

ij ttQOxeipwrjs Îv Gvvrd&cos TtQorjytirai (iVrb XY\V xaO-oAov 6%B6iv Idelv o^rjs rqs yifc agog

20 rbv ovgavov, r&v de xara IIZ'QOS qdr] xal *(p%ijs

rov [iv avsi'rj

rb dtf&hfalv rbv K6yov rbv itSQi rijg

&<5G)S rov Ao|ot> xvxAov xal r&v rdit&v rfjs xa&

otxovpfvrjs n re rijs itQbs aMtjAovs avr&v

xa6rov oQi&vra naga rag

1. xtrmfoj/u, | privet C. 2. pccftrifLdTcov] -[id- supra scr. D 3.

3. itQOsl&ovtaiv C. 5. nQOCysyovrng] BD, nqoysyovms AC.8. ^ga%ifov\ corr. ex XCL%(QV D 3

. 9. Mg. itQOGxsyivcpOTfs C 8.

11. ra] ins. D 3. 14. ij] supra_scr.

D 3. olog C. 15. $e]

del. C 2. 17.

fi']om. CD, x<p. ^ D 2

. 18. Srf\ Si C. 19.

TO] seq. ras. 1 litt. D. 23. hi re] eha D. 24.

-x/li- in ras. D.

MA0HMATIKHS 2TNTAEE&S A'.

sv rats rd%6iv diatpogag'

rovr&v fi-scoQicc r^v r&v koiit&v InfaKstyw evodars-

$av itciQfyei' dfvrsQOv ds nsgl ryg Âmjcife xiviJ6G)g

xal iris GeArjviax'fjs xal rav ravraig itt,6v{i(lcuv6vtG)v

dlt&H&ftV %&Qlg yap ryg rovrcw 3tQoxataA.tjil>G)s 5

ovds ra Ttegl rovg aGrsgas ol6v rs av yevoiro dtsô-

dixGJs ^scoQrlGca. rsAevraiov d' ovros &S ^905 ccvryv

r^v b'yodov TOV nsgl r&v KGregov AoyovKV sMr&s xal SVTCCV&CC ra rtsgl t^g r&v

(StpKiQag, sitoito ds ra Ttsgl T&V Jtevrs 10

f'xccGra ds rovt&v

[ISV XCll

fig rrjv avsvQ0iv %Q(&[ivoi, rolg

xal rccZg adiGTKXTOig t&v rs jtcdcu&v xal r&v

rag d' q>sijg r&v Karahtffa&v <pagii6- 15

a rcov iv ratg

rb [iv ovv xaftoAov roiovrov av

ori, r 6cpai,QOt,drig i^nv 6 ovgavbg nal yegsrai

)xai on ^ yv\ rca pv 6%rjiian xccl avrrj 6(pai,-

6rw agog afaftyGiv &g xa&' oAa pfQr} happa- 20

rr] ds &s6st, [i6rj rov Ttavrbg OVQKVOVre* $ yLsysfi'Si xal r&

%st, ngbg rr\v rcov

a<frQG)v Gcpatgav avrrj

1. ra&Gi BD. 2. svoScaTâv'] svo- e corr. D. 3.

rb TtfQt A. xivrjfffcos xat rfjg Of/lrjviaxryg] v-ul fff^rjvtax^g6(og D. 6. re] x

3

D. 7. $'] Ss D. 8. nQordcoiTO D.12. nfLQttGoiLS&cc] corr. ex TcsiQKGwine&a A 2

. 13. ivuqysGiv D,y e corr. Deinde add. xca comp. D 3

. 14. Ante re del.

nev C 2. 15. rj]QLGB(ov C, corr. C 2

. *'] Si D. 19. rco\corr. ex ro C 2

. 20. sen B. IccâvofisvriL C. 24. ccvrij]

ccvrr) EC.

noiovpf'vexev

rovrov <T exaGrov

y'.f

'Ori GcpaiQOSLd&s 6 ovgccvbg

Tag [iev ovv TtQ&rccg evvoiccg vtegi rovrcov coco

5 roiavrrjg rwbg TtaQarqQrjtfecos rolg JtaAcuoZs evAoyov

TtccQccyeyovevai,' S&QWV yag rov re %\kiQv xal r^v

nal toi>s d'AAovg aGtegas cpegopsvovs aito

iiti dv6^ag aisl xara

xal C(.Q%OILVOV$ plv10 onto rov raneivov xal &671EQ

J

| avrijs

QI&IISVOVS $ Kara IMXQOV els v^og, STtsiTa

xara rb uvaAoyov HQiQXO(ir

vovs re xal ev raiteivcc)-

ccv reAeov &67teQ fyrtfGovres el$

sir

15 peivccvras ev r& KcpuviGyiG) &67teQ cat

KvarfAAovrccs re xal dvvovrccs, rovg de XQOVOVS rov-

rovs xal k'xi rovs r&v avaroAcbv ncti dv0cov rojfovg

re KOI ofioiog tbg tniitav avrccnodido-

20 fiaAttfra de ccvrovg yyev efe rrjv 6tpttiQi,xr}v evvotav

fj rfov alel yaveQcbv a6rQ&v neQiGrgoyxccl jtegl xevrgov ev xal rb ccvrb

aroAog yag avayxuios exelvo rb

1. ^'] ^' D. 2. TtQodielisvGotie&cc D. 3. y'] B, om.

ACD, Xfqp. y D 2. GCpttiQOSlS&S 6 OVQKVOg] 6CpCClQOLdi]$ 6

OVQCCVOS Hal 6CpaLQOlS(Q$ D. 7. CpSQOflEVOVs] (fKCVO^SVOVg BC,corr. C a

. 8. &ei D. 13. yivopsvovg D. smg] o>s BC,corr. C 2

. coffee] ^GTCSQ ndliv D. 14. ndhv] n- e corr. A,om. D. 15. [LSLvavteg D, corr. D 3

. SIGTISQ] itaJkiv WCTCSQ D.16. 8] d- in ras. A. 17. Svascov] dvGfi&v D, supra (i ras.

18. cog] om. D, xca to? supra scr. D 3. 20. Ss] 8* D. 21.

ItSi CD. CCGTQfOV D.

MA0HMATIKH2 STNTABE&S A'. 11

eyivsro rqg OVQKVIOV GtpaiQccg r&v [iv pccMov ccvr&

itgbg rqv rrjg

xvxAovg v rfi TtSQiyQatpri itoiovvr&v, fcog av

rj <x7to6Tcc6i,g xal ft^()t r&v cupaviôyievGiv tpfrdGr}) xal 5

rovrcov ds ra per syyvg t&v ctlel qjavsgav

G)Q&v iit bUyov %QOVOV v x& cupaviGpKt

ra d' ano&ev avcdoycog jtdhv jtl nfaiovcf

fiv KQ%YIV dia inova ra roiavrcc ttyv JtQO

SVVOIKV ccvrovg AccfaZv, r^dri dl Kara TT\V (p%fig &&- 10

xccl ta hoiita tovtoig Kxohov&cc xccravoiiGcci

catAcbg r&v (pccwo[iVG)v ratg TQodo%oig iv-

voicug avriiiaQTVQOvvt&v.

cpQ yccQ, i rig vjrdOwro rr^v x&v atiTSQ&v tpogav

it v&iag ywoyLBvviv rt' aitiQOv (pQ60-cc^ xa&dttQ 15

ndiv 'do%v, rug ctv zmvori&GCri TQoitog, xcc& ov ditb

', 3iK><$ y&Q dvKxdujtruv edvvaro T<X CC

lit axt,Qov 60/w.o>î>a; rj n&g dvccxd^ytroyrK OVK

', rj jtcbg ovyl XKT;' bkiyov ineiovyievwv rcbv ^ye- 20

avrolg rolg d(pavi6[iolg,

xccl &63t

Ma p,r\v xal rb dvd7tr6&a r avrd x ri\g

xal Ttdfav fig ravryv ttTCoGfisvvvG&cu, r&v dôyo- 25

rdrcov av (pccvftrj itccvrfhcbg. LVCC ydg rig

3. ds

] Ss D. aTrcoTepco] tincozEQcot, AC, KHOTEQCIJI B,

ccno)TQa> D 3. 6. asl CD. 8. <T] mut. in ds D 2

. anaj&sv D 3.

14. KGTZQOJV] corr. ex &GTQCOV D 2. 16. sô|f D. 18. sdvvaro]

s- in ras. A, fidvvccro D. 22. xara] corr. ex v.u A 2. 24. aHa

pT]v xat] in ras. D. 25. ravrrjv] avr^v D. cdoyorccTOiv B.

12 KAATAIOT nTOAEMAIOT

rrjv ro6avrr]v rdîv Iv re rots iiy&6w xal reels

3to06rr]6i,v avr&v^ n ds dia6rrj[ia6i,v xal ronois xal

%QOVOIS OVT&S sfaf} xal cos rv%v cutorefatedai,xal

rods pv rtav TO îOOs rrjs yfjs avaitrwriv %iv yvtiLv,

5 r6de df 6fte0ri,xtjv^ fitUAov ds rb avrb rots psv avdx-

rsiv, rots ds Gpsvvvvcct,, xal r&v a6roa)v ra avra

rots 1*>V r^dri avrjiifieva rj sGpsGiisvcc rwy%aviv, roig

ds ^dfjccj, el' riS) WP^ ravrcc xdvrcc 6vy%G)Qij0i,ev

ovrcos ovrcc ysAoTtt) ri wv jtSQi rcov aiel (pccveg&v

10 Sftoijisv siTtsZv r&v iiijrs avccreMdvrcov îtjrs dvvovr&v;

rjdi Ttoiav alriccv ov%i ra psr dvanroîsva xctl Gfisv-

vvpeva Jtccvra%fi xal avarshfai, xal dvvsi, ra $ [if}

3td6%ovTK rovro itavrccî] 6nv atel vnlo yijg; ov

8^ y ret avra rots y&v akl avaq)%"Yi6rai KOI

15 Gfrat,, rots $ ovdw ovdJtor rovr&v Ttutizrai, Ttavrd-

vaoyovs ovros rov rovs avrovs u

T xal

xccv bjfotov Ti

20 rrjs t&v ovgavtcov fpooas V7t6%"rirai TtMjv rov 6<pat,-

QOfidovS) avfaovs avdyxq yiyvtG&ui rag anb rils yrjs

till ra iLQrj r&v ^rG)QG)v a7to6rd0iSi ovtov av avrrj

xal cos &v vrtoxfyrai,) cadre Qytiteiv xal ra r â^fO1

^xal ra nobs AA?JAov dia&râra rtov adrfocw avi6a

2. 8ictGxrin,ctGi C. 3. ut$] slv.- in ras. D. 4. i'^ftv] corr.

ex %ei B 1. 8. GVYXCOQSLGBISV C, sed corr.; -QTJGSI,- in ras. A.

9. &d CD. 10. dvvovrajv] alt. v ins. D 2. 13. &s D. 14.

&si D. 16. oi>rog] corr. ex ovtag D. 19. S'~\ Ss D. 20. Post

ovQuvtwv ras. 1 litt. D. tpog&s] corr. ex cpcoQ&g D; similia

posthac non notabo. vnoTLfttTui D, -ri- eras. 21. yivfG&at. D.22. onov 23. vTrox^rjrai] in mg. sup. add. D, mg. D 3

.

23. xca (pr.)] fjveil CD 3

. vsroxfijTat] corr. ex vTroxaiTjrca C 2,

D.'

xi[ om. D. 24. &Ur\la D.

MA0HMATIKHS STNTABE&S A'. 13

tots CCVTOLS xcc& xd0Tr}v itSQicpOQ&v fag KV

7toT ^v itl peiôvos, nore d' iitl IJTTOVOS

ojfQ ov% bqaxai Gvppccivov.

TO TtQOS TOIS bQi&VGW pit,OVK Ttt

ov% fj dnodTccGis eAdrrcw ovcfcc noiei,

rov vygov rov Ttegifyovros rv\v yv\v

vfjs rs fiascos fip&v xccl ccvr&v

xccl ra slg vd&Q suftA.rj&svra îsôva cpccC-

V8TCCI,) XCCI 00CO CCV XCCT&T8QG) %COQf}) TOtiOVTG) pSlloVCC.

itgotidyst, d' sis tv\v GcpcuQMriv SVVOIKV xal tec 10

TOICCVTCC TO Tft?)

dvVCC6&CCl MCCT* aMrjV VJCO&SGlV TCt

TCOV G)QO6X07ttC3V XttTCCtfXSVKS GVfKpCOVSlV Y} ÔVYJV TCCVTrjV^

xcdf

6ri Tils t&v OVQCCVLCW (poacts dx&hvTov TS xccl

evxivrjTOTaTrjs catccGcbv ovGys xccl r&v GjffliidTcov svxwrj-

TOTttTOV VTtdQ%l T&V ftV STtMe'd&V TO XVXfaxdv, TCOV 15

6e 6TSQSGJV TO 6tpCCl,Ql,x6v, d)0CCVTG)S & OTl) TG)V

6TIV TO. 7toA,VyG)VlG)TQCC) TCOV ^V 7fi7Cdo3V 6 XVX&OS

TG)V $ 0TQO)V ^ GCpCCtQCCj ^^COV $

6 OVQCCVOS t03V aMcOV 0G)[ldTG)V. 20

ov [lyy dMa xccl ditb (pvdix&v tivov k'GTiv dQ[ir}-

OLOV OTi TG)V

1. yuivfG&ai] corr. ex cpsQSG&ai D 3. obs] inter o> et s

ras. parua D. 2. d'] dt D. yivopwa CD. 3. SIKGT^-

OS] corr. ex Siaazriiidrcov D 3. ov%] corr. ex ovx D 3

. Antea ras. 1 litt. D. 4. OQIÔVGI D. 7. rs] om. D. yivo-

CD. 9. yiutoo-ceQcoi, BC. Z00?]?] corr. ex %<OQSI D 3.

psi&vcii BC, corr. B 1. 10. 8'] 8 CD. g^g] ins. D 2

.

11. KUTU D. 12 OJQOGHOTtfav] C 2D 3, UQOG*Onid>V ABCD 2

,

OQOGKOTCI&V D. 14. fuxn/TjxotraTTjs C, Bvv,ivi]riY.(ora,Tr]$ C 3.

xat] corr. ex KUTO, D 3. 15. v7C<xQ%i\ mut. in v7taQ%eL D 3

.

r&v] corr. ex TO C 2. sitmsdmv] corr. ex tnin&wv C 2

. 18.

sen B. TtohvytovoTeQK D, corr. D 2.

14 KAATAIOT IITOAEMAIOT

A7irO[lQ6rEQOS XOl b[lOlO[lEQE6rQ6s

ftirw 6 ai&ijo, rcbv ds bîoioô&v bfioioÔts ai sxi-

s $E faitpdvfiaL povai ijr xvxho-

v rots faiJtdoi,s xal v rots 6rOEOts5 rov $ al&Qos p? ovros frtiiiEdov

,

Karafaiiisrai avrbv dvai GcpaiQosidri. xal oftotog, on

^ <pv6is G&Httra ndvra ra [ilv iitiytiu xccl

X 3t

,ra d

5

iv rcS al&sQt, xal &la ndvra itdfov

10 $; 6iLOio[iQ(bv xal GyaiQixcctv, 7ti7CQ sitiTtsda ovra $ovx av Jtatii, rots $x ditttpOQ&v rijs yrjs

V7tb rbv avrbv %QOVOV bowGi xvxfaxbv iv<paivsrodid rovro ff fvAoyov swat, xal rbv itEQifyovra

avra al&BQa rrjs biotas ovra (pvGfcos Gtpaioofidil re

15 sivai xal dia rrjv b^,oioiiEQiav fyxvxMws f

xal

'. "Ori, xalfj yfj GyaiQOfidtjs 6riv nobs

f'On df xal

YI yv\ 6(paiQOidijs <3nv

20 cos xati' oha por] Aaiij$avo[ivr] , iidkiGr av ovr&s

xaravoriGaipfV rbv ijfoov yao italiv xal rrjv 6J.?jvr]v

xal rovs aMovs d0roas 0rtv Idftv ov xard rb avrb

rots fat vys T^S dvar&Aovrds r xal dvvovras,

1. xal 6[ioio[jiQ(>TQ6s GTLV~] A, supra scr. D 3,

om. D,BC. 2. 8s] $' D. 3. -vf-icci, fjrtgja-] mg. D 3

. 4.

si>(alt.)] om. D. roig arsQfois] r&v crsQE&v D. 7. xat] xat rd D.8. ccvofioioÊ | IISQ&V D. [isvroi] ds r&v D. 9. d'] 8 D.11. ccn&Gi D. 12. roncov'] corr. ex ronov C 3

. 13. 8'~\ re D.15. lyxDx^tcog] ivwAkl(o$ D. cp^QS6&Kt] -8Q- in ras. D. 17.

B, om. A CD. OTI 18. JU^TJ] on 6cpKiQ08i8i]g v.a.1r) yfj

mg. sup. D. 19. \(paiQOidr)s D. 20. ovrco D. 22. %6tiv\ins. D 3

. 23. n&ci D.

MA0HMATIKHS ZTNTASE&2 A'. 15

XQOtsgois y>v aid tots agog avarokag oixovtiw,

v6rQoig ds rots ngbg dvGyidg. rag yap vjtb rbv avrbv

dytor^.ov^vag exAfmrwas (pavratiiag xal

rocs GfAyviaxag VQi6xoîv ovx iv reels avralg

-)

rovrttinv rats tb foov ait%ov6aig ri\g iisGyjiflQias,

itaGiv dvayQccyoiisvas ,cUAa itdvrors ras

rots ccvccrohxtQrsQOis rcbv rr^Qâvrco

COQCCS v6reaiov6ccs t&v Ttaga rots dvnx&rsQOis. xal

rys diacpoQKS ds r&v GSQ&V dvahoyov rots ditt6rrm,a6i

rcbv %coQG)v evQiGxoiisvrjs GcpcciQixriv av ns efaor&s 10

rqv rrjs yils sitHpdvsiccv vitohdj3oi rijs xara rr\v xvgro-

rrjra xa,& oka pegy Aapf}avoiivr]s dôio^s^Siccs dva-

Adyog aid rag eitMQOG&riGsis tots ecpstfis xoioviisvrjs'

EL ds ye fjv rb ^%r\â srsgov, ovx av rovro Gvvtfiaivev,

&g i'dot, rig av xal BX rovrcov. 15

xottyg ply yap avri]g vitaQ%ov6rjg jtQorsQoig av

eyaivero dvarsMovrcc ra atirga rotg

STtmedov ds itaGiv apa xal xara rbv avrbv

rotg iitl rijg yijg avsrsMsv rs xal sdvvev, rgiy&vovds

T) rergaycbvov ij nvog akkov 6%tj[ictros r&v itokv- 20

y&vav TtaGiv av ttdkiv bôiog xal xara rb avrb rots

eitl rijg avri\g v&iag oixovGiv, 07tQ ovdaîcog yaivsrai

or i, de ovd xvkivdQOidrig av /'^, ivar\

7tQL(pQr\g 7ti<pdvia jtQbs rag avarokag xal rag

rj rrQa^vrj^ rcbv d 7ti7tda)v fiddfov at 25

1. det D. 3. XQOVOVOV C. ccnoTElovptvccs] corr. ex ano-A 3

. 6. rdg] ins. D 3. Ttctgd] om. D. 7. <xva-

ToliKOTSQOis BC, corr. B 2. 8. VCTSQÔVCCCS] v- ins. D 3

. 13.

ccst D. 17. "tec aGTQCc uvarsMovra. B (notas adpos. B 1

).

19. ccvttetev C. 20. de] corr. in rs D 2. 21. av] om. D.

22. ovdapr) D. 23. ort] inter o et n ras. 1 litt. C. 25.

e- in ras. D. snLTtsdmv] corr. ex STILTCS^COV D 3.

TtQQg TOVg tOV XOtfftOV tfdAoUS, OJtEQ CCV TlVSg

ifv cog 7ti&avG)T()ov ,Kid"v dqhov' ovdevl

av ovdsv atsl tpavsgbv iyiyvsro T&V

T&V 7tl TY\g xvQTY\g Iniyaveiag ofaovvT&v,5 itavra Jtatiiv xccl avsteMev xccl sdvvev, T)

ra avra xai

TO i'0ov aysGr&TK r&v xoAcov exaregov n&Giv del

atpavi} xa&fataTO' vvv d' o<?c} civ paMov agog r&g

KQXTOVS TtaQodsvCOlLSV, V060VTG) VGDV [IBV VOTKOTSQ&V

atitQcov KTtoKQVTtrovrai ra ntefova, x&v ds poQeiotegoiv

10 avayaivstai,, cog drjAov elvui, diori xccl svTav&a ^

^g yr^g xccl rag iitl ra ithdyia pdgvi iiti-

avaMy&g Ttoiov^wi Ttavra^&ev to

TO 6<Cd,Olda7todMVVGl,V lTCC TOi) XCCV

15 Kal agog fivdr}rtOT) Kara yuKQov CCVT&V av,6[iva ra

cc&KJtfQ % avrijg

, 3tQOTQov $

Trjg TOV vdarog sitiyaveiag.

'. "On ^.0rj TOV ovgavov

20 TOVTOV 81 &G)Qrid'VTog) l' Tig

av

1. onsq] corr. ex onev C 2. 2. nfi&avwreQOV C. 3.

fat CD. iysvsto D. 5. avsreUf D. Post r? add. -AUTO. D 3.

6. TO] ra D. nolcov] corr. ex TroHojv D. 7. $'] dt D.

OCTCD] o- supra scr. D 3. av] om. D. 8. nccQoStvcofisv] corr.

ex TtaQoSsvopev A 2,mut. in naQodsvofisv D, naôSevoîsv C.

votetOT^tov D. 9. ^Trox^'ujrTfTat D. T] om. D. $e]

supra scr. D 3. 10. dfjlov] $fj- e corr. D 3

. 11. [tegr}] -rj

in ras. D. 13. aTtodsinvvGi D. 7r()0(>7rZfa)jw/v] corr. ex KQOG-Ttteoptv D 3

. 14. XWQIOIS] corr. ex jjoôtg C 2. 15. rjvSrjnors]

-v- supra scr. D 3. 16. ftaldcaris D. 19. e'] B, om. ACD.

ort yfi\ mg. sup. D.

MA0HMATIKH2 STFTAgEfiS A'. 17

fiovog 6vvrte6dri66iJiSVK ra tpcd,v6(iva xsgsi ii0rjv rov OVQKVOV xa&djtfQ xwroov Gyaioccg vito-

6rrj0ai[id'a. rovrov yao drj [irj ovr&g %ovrog fdsi,

ijrot, rov plv aôvog xrbg elvai rfjv yrjv, MCCXSQOV ds

rav noA&v foov aitfysw, $ sitl rov a%ovog ovdav agogrbv srsQov r&v jrdAcov naQax%G)Qr]xsvai, ty ^r inl

rov aôvog ivai ntfrs xaroov r&v itoA&v faov

agog y&v ovv rfjv itg&fYiv r&v roi&v &t6iv Xtvcc

on, t [iv lg rb avor}

rb narco rivcbv 10

oqd'ir], rovroig av 6v[i7ti7troi 7tl

6()d"fjg rrjg GycciQccg rb pqd&oirf faijfUQfav yCvs-

ig avitia 7tdvror dicugoviiwav vnb rov boi&vrog

rov r vitQ yv\v nol rov vnb yrjv, iitl $ rijg

yxx^vrjg rbirj py yivG&Gt.i naUv oAog farmeQfav 15

7) [if)v rr\ iittcfev Ttaoodo) rys * &Qi>vijg roonijs

xccl rr^g %i>[iQi,vrjg KVIG&V rcbv dta^rrjîdrcov rovrov %

yivoiiev&v dice rb \iYi%Xi rbv iGrmeQivov xal

rcov TtccQccMrjAcov r&v rotg 7t6Aoig ri\ 3tgi-

tpogag yociô^vcov xvxAcov 8i%oroyiZ6&ai vitb rov dot- 20

Jovrog, AA' f'va rcbv TtaQK^^cov avra xal ijroi

vori,a)rQa)v. cbkitoA(fy>t?Tca de y vitb

,ore ra dta6rtf[iara ravrcc faa rvy%dvt,

3. ^17] om. D. s%6vtos] corr. ex EÔVTOJS C 3. 4 sq. a,

(j, y, d mg. D 2. 9. ngmr^v] -co- e corr. D. 11. Traâxfâj-

Qr]Y.vLav C, -v del. C 2. vorj&fir]] -i- e corr. C 2

. 14. xat

yfjv~\ supra scr. D 3. 15. 6y*niJUfKri}0] -t- inter duas ras. D.

r|] supra scr. D 3. 16. T] om. D. 18. iGr)[tQiv6v'] -i-

ins. C. 19. T&V nccQccllriK(Qv'] om. D. Supra rav rots ras. D.

nolots] corr. ex TcoHHoig D. Supra TtsQifpoQ&g add. ccpKiQag D 3-

21. a-uto5] corr. ex ccvtoiJv D. 22. VOTLCOTBQCOV] corr. ex

V(OTKOTQ(OV C, 6X VOTIOTQ(OV D 3. ta/U-oA-OyTJTat] COIT. CX OfiO-

Aoysirai D 3. yg] om. D. 23. rvy%dviv D, -v eras.

Ptolemaeus, ed. Heiberg. *2

18 KAATAIOT UTOAEMAIOT

l)rat xccl tds Ttagd tqv i6r^LQiav av

jiiSQccg iv rats ftsQivaig tgoitalg L'6ag elvai

rats [ii'(b66i tcbv Aa%i6tG)v fipfQcov v rats

5 tw&v Ttdkiv rj rtccQccx&QrjGis vjroTÔ'fn?, xccl

av Gvpfiaivoi, to [iijt TK [t'y&r] xal tec

T&V aGrgov l'6a xccl ta avta xcctd rs rbv e&ov xal

tbv 6XQi,ov OQ%ovra <paCv<5&a,i îtjt rbv fat* avaro-

ti] p>%Qi> [i6ovQKvtf<30)s XQtivov faov djtOTffaZGd'ai,

10 rip djfb ii6ovQavtJ6(QS trii> dvtiiv, artQ tvaQyfbg navrd-

CCVtiKltttl tOiS CpKiVOyLBVOlS-

tfy dVtQCtV t&V &0G)V, Xa& 7JV 7tl

tOV CCÔVOS OV6K 3tQOS tOV tQOV t&V TtohcdV 7CCCQK-

X%G)Q'T)xvla vorj&iJ6tcct,) itdkiv av tig

15 si tovft' ovt&s stysv, Haft' f'xadtov av t&v

to tov dgt&vtos 7tiitdov avi6a diatpoQcss 7toii

jtdvtote to te vitfQ yrjv xal to vitb yijv tov ovgavovxat' ciMyv xal aA,A.r)v ttaoa%G)()r]6i,v xal

xal xgbs aMrjAa, itl plv iiowqs "*

20 8i%otoyiiv avtr^v dvvaptvov tov oQi&vtoS) iitl $ tils

ys rtoiovGrjs rov tyyvtfQov t&v xoh&v ddto plv v7tQ yv\v 7tdvtot iiiovvtos, to dt

V7tb yfiv avôvtos-) &6t 6v[if}awiv to xal tov did

[i6G)v tcbv ^Gjdi&v xvxkov psyiGtov

25 <5o)m vicb tov tov oQi&vtos titntsdov, 07tQ ov

1. rag itccQcc rrjv] TO. sit' uvrijv seq. lac. 8 9 litt. D,corr. D 3

. 2. ev reefs] in ras. D. 3. TKL$ (alt.)] r corr. ex i D 3.

13. Tro/tcov] -o- e corr. C. 15. sl%Ev~\ corr. ex i%s D 2. 16.

TOV] bis D, sed corr. diacp&oQcos A, y^>. diKcpogoos mg. A 2,

17. TF] om. D. yfjv (alt.)] y corr. ex r D. 18. natd D.

TtQog] -s e corr. C. 21, atft D. 22. 8s] S' D. 23. rov]corr. ex to C 3

.

MA0HMATIKHS 2TNTASE.QS A'. 19

ovrog %ov O'fopfnrat, | p,v del xal TtaGi (paivo-

pVG)v v7tQ yrjg dcofifxarrjiiogtoV) ds r&v Aoiitcbv

dcpav&v ovr&v, sir' av ituKiv XWG)v [ilv ohcov xara

TO avrb (pawoiiBv&v V7CQ yv\, r&v ds hoirt&v apcc (li)

(pcuvoiisvcov CDS dyAov rvy%&veiv, on xal ta rfiriîara 5

rov ,G)8iaKOv di%OTO[isZTcu vjtb rov b^Côvros sx rov

rcc avra fi[iixvxA.i,a oA# nors iiev VTISQ y^v, TCOTS dl

vnb y^v oatoA.aiipdveGd'cci,.

xal xa&oAov d' av 6vveflat,vV) sfasg ^r\ i)it

avrbv rov l6rîQivbv sl% ryv ftfaivfy yi} 5 legos 10

CCQXTOVg dfrj 7tQOS [L6r]llpQlKV (X7txA,lVV TtQOS tOV

STSQOV T&V jrdAov, TO [trpdri [tyd^ ngbc; afadytiw v

rats farjiiAQtais rag avarohixas r&v yvoîovov

rats dvrixatg in v&ias ytyvsGftai xara r&v

aMtjAwv t& oQi&vri, ^xut^dmv^ fiitSQ avrix^vg Jtavra^ 15

&G)Qirai TtaQaxohov&ovv. yavfgbv d' avr6&v, on,

rp> rgfayv r&v &6G)v oiov r 7tQO%a)Qtv xa-

v r&v v rats ngarais wavn&ndrcov yt'

Gvvshovrt, 6^' slitEiv 7ta6a av 6wy%v&ir] rdfaov 20

rag av%0[iiK>6is rcbv w%fh](iQG)v

fari V3toxi,[ivr]s rrjg yfig iira rov

rag ryg 6Arjvrig txtefyetg xara ndvra ra [iQr]

rov ovQavov TtQog ryv xara dtd^rôv r& ^Mc) 6ra6iv

dvvaG&ai, ryg yijg noMaxig pf} iv ratg 25

1. cthi D. 4. fatsQ 5. vpawoiisvmv] supra scr. D 3. 6.

(pSiccKov] -a- supra scr. D 3. 7. oAa] seq. ras. 1 litt. D.

11. AnEiiHivs D. 12. Post pride eras, xi D. 14. si)9sug\corr. ex ev&eicas D. ytvsG&cti D seq. ras. 4 litt. 15. Post TGJ

eras. 81 D. tmTtfdav] corr. ex snntidai D 3. 19. Gvpfirjoo-

fisvmv'] ante -o- ras. C. 20. *'] Ss D. avvxv&eiri C. 21.

rat-is] corr. ex S B 1 G*. ccvô(iLo>G8is AD, corr. A 2. 23. sv.-

-t- in ras. D. TO} om. D. 24. xara] om. D.

2*

dia[iTQOv6cci,s ttagod

V rots &dTTo6t, TOV

v koyov %!> itgbc; ra

ri yij.

xal 6rîiov loyov e%si

i\ yij agog to p%Qi> rv\ t&v catkav&v xahov-

6<pKiQtt<5 efordtfnâ, iieyct jilv rex^tjgiov TO

ocjtb TCKVXOV ccvrils tcbv psgcbv rd rs [isysfrri xal ra

dia6tyJiiKTcc r&v a0rQ(Dv xara tovg avrovs %QOVOVS10 face xcd o'ftota cpcctvsd&ai, jravraî}, xafrccrteg ai dnb

diayoQ&v xA,i[idTa)v 7tl r&v ccvrcov XYIQ^SLQ ovds

ro sA.K%i,6tov svyfaxovrcci, diacpcovovdat,. ov pr^v

AA xaxstvo nccQa^Ttreov TO TOVS yv&novas tovg sv

CpdtJTtOTS [ISQSt, TilS yilS TI&SIISVOVS, Ti d TK T&V XQl-

15 XG)TG)V 6(pCCl,QC()V XVTQK TO CLVTO dvvaG&at, T& XKTK

cdtfd'fiav Tils yflS XWTQO) xccl dia6&t>iv Tag 8i07tTv6is

KKL T&S T&V Gxi&v 3tQt,ayG)'yas OVT&S biioAoyovs Tats

V7fOd'06i T&V (p(UVOllVCOV) O)g &V i til KVTOV TOV

Tils yns pfaov tiypstov yivbpzvui Tvy%avov.

20 tvuQyss $ 6rj[ilov TOV rav-0-' OVTCOS %i>v xal TO

TOV OVQCCVOVj Q7tQ OVX CiV 6VVâtVV^ i TO

2. sUdzroaiv D. 3. g'] om. A CD. on 4.yfj'j

iov hoyov %r) f) yr) TCQOS tec OVQUVIU mg. sup. D. 7.

QLOV D. 11. wXrjftaToov A. 14. Hîxcor&v] corr. ex

rwv A 2D 3. 15. SvvuGai A. %ar' D. 17. rat's] t corr.

ex i D 3. 18. vTto&fGfGiv A. cpKivopsvojv] cp- in ras. D.

dt

21] 7) St,' D, xat Si' D 3

. rov] om. BC. 20. IvuQyaSs C.

. &] supra scr. D 3. 23. et] corr. ex sis D.

MA0HMATIKHS 2TNTAEE&2 A'. 21

rijg

povov

agog rr\v rcbv OVQCCVL&V

av rb diet rov Kara rb

dt,%orop,lv ,rd ds 6Y

KV

'. "On ov KivyGiv riva

n yn-

Kara, ra avra d rots k'yiTCQOG&w di%d")J6Tat,, diott,

iivrwovv nCvYiGiv fig ra TtQOEiQqiisva TtAdyicc 10

rfjv yv\v oi6v r Ttoitfti&ctiij 6'Acog nf&faTciG&Ki

7tox rov xarci ro ndvrQov roitov ra ccvra yap 6vv-

i xal rv &6t,v ftMrv Ttaa TO

KV rig Kal rijg 7tl TO [teGov cpoQ&g rag ccfaiag iici- 15

fyirr^0Lv a7tci% y TOV, on,ij

t y^ rov [i6ov sits^i

roTtov TOV xoGpov xal ra fidor] TCCCVTK irf avrriv

,, ovr&g ovrog wccyyovgJ

| avr&v r&v yaivo-

7tQO%iQora,rov av ig rty

yivoiro TO 6(pcu,ooi,dovg xccl 20

g rov itavros, &g k'cpatim, djtodfdfLy^svrjg ryg yijg

2. TO (alt.)] om. EC. 3. TTJS yfjs~] om. C. ffTjfm'ov] corr. exD. 4. fjcdrjTtorovv] corr. ex fjGTtorovv D 3

. 7.'

\

om. A CD. cm 8. y?)] mg. sup. D. 7. Ttoistrai, [iszcc-

patLHijv D. 10. rd] seq. ras. 1 litt. A. 12. HSVTQOV] corr.

ex vJs\r^ov A 2. ccv Gwifiawsv D. 14. epoi C. TtegiGaJs D.

15. qpopag] mut. in cpoQctig C 3. fjrt^Tjrrjffftv] mut. in im-

tw^Gtuv D 3;fort. ini^riTfiGKL. 16. TS

yfj~]e corr. D 3

. TOV]corr. ex TCOV A 2

. 18. ivagyovg] supra scr. D 3. cpcuvopk-

v(ov\ seq. ov D, corr. in cbv D 3. 19. /taxftvo] seq. ras. 1 litt. A.

de] supra scr. D 3. 20. yivoizo] corr. ex ysvoiro D 3

.

vs C, v del. C 2.

ev aitatiiv ebdrag rots iiQ0t>v avrr^g rag re

xal rag rcbv ftdgog fyovr&v cfo^drov cpogdg, A^yo ds

rag Idtag avr&v, Jtgbg ogfrag ycovtag Ttavrore xal

7tavra%fi ywEGftai ra did -rife Kara rv\v

5 itaq)ijg dixpaMoiiVG) axhvsl sitins'da)

rb TOV&' OVT&S %W'> on XKL, si ^ avxexomovro

vrtb trjg emcpaveias ri\s Y^-) ndvtG)<$ av Bit avrb rb

KBVtQOV XaWJVT&V, 7td Xttlfj

7Ci TO XVtQOV CCyOVffK

v&Za Jtgbs OQ&as ycoviag ad ywftai t& dt,a rijg

10 Kara TTJV iitatf^v roftijg cpartro[iVG) rr^g Gcpatgag iti-

0601 $ Ttagadofcov ofovrai rb îtjr fafiyxwai, TCOV

lirjr <pQ6ftai rb rrjhxovro fiagos rifc yijg, doxovGi

H,OL TtQog ra xa&' Zavrovg ita^r] xal ov 3i(*b$ rb rov

15 oAov i'diov djtoftt,3tovrs rty GvyKQiGiv jtoiovpwoi,

diaâQrdvELV. ov yag av ol[iai, davjiaGrbv avrolg k'rt,

<paviri rb roiovrov, i 7Ci0rtjâiv ,ort, rovro rb rijg

o/lw rc5 7tQid%ovrL G&iiari,

Ttabg avrb koyov %i' dvvarbv ydg ovro

20 d6î rb Kara koyov kd%iGrov VTtb rov

T xal

rov ,v xrco

1. n&civ D. ft^><jn>] corr. ex (ISQEGI D. IIQOGVKVG D,? D 3

. 2. d] ^7? D. 4. yt'yvfff-9-at BC. f^nrcoGLv]corr. ex ntwGiv D 3

. 5. Sisâôîsvcp] 8 corr. ex a D 3.

cbdtvT? BC. 6. TO] om. D. 7. Post yfjs add. at yogaCmg. BC (pro scholio). ctvrb TO] utrumque -d in ras. B. 8.

%fVrpoi>] -ov in ras. B, nivrgov at tpoQcci D. 10. roft^j] -g

add. D 3. sniTtedav A, sed v eras. 12. nccQaSo'ôv] doôv C,

mg. yQ. naQa.8o(ôv} C 2, Aoôv B. Btfafajiiiftti D, sed corr.

13. TTjZtxoiJTo] mut. in TqJiiKovrov D 3. 14. avrovg D. 16.

av] supra scr. D. ?rt] supra scr. D 3. 17. sf] corr. ex ij C 3

.

19. ovrco] e corr. D 3.

MA0HMATIKHS 2TNTAgE5i2 A'. 23

av(o prjdwbs ovrog iv r& xoGpG) agog avrtfv,

vds V GtpaiQa Tig CCV TO VOlOVtOV 7tiVOt]-

r&v d iv avr<p 6vyxot,îdro)v rb ocfov eitl rij

idCa xal Kara yvtiiv savr&v yoga rcbv pv xovcpcov

xal A,iiTOicdv ig rb %& xal cos o? rv iii- 5

$ r

rqv OQ^V TtoifZGd'at, di,a rb xal ndvrcov

rb VTtQ Ksyakris, avo $ xaAovpfvov xal avro,

vViv fog ngbs tt\v itQi,%ov6av 7tt,cpdvi,av, r&v $

flaQa)v xal xa%v[iQG)v 7tl rb p6ov xal ws ngbs rb 10

xswsgov <pQOtiVG)V) doxovvrov d LS rb xdro

dia rb xal Ttdvrcov Jtdfav rfticov rb ngbs rovs

xakov[ivov $ xdrO) xal avrb vViv ftgbs rb

rijs yils tiwtffttiiv T flxor&s 7tQl rb pfaov Aanfi

vnb rijs ngbs AAi?Aa 7tavra%6&v fays xal opotas 15

dvnxoitils T xal dvrQi6G)S' roiydgrot, xal' ixoro3s

xaraA,aiif}dvrat, rb oAov Gr^s&pa ri^s yfjs pfyiGrov

ovr&s ov C3Q XQOS Ta (pQo^va en avrqv xal vnb rr\

Ttdvv Eka%i6rG)v pag&v op/iifc ar dij 7tavra%6^vxal &îtQ ra ^v^Tciitrovra xd%o^vrj. si 20

da y xal avr^ f)v rt,s yoga xowr} xal pia xali\

avrr\ rots ahhois pdQ6iv, Zcp&avw av itdvra

did rr^v roGavrqv rov yLsyd&ovg vjtQ(loA,riv xara(f>Q

xal v7tteiitTO fiv Ta re (pa xal ra xard pfyos r&v

1. ^Q'svog D. ctvxr\v\ ccvrov D (corrigere uoluit D 8).

3. a-urw] CCVTOLS BC. avvKQifidtav A. td] ins. D 3. OGOV]

mut. in OGOJ D 3. snl TJJ ISCa] corr. ex snuijSsicci. D 3

,STIL

rr\ Stai C, 'iitl rfj tSiai C 3. '4. avt&v D. qpoâ] corr. ex

cpOQoct D 3. 5. TO] corr. ex rov D. cptgeiccv C. 6. &VCCQQI-

7tio[iEvcov A 2 C 2 D. 7. IxadTotg] con*, ex gjta<7T7js D 3- 13.

civto] corr. ex ccvr& C 3,avrb vsvs A, cavtb VZVEI, A 2

. 14. ts]corr. ex ye D 3

. 18. cpcciQ6[ievcc D, corr. D 3. 21. cpogd] ante

$ ras. 1 litt. C. 22. alois C.

ficiQ&v o%ovpva 7tl TOV efe'pog, avrfj de Ta%i6TK rsfaov

av xit7tTG)Xi, KOI ccvTOv TOV ovQcuvov.

{lev xccl povov siuvoq&evzK TCCCVTCCIV ccv

g y oi'ovTcu, iti&avG)TQov, TOVTOIS

ovx %ovtS) o, xi avri7Coiv, Gvyxcctccrtd'fvtcii,)

ovdv ccvTolg avxiiiciQ'tvQYiGeiv, t rbv {isv

ovQccvbv axivrjrov vnoGruJGccivro Aoyov %KQW, rfjv $

yv[v 7CQl TOV ccvrbv

10 lit avatoAas xa6Trjs

T)KCil (X[l(p6TQCC XLVOtV 060vdtJ7tOT^ [lOVOV

rbv avtbv ccôva, wg (paîv^ xal Gvjjip&Q&g rri agog

$ ccvrovg^ on, t&v [iv itgl ra

15 (pCClVO^lBVOV VXV OV$V CCV /'(?(0g XCoAvOl XKTtt}> TrjV

a7tA,ov6rQav 7tt,pohr]v toi>& ovrcog %w, eforo d r&v

yt()i fipag ccvrovg xal r&v v asgi GviMtrcotiKT&v xcul

Ttavv av yÔLOTarov dcp&fLr] TO TOIOVTOV. LVCC

^vyic3QYi6o^v avTolg TO naga q>v6iv omog to,

20 A7tTO[lQ6TaTCC XCil XOV(p6TKTtt ij ^d' oAo?g XWi<5%'Ki t)

adiag)6Q(og Toig Tijg wavTiag (pv6cog T&V y nQl TOV

(XQa xal tfTTov A,rtTO[ii,$G)v wccQycbg ovTcog Tcc%vTQagTG)V yG)d6TQa)V ItdvTGZV (fOQag 3tOLOV^VG)V^ TK $

3. snivori&ivtu] corr. ex snovori&svTcov D. 5. y'] om. A.

6. GvvKaraTi&svrciL D. 7. avroig ovdtv D. zbv (isv] corr.

ex (isv rov D 3. 9. rov] bis C. 10. in''} sni D. ntgi-

crQocprjv] -otpijv in ras. D. 12. GvpsrQcos D, corr. D 3. 13.

nsQinarulri'tyBi] post -r\- ras. 1 litt. D. 14. MJ.rj&ev BCD.avrovs] -s add. D 3

. 15. ovSsv] corr. ex ovSs C 2,ov&tv D.

ncohvoi] H- corr. ex K in scrib. D. 17. TCSQI] nsgi rs D.rcbv sv CCSQI] A, rbv CCEQCC BCD. 18. ccv] corr. ex c:y C 3

,

om. D. 20. (ir]d'] -73- e corr. D. 21. adiucpoQcoc;] corr.

ex tftafooog C 2D 3. f corr. ex rs D 3

.

MA0HMATIKHS ZTNTASE&S A . 25

xal (layvrara Kivritiiv idiccv o%iav

ovr&g xal oîa^v TtoistG&ai, rcov yead&v ndfav 6fio-

e JtQos rfjv vn dM&v xivrjtiiv sm-

sviors %6vr&v, dW ovv bpokoyriGKisv av

rqv tfrpogp^v rijg <yrjg yiyvsG&oLi KitKG&v 5

anlag r&v Ttsgl avryv xivrjGecw cog av ToGamyv ev

av ra pvi pspyxora Bit avrils yiiccv asl rqv svccvtiav

ty yri xivrjGw zyaivsto Jtoiovîsvcc^ xccl ovr' av vscpog

note edetxvvro Ttagodsvov TCQQ/S avaroAas ovrs aAAo 10

n rtbv LTtTaîsvcov tj ftccôîVG)v (pftavov6ri ael Ttdvra

nod 7tQoââvov6^s r^v 7tQO<s dvarohccs

)&6ts rd AoiTtd jcdvra et$ rd 7tQO$ dv6[ids xal

si y&Q nai xov atQK cpijtiaisv avrf} GvyLitsQidysd&ai 15

xard rd avrd KOI l6ora%&g^ ovdsv forov ra xar

avrbv yivopsva (jwyxQijiara Jtdvrors dv sdoxst rv\

6vvan(potEQG)v xiviJGs&g v7toA.L7t6d-ai,) rj i'jt() xal

avrd co6XQ f}vco[iva rc5 aQi 6vyL7tQiriyro, ovxr

av ovdrQov ovrs TCgo^yov^Bva ovrs vnohsinonsva 20

syoiivsro, psvovra $ dsl xal ntfrs sv ratg itx^sîv

v ratg (tohatg itoiovyisvd nva it\(ivrp> r) (j,rd-

1. ncc%v[iQ6t<xTa] -at- e corr. A 2. Q&LCCV] post 6- ras.

1 litt. A. 2. r&v] -v supra scr. D 3. ytood&v] -d- corr.

ex "k D 3. 5. yiyveG&cii xj]g yfi$ B. yivEGfi'cti D. 6. ccvrriv\

-77- in ras. D 3. 8. sW D. <m'] supra ras. scr. D 3

. TTJ'V] r-

.e corr. D 3

. 9. ovr'] ofcs seq. ras. 1 litt. D. 11. T) (3aHo-

j^fvcov] supra scr. D 3. 12. TtQoHafipccvovGrjs] post -o- ras. 1

litt. B; 7tQOG).cc[ifiavovG7]g C, sed -G- del. C 2. 13. stg\ si's rf D.

17. yevoiitva D. 19. av/Li7rf(irjyTo] -r\- ins. C 2. 20. ovSt-

TfQov] ovdrfQK A 1

,mut. in ovd&eQct D 3

. 21. <J] d' D.

nrriGfGiv] irtrJGSGi B, cpogccis D, ôlaig D 3. Deinde ins. ftTjrf

v rarg cpOQuis mg. BC (pro scholio). 22. ôâr?] mr^GBGi D.

7t\a.vi]v\ ABCD, mg. yp. TraâA^wyrjv C 2.


,ayieo aTtavra ovrog tvaQycbg oo&îev dxorekov-

p,eva cog nyde poadvrriTog nvog oh&g rj ra%vri]rog

avrotg KTtQ tov pri etirdvai rqv yv\v

rj

f

. "On dvo diayogal rcbv nocarav

5 si0iv ev ro5 OVQCCVG).

Tavrccs [iev dfj rag vitod'6i,$ avayxai&s

sis tag xara peôs XKQccdfaeis xai ra$

dxohov&ovGac; ayxsctsi, xccl ^B%Î rcbv rotiov-

tcov ess sv xecpcdafois vnoTsrvTCcbGd'ai, ^sâicod'rjô^svKS

10 re xccl ETtinccQTVQrj&rjGoiievag rsfoov e% avtijs r^g r&v

axohov&(o$ xal scps^rjg ci7todi%d"ri6o[ievG)v TCQOS ra

cpai,v6[isva ^v^fpcoviag. XQOS ds rovroig f'fi xaxstvo

r&v xa&oXov n av Yiyritiawo dixatas ytôâftslv^ on,

dvo dittyooal r&v itQ&x&v xwtJGsav sitiiv ev rc5

1.5 ovQctvK), IILK per vy i\s (pegexai JCCCVTCC ano dvccroh&v

del aGavrcog xal i6ora%cbg jtoiov[ievrjg rfjv

xara nccQccMrjk&v dMtfAoig xvxA&v t&v

rotg ravrrjg rijg xdvra diicd&g

jrdAotg, d>v 6 pfyitixos xvxfog

20 farmeQivbg xcdelrcu dia TO povov avrbv VTCO peyidtov

ovrog TOV bat&vrog Siya jtdvrore dicuaeiG&Ki, xai rrjv

xar' avrbv yiyvQîvr^v rov fyCov iteoi,6Tao(priv farjueoiav

Ttobg afofrrjO'iv navra%ov noielv, rjde ereaa, xa& ty

4. rj'] om. A CD. on 5. OVQCCVW] mg. sup. D. 5. slew]supra scr. D 3

. 6. TtgoGkapflavofisvas D, sed corr. 8. &Q-corr. ex CCQ-H^GI, C 3

. 9. sv~\ sy C. vTtOTSTvnoG&cti C.

C. 10. re] om. D. 13. fjyrjGairo] -i-

ins. D. nQokcifiBiv] TO rtQokcefisiv D. 15. ftta] seq. ras. 1

litt. C. 16. Ante ini ras. 3 litt. D. 18. T7)g] -$ e corr. D.

19. Tro/lotg] corr. ex Tro/Uoig D. 22. yivopsvriv CD. 23.

7tccvra%fi D. ^] corr. ex at D 3.

MA0HMATTKH2 STNTAEE&S A'.

KI TG>V a6rQG)v 6<palQKi xccra ta

[ivrj (poga TtQiQvvtai nvccg tiTctxt,vrJ6i,g itsgl itohovg

xccl ov rovg ccvtovs tots Trig yfQOJttjg nsQicc-

xccl rccvrcc ds ovrcog EJJBIV fator&fys&cc dia

rb K pv rils wen \*>iuv sxccGrrjv qpSQav O-fo^tag 5

jtdvta djccdzaitAcbs t& iv r& ovgavti Kara r&v dfioei,-

d&v Kol jtKQa^^cav r& farftiSQwa) KVK^G) toncw

itgbs afa%"ri6w bg&G&Ki 7toiov[ivcc rag rs

KCil T<XS [isGovQccvriGsis xod t&S dvGsis idfov ovros

rotovrov rr^g ttQarys fpoQccg^ sx $ Tijg tystfig KOI 10

[lV ttMcC TCCCVTCC

KOI to,

xal tec TtQog roi>s oinsiovg r

xoitovg 7tl Ttheitirov td^coftara, xbv df ijhov xal tqvKeel TOVS JthavoiiEvovs aGtEQKS [lErccfidGEig 15

jtoiEZG&cct, Jtoixttag pw xccl

& &g ngbs ity xcc&ohov xivrjGw els ra

avccrohag xal vjto^L7to^Lvcc {JLEQV} t&v

aAAÂa diKOttjîara xccl &6itQ VTtb

ttQl>tt'yOllVG)V CCtfTQCOV. 20

ovv xccli\ Toiavrrj [lErdfiaGis r&v

xara itKQaînôv xvxA&v Eyivsto tat

TtEQi Ttohovs rovs inv ^g^nv

avrccQXES ccv EyCvEro \Liav %\yEl6ft&.i xal

2. noKovq] corr. ex noMovg D, ut saepius. 3.

-rov- e corr. D. 4. ds~\ d' D. Sid] -d e corr. D. 6. 6(io-

Lda>v] -et- in ras. post ras. 2 litt. A, opoiosid&v D. 7. xvxiw]om. D, comp. BD 3

,del. B 2

. roitoov] -v euan. D. 9. tSiov]corr. ex IStovc D. Idfov ovros] corr. ex tdiovvtos C 3

, mg.ovxog. 12. (paivetcct, D. 18. avvrriQOvvTcov] pr. T ins. D 3

,

post rjras. 2 litt. 19. aUâ] e corr. A. 20. CCGTSQCOV D.

21.17] supra scr. B 3C 3

. nlavo^vcov D. 22. xara] corr.

ex xal rcc BC 3. iy^vsro C, corr. C 3

.

rr)v avrrjv Ttdvr&v Tteoiyoodv axokov&ov rrj

m&avbv yap av ovrcog ecpdvrj Kal rb rr]v

avr&v nerdfiaGiv Ka& vnohefyeig diacpdoovg Kal

Kara dvri,KeL[ievr]v KivrjGLv ditorekeiG&ai. vvv de

5 ratg xgbg rag dvarohag [lerapddsGi

del yawovrai, 7tQ6s * agxrovg xal

ScoQOvîsvov rov iisy&ovs rr]s roiavrys

&6re doâu di ^cod'^scov nv&v rovro

rb 6vii7trG)[ia yiyvsti&aL itSQi avrovg, akX avo^dôv10 [lev &$ agog rqv roiavryv vitovoiav

, rEraypevys ds

&S bxb xvxhov Aolov JtQbg rbv far][iQi,vbv dnorshov-

fiEvrjg' o&v Kal 6 roiovrog xvxhog sig re xal 6 avrbg

xal r&v 3tAavG)ii8VG)v i'diog xaraAajjipdvsrai, aKQifiov-

psvog ply Kal cbtiiteQ yQaydpsvog vnb rrjg rov i\Uov

15 Kivri6G3$) TtSQiodsvopevog ds Kal vito re rrjg <5ehi]VYjg

Kal r&v nAavcoiiev&v itdvrore itegl avtbv dvatirge-

q>o[ievG)v Kal [irjde Kara rb rw%bv eKTUJtrovrcov rrjg

djtore[ivo[ievr]g avrov Ka& sKaorov etp' eKdreQa ra

pegr] jtaQaxcdQiJGe&g. enel de Kal [leyiGrog ovrog 6

20 KVKhog fteogetrat, did rb rc5 fccp Kal (toQeioregov Kal

voncSregov rov faypeQivov yiyveti&ai rbv rjfaov, Kal

jteol eva Kal rbv avr6v^ fog etpapev., aC r&v Tthavco-

lievcov Jtdvrcov xobg rag dvaroAdg iierafiddeig dito-

reAovvrat,, devreoav ravrrjv diayogav rrjg Ka&6Aov

25 KLvrjGe&g dvayKaiov i]v v7tQ6rr\<5a6&ai rr)v iteol nohovg

2. OVTCOS] corr. ex ovzco D 3. fcpavrji, A. 4. %ar' D.

anorsifiG&aL] -n- e corr. C 3, post n ras. 1 litt. A. 5. tag]

om. CD. (iETKcc686L D. 7. oficdov] post a ras. 1 litt. A.

8. &jco<ibj(yoov] ôQ"tJG(ov C, post -f- ras. 1 litt. D. 9. ytW-0-9-at CD. 10. to'] d' D. 15. T] om. BC. 20. xw fato]

corr. ex rb i'aov C 3. 21. yfofcd'ai D. 22. nicer ofievcov CD.

25. mvr)6(os~\ -c- corr. ex "k in scrib. D.

MA0HMATIKHS ZTNTASE&S A'. 29

xov xaxt,hr}H[ivov Aojov xvxhov xal sis t& IVKVXLK

av drj voôîev xov dice xcbv 3t6A,&v d[icpoxQG)V

XG)V 1tQOLQr]llVG)V XVX&G)V yQCCgJO^LSVOV llfyltiXOV

xvxA.oV) os f| dvdyxys xdxQov sxsiv&v, xovxfaxw xov 5

re far]iiQt,vbv Kal xbv JCQOS avrbv eyxexfaiisvov ,

TS xccl XQOS OQ&as y&viccs vspvzi,, ttGGuQa plv

Gr][ilcc xov Aoôi) xvxhov, dvo plr xa VTCO xov

xccxa did{iXQOv dMrj&ois yivoyiev

Qivd) G)V xb [iv KTtb [i6rj[jif$Qias ngbs ayxxovg 10

k'%ov xqv nccQodov saQivbv kiytxai, xb $ IVCCVXLOV

yLxortG)QLv6v',dvo d x& yivopwa vitb xov di a[i(po-

XQG)V XfbV JtoAcdV yQCC(pO}lVOV XVX&OV,

XCCl CCVXK 6^-

Aovdrt xccxa didjjifXQOV aAA^'Aotg, xaA,ov[ivcc d xgoTtixd^

G>V xb tiv Kitb p&cttfli$QfaQ xov foffli(>tvov lEiyLEQwby 15

xb d ait' CCQXXCW &Qivov.

i\ ^lv pta xccl TCQCSXITJ <poga xccl

3tQl%OV6CC X&S CtMaS JtddCCS 3tQl'yQCCCpOllVTq XCCl

XOV dl d^l(pOXQ(DV XCbV 3t6A,G)

xvxhov 7tQiayoîvov x xccl xa 20

a rtdvxa 6v[i7tQi,d'yovxos ditb dvaxoh&v itl

itsgl xovg xov forjpfftvov nohovs fepqxoxas7tl xov xahoviivov iisGripfiQivov, bs XOVXG) povG) xov

2. yogas] corr. ex niv . . . D. anoTJiov[ivr}v] corr. ex

ccnorelovfisvcov D 3. 5. Ante xvjdov eras, xv D. endrsgov]

-o- in ras. D 3. 7. reaoccQo] corr. ex rscasgcc D 3

. 12. ysvo-D. apoTcov -tov e corr. D. 13.

, -yiGTOv in ras., D. xat 20. xvxAov] mg. D 3

in textu supra scr. tefasi. 21. GwrcfQidyovros AC. sni]els D. 22. fop^-KOTocs] BCD, mut. in ^f^xora A, in

P^TJ-xorog B 3

. 23. pfGriiipQwov, og] corr. ex fifGr](iQivovs C. os]in ras. B 3

;corr. ex tog D, ut saepius. TOVTOJ] rov- e corr. B 3

.

naoi,ar}iivov diatpto&v rcli pf} xal dia rcbv rov

KVK&OV rt62.o)v jtdvrorf yodcpfG&ai, tn xal did rb nobg

ycoviag rco bgitpvri, 6vv%cbg voslG&ai, Katelrai

roiavrr) &6is xdroov r6 rs

5 V3to yv\v KOI rb vitb

Xttl T&V VV%Q"YULQG)V TOVg [l00VS %QOVOVS

3tQl%OHVr] [lV VJtO

a$ t&v

vxb r

10 <pa[iv, ttvti'jitQia'yoyisvri dl fig ra ivavtia 7tQ\

rov Aoov xvxhov jrdAovg, 01 xal avrol fofirjxoTfs adKara rov rqv XQ&rrjv itfoiyoafpriv Ttoiovvrog

rovrfart, rov dt' dfig)orO(ov r&v jrdAcov,

r fixdr&s 6vv avra) xal xara rr^v i$ ra evavria

15 dvroas <pooas Kivr{6iv r^v avr^v &&6W a\rov yoa<poivov <Si' avrr Lsfarov xal

rov

rcbv Kara

'H ply ovv

20 roiavryv av %oi ri\v K&6iv rcbv oyfMvr&v noovno-

aQ%6&ai rcbv Kara [ifyos dxo-

v7tdQ%iv fiyov^&a, Si jjg ^

1. diacpSQcov rov itqoiQr}yivov D. rw] corr. ex x&v C,

supra scr. D 3. ta>v\ corr. ex TO D 3

. 2. n6l(ov~] supra scr. D 3.

4. rffjin ras. D 3

. 5. yfjv (alt.)] y corr. ex r D 3. 6. vv^j]-

us'^cov] --91- ins. D 3

. %Qovovg] %QOV- e corr. D. 7. nsgi-

%o[ievrf\ fj 7tQi%oiJivr} D. 9. gjf^oju/fVrj] seq. ras. 1 litt. D.Ante cog ras. 34 litt. C. 10. Ss et$\ corr. ex (isv C. TOVS]

corr. ex TT)S C 3. 13. x&v] corr. ex xov C 2

. 14. ri\ seq.ras. 1 litt. D. 15. cttst I). GVVTJIQOVGIV] GWTriQOvGiv 01

noioi A. 16. avr&v D. 18. #'] om;ACD. 19. ngo-

didlr}tl>i$~] corr. ex TtQOGSid^fii^LS D. iv\ y C. 22. ^]corr. ex ot C 3

.

MA0HMATIKH2 2TNTASE&S A'. 31

r&v TtQoeiQriiLsvGdv jrcUoov rtSQHpSQeicc rov i

ccvr&v ygacpoiisvov iisyfarov xvxhov ityMxr] rig ov6a

rvy%dvi, xcctahcc[ifldvTai,) dvayxatov OQ&jiev Ttgofx-

rrjv ngay'pax siccv rr\ 7tr]A.ix6rr]Tog v&v iv rco

i. Tlsgl r^g TtrjAixoTyros r&v sv r& uv

sv&si&v.

ovv rv\v % EXOLÔV %9n0iv xavovixijv

nvcc psta ravrcc x&6iv itoiytio^d'cc xi\<s ytrj^xor^Tos 10

v 3tQi[iTQOv fig t

d rag vitb tag xccd''

t&V

lv rîrj^drcov &s rf}s diccîBtQOv dia r e

avr&v r&v 7Ciôyt,6^G)v cpavrj6o[ivov v rolg aQi&[iotg 15

tg QX Tfitjîara foyJQrjpivrjg. Ttgorsgov ds

nag av cag evi [idhdTa dt' oUyav xal r&v

ccvt&v &&Qrni&tG)v vn&6dvrov xal

STiipokriv ri]v xgbg rag m^^Lxdrr^rag ccvr&v

ojtcog ^ povov xr^Lîvcc ra /Ltfye'O1

^ t&v v&icbv 20

1. fifra|v] in ras. D 3. 2. ftsyi'tfrov] supra scr. D 3

. m\--TJ e corr. C 3

. 3. rvy^dvsi] om. A. 5. a?ra|] -n- e

corr. C. yf] corr. ex TS D 3. jLtfUTjcov-rsg] -a- e corr. C 3

,

CD.jnut. in iieUrjGcivTfs B 3D 3. 7. t'] om. A CD. rfjs

off] om. D. TW] om. D. 8. sv&fi&v] fv&si&v v.a.1 SK-

Ka.voviY.ri D. 12. ra$ vnb rds] scripsi, tag ABCD. l

f]p>i>-

v D. nKQccvâsig] mut. in TtccQccv^Giv D 3. Deinde

add. xal rag B 3. 13. vnorBivo^vu?] corr. ex vnonvo^vccs A.

rovrectLv C, comp. B. 14. noGO)v\ OGCOV BC. slai D,

comp. B. 17. fta/Uffra] -i- et -T- e corr. D 3. 18.

SEVTOV] -fi- et -^=- e corr. D 8. 19. rr]v\ om. D.

-a? in ras. D. 20. oncos] -it- in ras. D 3.

tG)S) AA xccl dice

odixi avrcbv 6v6tcc6G)g tbv

t&v

tG)V

v ecpodoig Kara rbv tij$ Qyxovtddos tgoitov

5 diet to 8v6%Qri<5tov t&v [lOQicuSiicbv ti t rolg

xal nQi,6[ioig axoAovd"tj(5oiiv rov

ccsl xata6ro%a6[ivoi,) xccl xa& o<5ov civ to

tov yt^bg

10 "EtitG) dr\ TtQ&tov fiiiixvxfaov to ART ml

tQOV t^g AAT 7tQl XVtQOV tO Z/, XCCl .KttQ tOV

tfj AT Ttoog oo&ccg ycoviccg

BV

YIAT xata to E^ xal

15 Ttt,V%&G} TI EB, Kttl XL0d"G)

avtfj l'6rj TI EZ, xal ETt^v^G) ^fjZB. A.y(O) ott,

TI pv Zz/

dfxay&vov ftitlv

dlBZ20 V&Zci

Kata to E, xal 7tQO<5Xi,ta tig avtfi t

,tb V710 t&V FZ XCCl Zz/ 3tOl%6[lVOV

1. Ij^oofifv] %oo- e corr. C 3. t&v} t- e corr. D. 3.

] lHftCt%lQl6ll%'K B, COrT. in [LSTCC%lQioilld'Cl D 3.

Zgriaope&'a] corr. ex j^TjacbfisO'a: C 2. 5. STL] post e- ras. 1

litt. D. re] r- ins. D 3. 8. SLCC^QSL C. 10. 8j] eras. D.

11. AJT] e corr. D. ^(pr.)] corr. ex A D 3. 13. dufc&a D.

15. &reev# >

a> rj]mut. in ini&vi&tiGriis rfjs B 3

; tTtt&vx&siGrjs

r^g, -si- e corr., D. xca] om. D, eras. B. 16. avx^\ u>v\ttvxfn. A,corr. in ravrrjt C 3

. xat 17. ZB] supra scr. D 2. 16.

corr. ex m&v%Q'cQ C 2. 17. ZB] Z in ras. A.

seq. ras. 1 litt. A. 17]in ras. D 3

. 18. dwaymvov]e corr. D 3

. 19. EZ] B- in ras. BC 3,ZE D. 21. E] seq.

ras. 1 litt. C. 22. FZ] F in ras. D 8. o^otycbvtov A.

MA0HMATIKHS STNTASESS A'. 33

VLOV {isra rov ajtb rijg Ed TETQaycnvov i'6ov

TG) ano rijg EZ rerâyava) [Eucl. II, 6], TOVTSGTIV

t& aitb Tijg BE, fasl fay 0rlv % EB T% ZE. dUaT& ebro Tijg EB tsryaycovG) face i<5xl ret aitb r&v

E4 xal 4B TSTQaycova [Euel. 1,47]' TO ago. VTtb rCbv 5

JTZ xal Zz/ 7CQie%6^svov oQ&o'yawov pera rov

tfi /IE rsTQayavov foov ttixiv rotg CCTCO t&v

4B TSTQay&vois. xccl xowov oupcuQS&svrog rov aitb

rijs EJ rergccyavov Aoinbv TO vno r&v FZ xal Zz/

faov i<5tlv TK> aitb Trig z/5, rovrsGriv T& aito rijg 10

jATf)ZF ago, &KQOV xccl pzGov Aoyov rsr^rai, xara

TO z/ [Eucl. VI def. 3]. licel ovv % rov Qayavov xal

$1 rov dsxay&vov nkevQa r&v slg rov avrbv xvxkov

fyyQacpoîsvov Inl rr\g avrfjg sv&stag axoov xal [istiov

Myov TfyvovTai [Eucl. XIII7 9], ij

ds FJ sx rov 15

XZVTQOV ov6a rr^v rov sfcay&vov xeQi,8%i nkevQav

[Eucl. IV, 15 coroll.], % JZ aga 6rlv fay ry rov

dexaytivov itfavga. bîoicog de, eitsl ^ TOV TtevTaya)-

vov TckzvQa dvvarai, rr^v rs TOV sâycbvov xal ri\v rov

dsxay&vov r&v sig TOV avrbv xvxhov syyâcpo^svov 20

[Eucl. XIII, 10], rov ds B4Z ooftoycoviov TO anb

1. (Ltsra rov &-] in ras. C. EJ] 4E D. SGTIV] iozi B,om. D. 2. TOO Tovrf'trrtv] ins. B 3

,om. C. rovrsGri B.

3. TW] corr. ex TO C 3. ITISL] mut. in snsiSijnsQ D 3

. 19 EB]supra scr. D 3

. 4. TW] corr. ex TO C 3. ZGTLV D. TO] corr.

ex TO C 3. 5. TfTQccycovct] comp. supra scr. D 3

. 7. z/E]Ed D. sGxi B. 8. JB~] noil JB D. xvcQuywvoi,<s. xat]supra scr. D 3

. 9. TSTgaymvov] ins. D 3. TO] seq. ras. 1

litt. D. vno] v- e corr. D 3. r&v] corr. ex r& C. Zzf| Z

ins;C.

?

10. Tw(pr.)] corr. ex TO B 2 C 3 11. ZF] corr. ex ZI C 3.

O.QCC] &QCC fv&ffa D. 12. ^] z/. V.KI IGIIV TO [iiov TfifjfJia

TO 4T D. ^J supra scr. A 2,ins. B 3

. 13. elg] e corr. C 2,

corr. ex iv. B 2. 14. yyQ<xcpo[iva>v] pr. y supra scr. A 2

. 17.

i'cri EGTLV D.

Ptolemaeus, ed. Heiberg. 3

BZ rerodycovov fcov i&r\v rip re anb rrjg

ijris etirlv eâycbvov ntevQK, xal red ccnb rrjs

[Eucl. I7 47], iJTis e6rlv dexcry&vov Tttevgd, j]

BZagcc fay etirlv rfj rov nevrayavov TtAevoa.

5 Inel ovv, fog Etpyv, vitori&e[ied'a ri)v rov xvxkov

didperaov r^îdrov (w, yiverai 8ia ra

ftfi/ JE riyLfasia. ov6a rijg ex rov KBVXQOV

A xal rb an' avrfig % % de BJ ex rov xevraov ov6a

rpyiJidrcov | xctl rb cutb avrfjs y%, rb de anb r^g EB,10 rovreGnv rb anb rijs EZ, r&v enl rb ccvrb ficp' prjxet,

aacc etirccirjEZ riirjpdr&v % d Ise eyyidrcc, xal Aomf]

ijz/Z r&v ccvr&v AJ d ve. y aoa rov dexccyavov

vitoreiVovGcc de xeoKpeoeiav roiovr&v AST, ot'ov

6 xvxAos r%, roiovr&v etirai AJ d ve^ oicov ^15 diaperyog lyx. ita'kiv eitel pey z/Z r^rjîdrcov e&rl

AJ d ~ve, rb de Kitb Kvri\g proe d If, eGrt, de xal rb

anb rijs 4B r&v avrcbv y%, a Gvvre&evrcc noiel rb

anb ri}s BZ rerodyavov fiôe d If, prjxet, ccoa

1. foov] supra scr. D 3. 2. âycovov ntevQa] in ras. A,

3. sW B. 4. for] icTiv D. TOV] supra scr. D 3. 5. fW]

inc. fol. 15 alia manu D.I'qprjv] mut. in scpcciiev B 3

,sed

euan. 8. &n'] ano B. BJ] J P, A in ras., C 3. OVGCC]

om.D. 9. <bro(pr.)] A, an BCD. 10. EZ] corr. ex E D.11. ma] A, l<nv BCD.

?j] ins. C 3. EZ] corr. ex ESJ D.

Post fyytdro: add. / C, mg. (pro scholio): '/ $6ri ds noif)

4E A,''. 12. ^Z] corr. ex z/S D. 13. TOIOVTCOV] -a>v e

corr. C. orcov] -to- corr. ex o C 3. 14. TOWVTCOV] corr. ex

roiovTOV C 3. I'ffrat] conip. B, omnibus litteris mg. B 2

;simi-

liter saepius; seq. ras. D. d] ins. D 3. ol'wv~\ corr. ex otov C 3

.

15. SidfjLerQos] ante p ras. 1 litt. A. ndliiv 16. Vs~\ BD,mg. A 3

(xElfievoy) et pro scholio C. 15. fast] ds ind A 3.

serf] IGTIV D, comp. BC. 16. ccno] an D. if] inter t

et s ras. A, mg. yp. xiF A 2, supra c scr. # B 2

. ^CTtv D. 17.

4B] BJ D. TWJ/] corr. ex TW A 2. tVMf^wa] alt. v supra

scr. D 3. 18. BZ] supra Z ras. D. If] supra e scr. tf B 2

,

in ras. D. Supra fiTy/tft ras. D.

MA0HMATIKHS STNTAjEjE&S A'. 35

fjBZ rprjiadrcov o~ A/3 y fyyitira. xal

r\rov itsvra-

yCOVOV aoa ItkeVQK, V7COrlVOV0a ds [lOlQag Oj3, OICOV

i6x\v 6 xvxhog T|, roiovrcav 6rlv o A/3 y, otoi/17

did[iroog (W' cpavfobv ds avr6d"sv, on xalr\

rov

thevQa, vitorsivovda d poioac; |, ^tftfiy 5

roi) xevroov r^rjîKrcov stfrlv |. oîoicog

fti/ TOV TSTQccyavov TttevQK, vitorstvovGa

ds poiQccs 9, 8vvK[iei, diithccGLa edrlv rrjs & rov

xevrgov, % ds rov roiy&vov ntevocc, vitoreCvovtiu de

[loioas ^jc, dvvd[it, rrjs avrifc fanv rQnthatifaV) rb 10

ds outb rrjg IK rov xevrgov rprjfUxTtov 6rlv j

6srca rb psv ccnb rr^Q rov rsroccycovova

rb $ alto ri]g rov rgiy&vov Mw. codrs xal

ply rag 9 poiQag vitoreCvov6a sv&slcc roiovrcw

3rd va I iyyitircc, oi&v $ di,d[isrQog ^3c, fjds r&g ~QX 15

r&v avr&v ~gy ve wy.

aids [isv ovr&g J][LIV sx 7too%iQov xal xa&' avrag

sttri<pd'C()6av.lxal 6rai, cpavfobv svrsv&sv, on, r&v

didoyiVG)v sv&fi&v | v%oovg didovrai xal ai vytb

rag 2,iitov6ag eig rb fj[juxvxAiov itSQicpfOfiag vitorsi- 20

1. o A|3J ol|3

C. 2. o|3] supra rasuram D 3. 4. to'] ^s

xat D. xat] om. D. 5. [taigas] n AB, ut saepe; [tD semper

fere. 8. [taigas'] ft ABC, ft D. 9uf3Laelcc] mut. in dmlaGicovB 8

,8inlK6ia>v D. 9. TOV] TO LGontevgov D. 12. roi)] om. D.

13. d^] d' D. TOW] om. D. rgiymvov] rgi- in ras. D.

M] C, corr. ex MAB 2, jt corr. ex

ft- post ras. 7 litt. D 3;

a'eo

add. mg. C 3. 15. fyytora] -ffra add. D 3

. 17. Post pe'i; add.

ovv comp. C 2. 18. Ante Y.CCL ras. 4 litt. D. carat] corr. ex

(m D 3,

mut. in fWco B 2. ^vrcDêv] avto&tv, supra auro-

ras., D. r&v 8i8o^v(ov] Si8oy.v(ov r&v edd.; sed genetiuusreconditiore quodam modo a Hfinovoas TtsgiysQeias pendet.

19. af] supra scr. B 2 C 2.

36 KAATAIOT 11TOAEMAIOT

vov6ai did TO TO. an* avT&v 6vvTLd~^va itoiiv TO

dnb Tils diayiETQOV TfTgdy&vov olov, %id^ f]{)7tb

Tag AS: [loigag v&ia T{ir][idTG)v fdffy&r] Af d v xal

TO dri* avTfjs aTO dZ*f,

TO $ dnb Tfjta

5 T[ir]iidTG)v 6Tlv Mydv, 6Tai xal TO ^iV dito

TCCQ foiitovdas iS to YULIXVX"a

TKIV koiTt&v Myxd v ^i, avTri dl[IYJXEI, TCOV

avt&v Qid Af fyyiGTcC) xal itl T&V cckk&v oftoto^.

OV $ TQ07COV CUtO TOVTG3V Xttl CCi AoiJtCll T&V XCiTK

10 llQO$ dofrtflSOVTCil,, dl%OllV Cp%iiS 7tQOXd'[lV

IICCTLOV fVXQqGTOV ttdw JtQOS tV\V TtCiQOVtiaV

TV%OV TO ABT/1, xal 7t^v^G)6av KL AT xal

15 8iXTOV, OTL TO VTtO T&V AT XCil B4OQ&O'yajviov i'Gov Ifal 6vvct[i<poT()oi,s TK> T vitb xCbv

AB, 4F xal T<p vnb T&V Ad, BF. xffa&o yag TTJ

vitb T&V 4BF y&via l6r\ % vnb ABE. lav ovv XOIVYJV

TtQoG&Gbiiw xty bitb EB4, <5Tai xal % vito AB420 y&via fay TT} V7tb EBF. 6Tiv dl xal % vnb B4A

2. olov] corr. ex otcov B SC. 4. is] supra s scr. S B 2

. 5.

JVf] corr. ex ft A, IIVQL e corr. D 3. 6. /notices] ft mut. in ft A 2

.

a od1. M] corr. ex ft A 2

, ftv^t e corr. D 3. j] corr. ex d D 3

.

jiff] supra scr. s B 2. 8. /l] supra scr. g B 2

. 9. Jioiicat]

-01- e corr. C 2. r&v~\ om. B. 11. navv] om. B. 13. Mg.

ZT^/LUX BC. 14. -cv%6v\ om. D. AP~\ corr. ex AEP D.

15. deiKTSov --Bdi\ supra scr. D 3

. ort] ovv on D 3.

16. TC^ corr. ex TO C 2. 17. A B, z/f

1

]e corr. D. rw] corr.

ex r&v D. xc^^ca 18. AET\ supra scr. D 3. 18. x&v]

om. D 3.

17] supra scr. D 3. Post ABE add. Inel ovv icy

sc-clv r) (supra scr. D 3) vnb 4BP ymvlu ty vnb ABE D et mg.

pro scholio BC; V- add. C 3. ovv] om. D, del. C.

MA0HMAT1KHS 1TNTASE&2 A'. 37

TTJ vnb BFE fay [Eucl. 111,21]' TO yap CCVTO

vnoTtvov6iv' faoy&viov KQK etirlv rb ABATO) BFE TQiytbvoj. coGxe xccl

avcttoyov i6nv, &s n BF ngbg

Tr}v FE, OVT&S YJBzJ ngbg iv\v 5

z/A [Eucl. VI, 4]* rb KQCC vnb

B4, FE [Eucl. VI, 16].

sitsl far} 6xlvfj VTCO ABE yavia

tri faito 4BF ycovitt) S&TIV ds xal 10

v]vnb BAE fay tr\ VTCO B4F, Itioy&viov CCQCC farlv

ro ABE rgCycovov ro5 BF^d TQiyavc)' av&KQyQv

6Tiv, K>S i\BA XQOS AE) f)

B4 Jt^bg 4F' TO

vnb BA, AT faov farlv T& vnb B4, AE.de xal TO vnb BF, AA foov r& vnb B4, FE' xctl 15

[Eucl. II, 1] &QK TO vnb AF, B4 faov

rc5 TS vnb AB^ 4F xal T& vnb

BF' onsg sdfi det^cu.

TOVTOV nQOXT&VTos 6TO r}^ixvxhov TO ABF4Inl dicc^LTQov T^s AA, xal anb TOV A dvo dirftftca- 20

3. ro5] e corr. D 3. 5. ryv (alt.)] om. D. 7. ET] T&V

FB D.'

8. BJ] 4B C, r&v BJ corr. ex rb BJ D 3. 10.

ycovia] om. D. 11. -no BJF -- 12. TQiycovov] mg. B 1.

11. tcoymviov 12. T^tycbvw] mg. C 3. 11. tari C 3

, comp. B.12. ABE] BAE C 3

. rwj'corr. ex no B 1

,ex TO D 3

. EFz/]BdP BC 3

. rptycbvra] TQiywvmvou etiam in textu C. 14. AnteBA ins. r&v D 3

. Jr] TA D. leti B. rw] corr. ex ro D 3.

AE] EA D. 15. to] corr. ex TW B^ 3.

"

vno (pr.)] vnbT&V E 1 D. EF vno] om. C.

'

BF TE] mg. B 1

,in

textu ras. 4 litt. ET, AJ] B4, FE B 1 D. IGOV\ -ov in

ras. A 2. TW] corr. ex ro D 3

. Ez/, FE] T&V BF, AJ B^.16. AF] T&V AF D. taxi D. 17. cvvcc(i(poT^QOtg] G- corr.

ex v in scrib. D. J F] F4 D. 18. BF] FB D. 19.

TOVTO rb ftemQrjiJicc Y.CC&' vn8QO%r]v tiyercci. mg. B pro scholio^,

y mg. D. 20. A] seq. ras. 1 litt. B.

<5av ai AB, A F, xal 6TG) xaT$a avT&v do&ftGa

^t, oicov-Y] did[iTQOs do&t<5a pjc, xal

BF. Af'yo), OTI xal avTri dsdoTai.

ai Bz/, FJ'5 aga sltilv dyhovoTi

dia TO keCrtsiv BXBLV&V sis

sjtsl ovv iv

0TIV TO

TO aga VTCO AB, JTz/ [iTa TOV

10 vrtb T&V A z/, BF foov IGTLV

TG) vnb AF, Bz/. xaC i6nv TO

T vnb T&V AF^BJ do&ev xal TO vnb AB, F4' xal

hoinbv aga TO vnb Ad, BF do&v itixiv. xai

A z/ didpfTQOs' do&i0a aga i&tlv xal ^ BF15 xal <pavQbv fj[itv yfyovsv, ort, av doft&Giv dvo

(pBQiai xal ai vn avTas vd"ia^ 8o%~i6a k'GTai xalf]

iv\v vnsQOfflv Toby dvo TtfQHpfQsicdv vnoTsivovtia sv&ia.

drfiov df, OTI dia TOVTOV TOV ^C3Qr^iaTog aMas T ovx

v&ias fyyodipoiiw anb T&V v Tats xa&

1. CIVT&V] om. D. 2. px] supra scr. D 1. 4. Bz/] corr.

ex BA C 3. 5. CCQCC stow] om. D. 8. xstQd.nte'VQOv] -ulvv-

supra ras. 2 litt. D. 9. &QCC] supra scr. D. Post vno add.

T&V D 3. 10. r&v] om. D. BT] B e corr. B. 11. BJ]

B4 d C, 4B D. V.KL 12. Softtv] BD, mg. C 3,

om. A.

11. SGTLV D, comp. B. 12. ]om. A. r&v AT, B4]

AB, TA D. xat] So&sv -AuC AC, doftsv & %ca A 3. AB,

AT, B4 D. 13. ^0-9-^ KGTIV] -v del. C, SGTLV SO&EV D.

t] ins. D 3. eariv] mut. in txi B 3

,Iti D. 14. Post

add. dofrsiGa B 1 C 2. fffrtV] EGTCCL D. 16. ai VTC']

corr. ex en' D 3. do&eiGcc tcrcci] do&siGcci &GIV tGrca do-

&EIGK D. SGTCCL] mut. in cofft C a. 17. vnsQo^riv] post 9

ras. 1 litt. A. 18. ort] on KCLI D. TF] mg. B 1. ovx] in

ras. B 1. 19. 6Myu$] -U'y- in ras. D 3

. iyy^dipo^v'] pr. yin ras. D 3

. need' ccvrdg] xar' KVTCC$ D.

MA0HMATIKHS 2TNTASE&S A'. 39

vnEQO%G)v xal dy xal ryv vnb rag

EnEidynEQ EÔÎEV ryv rs vnb rag f xal ryvvnb rag o/3.

nahv ngoxEfad-G) do&Efayg rwbg Ev&eiag EV xvxAa) ryvvnb rb ypiGv ryg vnorsivopEvyg nsQupEosiag svd'Etav 5

svQEiv. xal 0ro ypixvxfaov rb ABF snl dtapEroov ryg

AT xal do&Eltia ev&eia y T5,xal y FB nQi<pQt,a 8%a rs-

^J tpijtid'C) xara rb d, xal ine-

Êvyfiodttv at AB, Ad, Bd, 10

EZP dT, xal dnb rov d Inl r^vAT xd&srog y%&n y JZ.

onr\ZF ruiiGEia i6ri ryg r&v AB xal AT VTCSQ-

xefa&G) yap trfjjAB fay % AE, xal site-

17AE. STtsl i'6rj farlv

r\AB rfi AE, xoivri 15

derj Ad, dvo drj ai AB, Ad dvo ralg AE,

Ad faai, sfalv ExarsQa sxarsQa. xal y&vta % vitb

BAd y&via rfi vnb EAd fay 6rw [Eucl. 111,27]-

xal fidtiig aga % Bd flaGsi rfi dE fay idriv [Eucl.

I, 4]. aUa % Bd ry dP fay itixiv xal y dT aga 20

ry dE fay iGtCv. litsl ovv faoGxEfovg ovrog rQt,y&-

vov rov dET aito ryg xoov<pyg litl ryv fi&Giv xd&Erog

1. dedofitvoov] dedopevais D, -atg eras. dcbfoxa] t|3D.

2. floras] ^ vTtorsLVOVGUV D. 3. Post o{3 add. o D, onegi'du Ssiâi D 3

. 4. 8 mg. D. e&Q-efag nvog D. 5. vno\v- e corr. D. 6. xat] om. D. 7. 8v&efa r) FB xat] ins. D 3

.

FB] BT D. 10. at] om. C. 13. lanv D. 16. AB]BA D. dvo] Svel D. AE] EA D. 17. frca] COIT. exi'scc D. SKCCTSQCC] seq. ras. 3 litt. B. 18. BAJ] corr. exABT D 3

. SGTLV 20. SGTLV] mg. B 1. 19. xat] om. D.

I 20. IGTIV] om. C. 19. IGTIV i'cj} B. 20. &Ud]-AKL BD. JT] rj D. faq SGTLV] A, tcriv IGT] BD.

Seq. v.a.1 17 JT KQK xy JE IGJ\ SGTLV mg. B 1

,del. B 2

. J F]J D. 22. JEF] FJE D.

fyrai % z/Z, fay farlv % EZ if} ZT [Eucl. I, 26].

dU' $ ET <tty fj vnQO%ri <snv r&v AB xal ATv&i,G)v fj agcc ZF fififaeid &6nv rijg r&v avrcov

avro&V dsdorai xali\

fatnovtia fig rb

f] AB, fa&ifocmu, xal % ZJT rmfaziK ovtia.

T&V AT xal AB V7tgo%ri<s. aW fad iv op-O-o-

TCO ATA XK&&OV iigftf&tyg rijg z/Z faoycbviov

rb AAT QQftoy&viQv t& z/TZ [Eucl. VI, 8],

10 KKL <5TiV) ag % AT xgbg TA, rjTd JtQog FZ, TO

KQa vnb r&v AT^TZ, 3tQi%6iJivov ogftoycbviov faov

<5rlv r& anb ryg TA rsTQay&v(p. do&lv dl TO vnb

r&v AT, FZ' do&v KQK 6mv nccl TO anb ri\g JTz/

tsrQdy&vov. &6r xul [IIJXM f) Td v&Za. do&

15 rv\v rjiii6i,av vnoTfivovGcc tr\g BT 7tQi(pQiag.teal dia rovrov drj ndhv rov &coQtfiiaTog

re Arjcpd-ujtiovrai, nfatGrcci, xata rag ruLi6eiag rav

toV) xal dq xal anb ri\g rag t/3 {lOigag vitorei-

vvfruag ijre vnb rag g xal $ vnb rag y xal

20 ^ vnb rv\v \iiav r^iiev xali\ vnb rb ijiiuSv rsrccgrov

x rcbv

2. ccUd D. 4. v&Las~\ f-v&sius do&eicris I 5. vno-

xetftfVrjg] del. D. Supra scr. 77701 dfdo^vris B 2, Ssdo^svrjs

mg. C 2. dsdoTca] corr. ex dtdorai, D. 6. Ante pr. 7)

ras. 1

litt. D. xu] postea ins. D 3. 7. &m'] om. D. 8. TW

ATJ] vgiymva TOO AJF D. 9. A AT] ATJ D. z/TZ]FJZ corr. ex JZ D 3

. 10. FJ (alt.)] mut. in 4T C 3. 11.

Vcov] add. D 3. 12. do&sv d -- 14. TeTQctytovov] om. A.

12. fo'] dt 86TIV D. 13. rZ] FZ m^Mf^HNK)* D. 15. TTjVJe corr. A. BF] e corr. D 8

. TteQicpeQfias] -g e corr. C T

7CQl(pQiag 07tQ $81, Sti&l D. 16. mg. D. 17. 7tQOK-n&fufvcav D. 19. ?] ?| B. 20. ijpLGv (utrumque)] comp.BD. TO] rrjv D. T^TQI^TOV] d' D (similia posthac nonnotabo).

ti\v plv vnb T^V ^Cav ij^iav poigav roiovr&v a Atf Is

tyyiGta, oiov failvv\ diaperyog px, T^V ds vnb TO

i' d' T&V avT&v o ^ ^.

TtdkiV 6TG) XVX&OS 6 ABF4 1tQl dlK{lST()OV [LV

TYJV A/l, XSVTQOV $ TO Z, XCll KltQ tOV A CC7CeL^(f>^G)- 5

Gctv dvo itSQKpeQficci, doftstGcu xara rb ^rjg ccC

AB, BT vn' ccvrag

xal ccvral ddo^f

vat.

OTi, CCV ltt&V%G)llV TJJV 10

AT, 8o&Yi<5TUi xai avrij.

y&Q dice TOV B did-

TOV Kvxkovri BZ.E,

xal iit^vffiKttiav ai

^ KVTO&W, OTL dice

FE, dice d rfv ABxal dia Ta avTa

15

TO

FE, 4E' d^ovTyv BT do&rj<5Tat, xal

0Taiij

TS B4 xalYJ

[HtQ06&V ,fad V XVX&G)

BF4E, xal diriyyiBvai ffolv aC B4, FE, TO vitb T&V

diyyiLWCOV 7tQi%6n,VOV OoftoyCOViOV I'GOV (5T\V 6VVa[l- 20

(poTQOig Totg V7cb T&V artfvavTiov &6T, fjtfl dfdo-

[ivov TOV vjtb T&V B4, FE dsdoTKi xal TO vitb

T&V BF, 4E, ddoTai aoa xal TO vxb BE, F4. $-

1. Supra a scr. tvog B 3. 2. TO] tr\v D. 3. /_']

in

ras. A. o] A, o BCD, ovdev comp. A 3D 3. 7. tni&vi&co-

CKv BC; 7ti,&v\ D, -05" add. D 3. 8. ev&stca] corr. ex ev-

&SIKS D 3. 12. did] KTCO D. 14. tm&vx&coGav BC. 15.

JT] TA D. Sri] ds D. CCVTO&SV] post -6- del. i C. did]in ras. D 3

. 16. doQ"r\GtTcu (alt.)] SoQ-ijcovccci D. 17. rd] corr.

ex T D 3. 18. lv\ -v in ras. D 3

. 19. BJ, FE] in ras. A.20. lathi] -v eras. D. 21. vno] v- in ras. D 3

. 22. BJ]BT C. direct] corr. ex dCSorcti D 3

. 23. BT] mut. in B4 C 8;

BE, PzJ supra scr. D 3. dsdorca (pr.) FJ] om. D.

$s-] mg. A 1. SsSorai (alt.)] dedovrca D, sed v eras.

42 KAATAIOT DTOAEMAIOT

ds xalfjBE did^TQog, xal Aowr?) rj

F4],

xal dia TOVTO xalrj

tefaovGa ig TO

FA' tiers,

eav dofr&Gw dvo itQi<pQiKi xal

at vrt' avTag ev&stKi,, dod-tfGsrcci, xal ^ 0vvaî(poTQag

5 rag TtfQiyfQfiag xara GvvfttGiv vnorswovcfcc sv&SLa

dt: rovrov rov ^sco^âros.

(pccvsgbv df, on Gwriftivrts ad psTa r&v xgoex-

T&l[ieVG)V 7tCi<55)V 1T]V VJtO tfjV CC [_'

6vvcc7tTO[ivcts STtikoyiôiisvoi, TtccGag c

10 otiai dig yivoyisvai tgCrov [ifyog f|ov(?tv, xal \i6vai h'n

at ^,ra^v rcbv ava a [_'

dvo xa&' ZxaGrov i^Q^Bvai^ f

lOV^B^K t^V ty'yQKyijV. K)<JT, KV

TJJV VTtO TO fllLllLOlQlOV V&iaV VQG){lV, KVTr] KttTtt

15 TB xv\v 6vv&<5iv KOI tv\v vit^Q^v t^v agog Tag Ta

diaGTtfiiaTa 7tQL%ov6ag xal dtdoiiwag i>&iag xal

Tag hoiTtag Tag pTav TtaGag iftLw GvvavaitkriQ&Gsi.

7ti df dofafarjg Tivbg v&iag &g Tijg vitb TYJV a i'

{lOLQaV i\TO TQITQV Tf}g aVT^g 7tQl<p()iag V7COTlVOV0a

20 dia T&V yQaîii&v ov didoTcti Tt&g' i de y dvvaTov

i\v, l'%0{Lv av avTo&v xal TYJV vitb TO

1. 8s] corr. ex SL D 3. AotTrrj] r\ loinri A. Deinde add.

KQK D s. 17] BC, rj vTtb rfv AD, vnb rrjV eras. D. 3. FA]

AT onsQ fSst, dsti-ui D. 4. vno D. do&iJGETtti] corr. ex

SoQ"f\60vi;cii D 3. 6. rovrov] rov rovrov C, om. D. roi;] rov

roiovrov D. 7. H mg. D et in textu D 2. 8s] mut. in Stf

B 3D 3. nQOwri&Epsvcav D. 9. cvvaTtro^vccg] -n- in ras. D 3

.

^yypai/)Ofifv] pr. y in ras. D 3. 10. ooui] corr. ex oa ai C 2D 3

.

ysvopevat, D. 11. 7ieQifaicpd"}J6ovr<xL] corr. ex neQdr](pd"i]-Govrcci C 2D 3

. r&v] post ras. 3 litt. D. 13. xa^'] %al xa-91'

D.

14. ccvrr]] BC 2, avrfi A et corr. in avrri D, avrij C. 15.

rag] corr. ex rd A. 16. dsdo^vag] -fte- supra scr. A 1.

17. rag (alt.)] xcu rag corr. ex xara D. 19. fioiQav] sic AC.

7) TO] corr. ex r\roi D. rfjs ccvrrj?] corr. ex rfjs D 3. 20.

SCSorai] dsdorai corr. ex dsdcorui D.

rqv V7to ri]v cc {LOLQCCV onto rs

vnb rqv cc // JIOIQCCV xccl rr^g vitb // d' vno^lêvoi

o, xav pr} ytQog rb xa&ohov dvvrjrcci, rag

6(Hn/, iiti y rG)v ovrcog &a%farcov rb

off rag G)Qi6êvag aitaQdMccxrov dvvair' av 6vvrr]Qtv. 5

hey& YKQ, on, lav v XVX^G) dta^wedvo fv-O-ftat, rj H,%G)V nabg rqv ikaGGova

%i r[itQ $ 7tl rijg [ifftovog v&Lag

ri]v 7tl ri\g fhaGGovog.

6 ABT4, xal dt,tj%&G)6*av iv avrci) 10

dvo sv&siai aviGoi, ttdtiGov {ikv fj AB, îfi^cov dfr\

BF. Afô, on,i\FB v&ta

6ova Aoyov %i, rjrtfQ r\BF

\ T~J

itQicpQi,a itgbg rr^v BA TCSQL- 15

tpQi,av. rfriitJG&G) yap rjvnb

ABF y&vCa dC%ct vitb ri\g

B4, xal 7t%v%d'G)6av r\r

/i AEF xai $ Ad xalr\

T4.

xal 7tdj]

vjtb ABF ycovia di%a rrîrjrai vitb 20

1. fJLS&oSsvGoîfv^ corr. ex [if&odfvGaiifv C 2. 2.

om. D. vno] vnb TO D. 3. Iri^drtov] -n- in ras. A.

corr. ex ju-ot C 3. 4. nr{Liv.orr\ra.^\ corr. ex

fâ^tdrajv] corr. ex iKdîGtov C 3. 5.

corr. ex ci)Qi6\[iva$ A 1. _ SVVUIT' &v~] dvvarai D. 6.

mg. BC. avtaoi, 8vo~] |3&VIGOL D. 7. slaGGova (pr.)] ante v

ras. 2 litt. A. ^CCGGOVK (alt.)] AD, om. BC, add. C 3 et mg. B 1.

8. (Ltfôvoff] -g in ras. D 3. 9. 7rt] ccito B. sldrrovos D.

11. KViGOi ev&stccL D. 12. FB] BT D. 13. KQOS 15.

7CQL<pQicc] mg. B X C 3. 13. fv&fLccv] om. B*D. sUdrrovcc C.

14. i]7tQ] r\ C 3. Br] FB B X D. 15. TCQOS 7tQi(peQi,av~\

et in textu C et in mg. C 3. 16. ? mg. D. 17. Sfya ycovi'a D.

20. Y.ai fTTft 7CL OVV D.

A /I [Eucl. Ill, 26, 29], JWI&DV 6*rjTE tfg EA

[Eucl. VI, 3]. %<& d?) arco TOV z/

T?)f AEP 1] z/Z. rfl roivvv ^et'fwv

v4z/ T% J5z/, ^ 6* .EJz/ Ttjg z/Z, 6

5 TCO z/, 6^<m?fi<m ds ro5 z/.B

xv\v i&v A z/ r[iet) tinsgnzGstreet, ds r^v z/Z.

y&G) dij 6 HE, xal sxfiep^&G) i\ z/Z@. xal

6 /ni> 4E Topsvs iizifav <5rlv rov

TO ^ 4EA tQiy&VOV ILlt,QV tOV 4EH TOllS&g, TO

10 (>a z/JZ tQiy&vov TCQOS TO 4EA TQiycovov skdti-

tiovcc Adyov ^t ^() 6 4E Toptvs JCQOS rov /IEH.AA' wg f*v TO z/Z T^t'/covov ^po^ TO JEA r$iy&-

vov, ovr&g $ EZ ev&stcc agog r^v EA [Eucl. VI, 1],

cbg df 6 /IE ro[ivs agog rbv A'EH TOftf'a, ovr&s

15 ^ vnb Z.4E y&via Ttgbg r^v bito EA A'r\ aga ZE

sv&sta agog ryv EA &K<56ovK hoyov Zyjti iJ7tQ 17

VTCO Zz/.E y&via itgbs ryv vitb EA A. xal 6vv&vri,

aga i\ZA ev&ia itgbs rqv EA hd06ovcc koyov %t,

r^nQ YI VTCO Zz/A y&via 7t$bg rr^v vnb AAE' KOI

20 rCbv fiyoviLW&v roc diTthaGicC) f]FA v&tcc ngog rr\v

AE ttaGGova Myov %i ijjtfQ i]vnb TAA y&via

4. 6 ago] 6 a- e corr. D 2. ju-fV] om. D. 5.

8ii] Y.a.1 8i.a6Triu.an D. 6. re(ifr] corr. ex rspvei D. zf Z]corr. ex AZ B 1

,AZ C. 7. HE] corr. ex E<9 D, supra

ras. 1 litt. xai tnEi] end ovv D. 8. iaxCv 9. jLtfi^ov]

supra scr. D 3(fcrt). 10. To Z/EZ a(>a TQiycovov KQOS rbv

4E@ rofiEcc skdrrova koyov %i ijnfQ rb 4EA rgfycovov KQOSrbv JEH rofiscc

'

IvaUa.!- mg. pro scholio B et nonnullis uerbis

recisis C. JEA rQiyavov] A? arQiycovov D. 11. Ante Adyovras. 1 litt. A. 12. rgCycovov (alt.)] om. D. 13. EA} AE B,corr. B 1

. 14. rofif'a] om. D. 15. Post pr. VTCO ras. 1 litt. C.

16.?)]

add. D 3. 17. Zz/E vno] supra scr. D 3

. EJA]E4A ycovfav D. 20. FA] FA &QCC D. 21. FJA] seq.ras. 1 litt. A.

vnb EAA' xal diMvn17FE v&ta jrpog rrjv EA

koyov %t, ijjfQ f)vito FAE yovicc TCQOS xr\v

vitb EA A. AA' &$ {ilv ^ FE ev&fiK itgbs rqv EA,ovras rj

FB ev&etcc TCQog rr^v BA [Eucl. VI, 3], o>g df

^ VTtb FAB y&vCa TCQOS rr\v vitb BAA, ovt&s i\FB TISQI- 5

<p$Lcc xgbg rv\v BA [Eucl. VI, 33]' r\FB agcc fv&tfa

agog ryv BA IkaGGova Aoyov %i, i]7tQ i\FB TISQL-

BA 7tQi(pQl,CCV.

rovrov drj ovv vitoxt,[ivov

6 ABF, xal di- 10

iv CCVTCO dvO V&tai

ijT AB XCil

f} AF, V7tOXL6&0)

$ 71Q&XQV fj {LBV AB VTtO-

Tivov6cc [nag [IOIQCCS [_' d', fj

dl AF polQav cc. fad % AF 15

5? rriv BAf\AF

, 1]$ AF 7tQl(pQl,a faiTQlTOS StiXlV t^ AB, fj

FA ago, v&ia ri]g BA ttaGGcov 6rlvTI sitiTQirog.

aMai\AB v&ia dL%&r] roiovT&v o ^ ^, oi&v 20

0TtVYj dld[JLTQO$ ^' fj KQK FA V&lC

i<5xlv r&v avrCbv a/3

v' TCCVTCC y&Q fatrQitd

xGbv o 7.

1. E4A] A4E D. SiflovTi 1^] Sielovrrii D, i suprascr. D 3

. 3. E4A] A e corr. C 2. ev&eiK] om. D. 4.

tv&Eia] om. D. 5. rj (pr.)] om. C. BJA]-Be corr. D 3.

6. TTJV 7. TtQOs] mg. B 1. 6. r]

1. EA} add. C 2. 8.

TtSQLCptQSWV OTttQ dtl (Hdtl D 3) SfL^Cii D. 9. ^ mg. D. OVV^

om. D. 13.TJ jLteV] [isv i] D. 14. fuas] supra scr. D 8

.

15. a] mut. in ar D 3. 17.

TJ] supra scr. A4,om. C. Mg.

TO IfipiLu pro scholio BC. 20. o] o C, ut saepius. 21. PA]AT D. 22. snuQicTu C. 23. rj] supra scr. D 3

.

46 KAATAIOT HTOAEMATOT

Ildfav itl rrlg avri]g xarayQayfis r\ plv ABsv&eta vitoxeiG&K) vitorswovtia potQav a, ^ de ATyLolgav a l_'. Kara ra avrd d^ iitsl

$\AT iteQuplgEia

rtfg AB <5riv ^fuoAla, r\FA aga SV&SIK r^g BA

5 &d66G)v 6rlv rj fiiiiofaos. aM.a rqv ATTOIOVTGJV oi)0ccv a Ad tf, otcov 6rlv

v\

f] aga AB sv&stcc [isifcv stirlv r&v avr&v &($!>'

rovr&v yaQ iîMid sdnv rot TCQOXS^SVCC a Ad Is.

attire, sjtsl r&v avt&v edsfyftrj xal {istfav xal

10 ^ Tfjv \iiav \HQigav vitorsCvovtia i>&ta, xal

driôvon fôpsv TOIOVT&V afi

v fyyiGTa, oicov 6rlv

rj did{itQog ^c, xal dia ra nQodtSsiyptva xal r^v

vitb rb fitiiiioiQiov, rjrtg VQi6xsrai, robv avr&v o A,a xs

lyyiGttt. xal 6vvava7tA.r)()K)d")]<)rai, ra Aoiitd) cos

15 diatirtfiiara x y&v rijg TCQQS rr^v yiiav rjiiitiv

Aoyov svXv cos snl rov TtQ&rov diaGrtfiiaros 6vv-

rov fuiiyioiQiov duxvvyiBvris ryg vnb rag ($

x d rijs vnQO%ijs rijs XQOS rag ~y ftoâ?

xal rfjs VTtb rag /3 L' didop&njs' caGavr&s dl xal 7tl

20 rcbv koiitcbv.

% [itv ovv TtQayparsCa rfbv iv rep xvxAa)

ovrag dv oi[iai gatira iira%eiQi6&siYi. iva df, cag

3. nsQLCpSQSia 5. AP] mg. D 3

(ttc^teyop).4.

lanv D 3. FA &ga\ AP D 3

. B A] AB D 3. 6. ovoav] supra

scr. D. 7. AB] BA D. 8. 5 Ad I?] corr. ex ^1 dls D 3.

9. coffr' D. 12. TtQOvnodfSsiyiiEvci D. 14. tog f'qpaêv TCC

loiita. D. 16. itQwrov] corr. ex a D 3. cvvftsofas] I) (-? e

corr.), TVJS 6vv&s6(o$ ABC. 19. xat (pr.)] eras. D. 22. <Jf]

8' D. Iqprjv] corr. ex f'qprj C 2, I'qprj B.

MA0HMATIKH2 STNTASESS A'. 47

ExaGTrjg T&V %QEI&V f'J Itofyov rag

TG)V EV&El&V EXXEljJLEVCCg ,XCCVOVHX

dva 6Ti%ovg [IE dice TO GVJJLHETQOV, (bv TCC [IEV Tt

i, Tag nyfaxoTrjTccg r&v rtQi,(pQ(,G)v

7tccQrjv%rjHEvccs, ra de devrsga rag t&v 5

TQircc TO X iifyog Tf}g Haft1

ExatiTov tyupofyiov T&V

iva E%OVTS xccl Tyv TOV vbg

adiayogovGccv TCQOS ai'6d"rj6iv 10

vs xcci T&V ÊTCC^V TOV

Tag 7ti,f:lccM,ov6ag

aiiEd-a. EvxciTavorjTOv d\ ort dia T&V KVT&V xai

)XCCV V dltiTCCyilGJ yEVG)^L8^(X,

itQi Tiva T&V iv T& xaroviq) nagcc- 15

xfipEvcov V&LG)V) QttdCav TCOirjô^fQ'a TIJV TE s&xal Tr\v EitavoQ&coGLV T^TOI catb Trjg vitb T^V

Tijg Eiti,r}TOviiEvr]g 7) Tqg TtQog aMccg Tivag T&V

vx()o%ijg tj Tijg Tr\v faiTtovGav eig TO

EQHpEQEiaV V7tOTEl,VOV6rjg EV&ELCCg. KKl 0TIV fj20

TOV XCCVOVIOV XCCTayQCCCpfj TOlCCVTlf]'

1. %QeiO)v~] mut. in wqastov D 3. 3. ava] ins. D 3

.

,-i- corr. ex o, D. 5. r]iii[i6

l

Qiov D. 6.

-is e corr. C. 8. i'] I ABC, TQICCKOGTOV D.

D. 9. LVO.fôvrfg]

bis D, sed corr. 10.

QOVGCCV] mut. in adiacpoQOvs &v A 2. ccl'ad"r}6iv] -GIV in ras. B 1

.

11. e etoifiov] om. C. 12. ETCiâUovGccs'] -ni- in ras. B 2.

13. dvvdû BC. *'] 3s D. 14. ysvo^cc C. 16. rijv]

TJ extr. lin. A, T^V A 4. 20. nut IGTLV] tonv ds D. 21.

ij D. XUVTJ] D.


ia'. Kctvoviov

TT

MA0HMATIKH2 2TNTABE&S A'. 49

tp /


Q81WV

MA0HMATIKHZ! 2TNTABE&2 A'. 51

A

52 KAATAIOT HTOAJEMAIOT

*W -

MA0EMATIKHS STNTAEESS A'. 53

vt.ll


QSl&V

MA0HMATIKHS A'. 55

It


Qfl&V

MA0HMATIKHS A'. 57

tflL'


QGiiov

MA0HMATIKHS ZTNTAgESS A'. 59

QXS


TtfQMpB-OiO)V

MA0HMATIKHS STNTASE&S A'. 61

9PtL'


QfLtOV

MA0HMATIKHZ STNTASE&2 A'. 63

P

Tils iiTa%v T&V TQOTCLX&V

r} Trjs TtqfaxoTrjTOs T&V iv Tip

7CQ&TOV KV ^ XK&KltGQ /JtO^

6 Ao|6g xal dta [ifa&v T&V Jradtov xvxhos

5 XQOS rbv far][iQiv6v, rovrfarw tCva Aoyov %i, 6

a7toha[ipccvo[ivr]v afaov [iTa%v r&v

rtQi,(pQiav, fi fcr]v CCTC^L drjAovori, xal rcov

XCCTQOV <5riiLeiG)v rb xara rbv fariyiQiv6v.

10 d9

fiinZv rb roiovrov dgyavixcbg xara^cc^ftccvrca

TWOS ccrtAij

&l, TTOQVV[lVOVo5 xQrjGonf&a [i6r]ii{lQiv(p dt,&6vTs CCVTOV fig TCC vito-

15 Xl'[lVCC TOV [lyi6TOV XVX&OV T[MJlt,CCTa T% Xttl TOVTCOV

) 1$ 00K tyx&Qft ^Q^' 7tlTK TQOV XVX-

TOV lQrj[lVOV VKQll66aVTSCCVT&V 7tl /Lttg [lVl,V

)A,VTG)S VTtO TOV

20 dvvaG&ai TOV &d66ova xvxhov iv red

7tQOS ttQKTOVg T

dvo TLV&V xccTa did^TQov TprjuccTcov TOV

XVX&OV XCCTCC TfjS TOCiS TG)V

1. t^'] om. AD. Ti]s] corr. ex r&v D 3. 3.

corr. ex slnco^sv B. 4. t&v] om. D. JyK&dijrca C, corr. C 3.

8. J] r/ A. 9. TO] mut. in td D 3. 10. diuKa^KVsrai D.

12. TTE $1 Karcc6H8vfig mg. B, xaTaaxfu^g mg. C. 14. w] e

corr. B, T77g TCSQicpegsfas <j>D. 18. (isv jtitag]

bis C, sedcorr. Post psveiv del. B. 22. xara] r&v Kara D, r&vins. B 8

. 23. XVH^OV] xvxZtffxov D. TCQLGfidna] mut. in

C 3, Trqy^arta corr. ex nQiypaxiK D 1

.

fact vEvovrcc itobg ccMrjAcc re xccl rb XEVTQOV rcbv

xvx&cw axQificag itccQa&EVTEg Kara peGov rov rthccrovg

ccvr&v yvojiovicc keitrcc Gwdrtrovrcc rr\ TOV

XCCI dlTlQÊVOV XVX&OV TtkEVQK. 0V dij XCcl

GCCVTEg CC6<pcdG)g ETtl TG)V TtttQ SXCCtira %Q(,&V Eltl 5

Grvkfaxov GVIIIISTQOV xal xarcctirriGavrss EV VTtcci&QG)

rr^v rov Gxvkfaxov ficcGiv iv axfovst agog rb rov 6^t-

Ertfasdov edutpei 7tccQa(pvhtt%oiisV) o'jrcjg rb iiti-

rcbv xvx^cov 7tgbs [IEV rb rov doôvrog OQ&OV

f],Tc5 df rov iLE6ri^QLVOv TtccQaMqhov rovrcov ds rb 10

IIEV TtQOTEQOV tilCl XCC&ETIOV ÊôdEVE

pV Kitb rov xara xogvyviv EGOJJLEVOV

IIEVOV df, ECOS av EX rijs r&v V

ETtl rb xccra diccpEroov itoiijd'rjTat, ri\v nQoGvEvGiv^ rb

$ dEVTEQOV ILEGyilflQLVilS yQCC^l^S V6^^l(DS fÂ^ftftfV^^ 15

EV r& vnb rbv 6rvM<5xov EitiitedG) xccl Tt

fts ra itkuyia, r&v xvxAcov, &$ civ

'yQa^fl rb EitiTtEdov avrcbv diOTtTEvrjrcci. roiavrrjg d^

rijg &E6E&S 'yivoîEvrjg rr]Qov[iv rr\v ytobg ccoxrovg

xccl [i6r]ii(}QiKv rov r\Mov 7tccQcc%c()or]6i,v TtaocccpEQOvrES 20

iv rcclg (lEGyppQicug rbv svrbg xvxMdxoV) Ecog av rb

vTCoxccro TtgiGiidriov oAov vcp' oAov rov

1. L'GK] xal i'aa D. 2. fifoov] corr. ex (iscov D 3. 3.

ovLcc Isnra GVV-] supra scr. D 3. 4. IvaQfioaavrss] corr.

ex svccQii6ovi;$ D 3. TctQi ftsceoog mg. BC. 6. xaracrTjaav-

rsg] KccQ'iGTdv'tEs D- 7. &îvsi * et mg. ^? (h. e. nccQ-

ccUrilG)) B. 9. TO] supra scr. D 3. 10. Post $ ras. 1 litt. D.

11. y.QT]pvKiLvov\ B 2D 3, KQi(jLva[iEvov ABCD. 12. arHietov]

corr. ex Gr\\isiov C 2. 13. &v\ a extr. lin. A, corr. A 4

. vno-

BD, corr. B 2. 15. svc^fifjioos C.

16. 7tCCQ<X(pSQO[lVa)v] CD, TtSQICpZQOllSVOOV A XB. 18. TCSQL

^Tjcecog mg. BC. 21. (iG7](iQivcas D, sed corr. 22. TtQiGpd-

riov] mut. in m^y^d-ciov C 3; nriy^driov , r\

e corr., D. TOV]corr. ex r6 D 8

.

Ptolemaeus, ed Heiberg. 5

66 . KAATAIOT HTOAEMAIOT

xal rovrov yivQîvQv disdrjucuvsv r}{iiv ra

rS)v yvwiiovicov axoa^ notice r^jîara rov xara xoov-

tpriv xa6roT rb rov r\Mov XWTOOV acpsGrrjxsv 7cl

TOV urtqiipgivov.

5 ri> ds v%arj6T6raov ertoioviie&a xv\v roiavrrjv

xaTcujxsvKticcvres ccvrl rcov KVK^CDV

xfav&idcc TeTQccycwov xal a

xccl

10 nvl Ttgbs ifi [M& i&v y&vi&v fyQKâîfv xvx&ov

cbro TOV xara rb xwrgov

tQi(pQ{ccs rag tr^v

vn r tâgtriôQLOV OQ"\v ycoviav itQL%ov6ccs

v&iccs xal diA6vtg oiioi&s r^v 3tQt,q)Qi,av slg rag

15 9 poiQag xal ra rovrav [iQr]. pera df ravra 7tl

yuK<$ T&V v&i,G)v rfjg [iA,A,ov6r]g oQd"f}g re

Ttgbg rb rov OQôvrog 7tfadov xal TtQog

rv\v &<5iv ^LV [i7toA,faavTg OQ&a xal L'6a

dvo xvMvdQiK jjuxaa xara rb OJIOLOV rToovvîva^ Tb

20 /iv 7t avrov rov xara TO XBVTQOV Grftisiov Jtol avrb

TO pfaov axQip&g, rb $ Jtgbg ro5 xdro nsQan rijg

1. 6mK6&j}~\ 6- euan. A. difcrjpavsv corr. in

vsv D 3. 2. yv(o\n6v(ov D. 5. Ttegl HUT<x6KSvfi$

mg. BC. 8v%QT]GTOTQKv D. 6. Aifi"t]vr]v B. 7.

BCD, corr. D 3. Kid.6'tQoyov~\ A, add. sv (om. D)

Ttldrsi y.al fidftu itgbs to ^f^Tjx/vat KKTK ngoTKcpov BD, et mg.pro scholio C (offica <jqpa/l/ta add. eadem manu). 8. ano-

r\TET<xiLvr]v D. 10. lyQcctyKiisv] 79- in ras. A. 11. xfV-

TQOV D. 12. Grjfjisiov] corr. ex Grjptiov C. rag] suprascr. A 1

. 14. dif-ttvTsg] corr. ex. diEl&ovres B 2C. 15. enl]

Kara. D. 16. [iehov6r]$ D. TE eaec&cci] ri&eG&ai D. 17.

3rpdg(pr.) yiat] om. B, mg. C 3. 18. fynoliiGuvTEs] mut. in

EV7toUGK\TS B 3,

SVETlQlr\6&.\LW D. 19. Y.vMv8QlCi] post Veras, n D. opoiov] o- ins. D 3

.

MA0HMATIKHS STNTASEaS A'. 67

rv\v secr

ttfavgav itaga xv\v ev rc5

rr\v ft&iv TG> TOV

V EitiTtedcp, xal XK&STIG) dice t&v

ts xal 6^-9-^v XQOS TO snfaedov rov

jv di' avt&v ev&etav axgiflovvTsg VTto&spaTi&v ita

kem&v TO svds'ov diOQ&oviisvwv Tr]Qov[iv

iv Talg }i6rj^ftQLCCLs Tr\v aitb TOV agog rc3

KEVTQCp KvklvdQLOV yiVQîvY\V 6KLKV 7tCCQaTl,d'VTg 11 10

/

yQK^svrj ytQi<pGQ8ia XQog TO xaTadr}-

TOV T07COV <p(X,lV6d'ai KCcl TCCVT^g TO

6ypwvpevot> TO HUT' KVTOV TH^CC Tqg TOV

itl TOV ii6rj[ipQivov nagodov 15

TOV fjMov.

in drj T&V TOIOVT&V jrccQCCTrjQiJGfcav xcci iidAiGTct

TCQV itol Tag TQonag avTag V\\LIV KVCCKQWOIISVGW iitl

nteiovag 7tQiodovg TO, face Kai TCI CCVTCC T[nj[iaTcc TOV

v nvxhov ncd XCCTK Tag &Qi,vag TQOitag xal 20

Tag %iiiQivag T^g 6rj[iid)6G)g cog iitiitav anb

TOV xaTa xoQv<pf}v dTtoAappavovGrjg 6rîiov xaTfAafio-

[i&a TYJV dnb TOV POQMOTKTOV TtBQUTog iitl TO VOTLCO-

TCCTOV 7tQlCpQiaV, iJTig 0TiVf] [IfTa^V TG)V TQOTtM&V

1. TtEQti &GCQS mg. BC. 3. yQccîijv C. 5. KvMvSqmv D,

deinde del. KKQifaZ TS xat. 6. unlivf)] &y.UvftH

D. ra]

postea ins. D. 7. ndUv" riv&v B. 8. ten-lav] in ras. D,JiSTtrov BC. itQi %gr}G(o<s mg. BC. 9. wGavtoog] oôtoog D.

rb y.tvxgov D. 10. xvMvdQOv D. 13. avrov] avro seq.ras. 1 litt. D. 14. diccaâtvov] d- in ras. A. 17. dij] posteains. B. 20. xara] supra scr. A 1

. 21. cog] supra scr. A. 22.

v]t A.

corr. ex arnistov C, supra scr. D 3. 24. TteQitpfysiv A.

sett A. rj] supra scr. A 1. TôTttxwv] r- postea ins. C.


,Ttavrore yivQ\Livv\v ^ xctl peC&vog [lev TJ

arog, elaGGovog de fjiifoovg rerdgrov,

dt ov tivvayerai 6%edbv 6 avrbg Adyog rc5 rov 'Ega-

roG&svovs, c5 xal 6f

'IrtJtaQ%os 6vve%gâto5 yap TOiovtcDv 1^ psto&V r&v tQOTtiK&v Ice

OLCOV 6Tiv 6 n,6rjit,($()ivbs ivy.

ds avro&sv ex ri^s itgoxsLiisvrj

Keel ra r&v oiMJ6(ov, v cclg av

rag rriQt]6i,s^ fyKJUpaxtt ^CC^KVO^VCOV tov re

10 percc^v Grftieiov r&v dvo nfyccrcov, b yiverou, Kara rbv

,xal rijg êra^v rovrov re xal rov xara

ov TteQicpeQeCag, i] fayv dÂovdrt nal ot

7t6Aoi, rov bgt&vros a

eig rag

15 'AKokovftov d' ovrog ajtodet^cu xal rag xccrcc

rcbv a7t

V percc^v rov re l^rjêQivov xal rov dia

r&v Jcadtov xvxAov rcbv yQafpoê

dice r&v rov farnieQivov nohov

20 paria pQa%ea xal ev^ri^ra^ di' cav rag itkeitirag 6%edbvrcbv GcpaiQM&g fteooovnevcw, &g em

xal iie&odix&reQOV TCoirjGope&a.

eig dvo di) ev&eCag rag AB xal AT

2. Se] Ss ij D. 3. TOT] TO C. 5. peragv] -|- posteains. C. 13. Trolot] TroHo/C. 14. ty'] C, yt B, om. AD.

15. ovros] -v- ins. D 3. 17. pscov D. 21. GcpaiQiK&v

D, supra scr. ccpSQM&g &ea>Qov[iva)v D 3. 23.

eig dvo dij] postea ins. D. a' A^/u-^cc evftvygauiiov KKTCC ovv-

mg. BC.

MA0HMATIKHS 2TNTAEE&S A'. 69

dvo sv&slai,

TO Zrs BE Kal

r\TA rspvsrcoGav a

on, b rijg TA jtobg AE Adyog Gvvrinrai SK

rs vov tils Td TtQog 4Z Kal rov rijg ZB JtQog BE.

yaa dice rov E TTJ TAefaw ai TA Kal EH, 6 rijg FA

itabg EA Adyog 6 avrog s6nv r&

rijg TA xabg EH [Eucl. VI, 4].

sv $i]ZA' 6 aoa rijg TA

EH Adyog 6vyKi[ivog sGrai, 10

SK rs rov rijg TA Jtgbg z/Z Kal

rov rijg A'Z nabg HE' &6rs Kal

6 rijg FA itgbg AE Adyog

Ksirai SK rs rov rijg TAz/Z Kal rov rijg z/Z itobg HE. 15

ds Kal 6 rijg z/Z Ttobg HE Adyog 6 avrbg ro5

ZB xabg BE [Eucl. VI, 4] dt,a rb naoaMrjAovgslvai rag EH Kal ZA' 6 aga rijg FA itabg AE

Adyog (SvyKSirau SK rs rov rijg TA Ttobg z/Z Kal rov

rijg ZB Ttabg BE' oitsa xaosKSiro dsl^ai. 20

Kara ra avra d dsi^^srai, on Kal Kara diai-

Q6iv b rijg FE agog EA Adyog Gvvrptrai SK rs rov

rijg FZ Jtobg A 2, Kal rov rijg AB nabg BA, dia rov

A rri EB jrapaAA^'Aov ^O^tfiyg Kal itQO<5eKfttri&siting

sit avrr^v rijg F4H. sitsl yag ttdkiv TtaQa&hrjAog 25

1. FJ] AT D. 7. EA\ AE D. 9. ilfr&w SE] wlD. 10. TCQOS] corr. ex TTQO D 3

. 11. zfZ] Z4 D.

12. z/Z] Zz/ D. HE] EH D. 15. HE] EH D. 16.

HE] EH D. 17. ZB] E Z D. 20. ZE] BZ D. 21.

l7)ti[ici vccra Siuigtaiv mg. BC. 23. z/Z] Zz/ D. z/E] Ez/JB mg. D 3

. 24. rfj] seq. ras. 1 litt. B.

D. 25. Fz/H] corr. ex Fz/ D 3

Z47 AH Tfi EZ, eGTiv, cog i\

FZ xabg ZH [Eucl. VI, 2]. aUa

Aaiifiavo[ivrig 6 Tijg FZ itobg

ZH Adyog Gvyxeircti ex re rov

5 Tf}g FZ rtobg Z4 xal rov Trjg

z/Z Ttgbg ZH' 6nv d 6 ri\g

4Z rtQbg ZH Ad/og 6 avrbg

TK> Trig 4B nabg BA dia TO

fig Jtaoahkrjhovg rag AH xal

10 ZB dirjx&ctt, rag BA xal ZH'6 aga rrjg FZ agog ZH Adyog Gwrptrai ex re rov

rrig FZ TtQog z/Z xal rov Trjg 4B nobg BA. akka

T& rr^g FZ ytobg ZH koycp b avrog etiTiv b r^g FEagog EA' xal 6 Trjg FE aoa Jtobg EA Ad/og Gvy-

15 X(,TUI, x re rov rrjg FZ JtQog 4Z xal rov ri}$

JiQog BA' ojfeo edei detâi,.

Ttdfov e6TG) xvxhog b ABF,ov xe'vraov TO z/, xal ft'A^'gpO'Gj

ejtl Tr^g ftSQiysQsfas uvrov rv-

20 %6vra, TQia Grftifta ra A, 5, P,

&6rs exaTs'gav T&V AB, B F7tQi<peQei,(bv &a66ova eivca f]p>i-

TO

25 opoiov vTtaxovsGd'G)' xal 7t&v%d'G}6av atAFxal zJEB.

QOS] bis D. 3. laâvoîvr]?} corr.

"D. 6. JZ] ZJ D. 12. JZ]

D, JB mg. D 3. 14. Mat EA] om.

rr. ex A D 3.

1. ry\ rfjg BC. 2.

ex laiijlapoiisvrig B 2. ngo

ZJ D. JB]BC. EA (alt.)] corr. ex A D 3

. 15. TZ rfjs] mg. A 1.

TZ] ZT D. 4Z] ZJ D. 16. faeg ?8ei d%cu] om. D.

17. y' JUjfApa wAlwov mg. BC. 20. id] om. D. 24. Za^t-

âvo/nâjv] ^, corr. ex f D. 25. ofioiov] avro corr. ex avrS) D.

at] bis C.

MA0HMATIKHS 2TNTASE&2 A'. 71

cog

rtQt,(p()iag ftgbg rr\v vjtb r^v diTtAijv rrjg -B-T*,

ngbg rrjv EF sv&etccv.

KK&STQI aitb rwv A xccl Fre AZ xal % FH. exsl

AZ rf) FH, xal diijxTcci, stg ccvrag sv&elcc, ^

AEF, l<5tiv, cog % AZ agog r^v FH, ovrog % AEagog EF [Eucl. VI, 4]. aU' 6 ccvrog tenv H6yog 6

rrjg AZ agog FH xcci tijg VTCQ r^v ntKv\v rqg ABagog rr\v tinb tyr diitlr^v rrjg BF' ^(i- 10

arQcc xccrQccg' KK\ 6 rilg AE CCQK agogEF k6yog 6 avr6g 6nvAB Ttgbg rr\v bitb r^v dirtkrjv rfjg BF' ortQ

on, xccv do&G)6iv ijrs AF oArj 15

7tQlCpQl,K KOi 6 Ad/0? 6 Tljg

rr\v 8iitfa]v rijg AB itgb$

vnb rrp> diTthijv r^g BF,ca xccl BKKTBQK r&v AB

KOI BF 7CQl,(pQL&V. XT&t- 20

faet&tybm % Ad, xccl

rov z/ xa&Tog 7tl xr\v AEF rjz/Z. on

ovv rr\g AF TteQicpegsiag do&i'6yg ijT vnb

1. rfjg 2. BF] mg. BC 3, rf]s BT etiam in textu BC.

3. KOS supra scr. D 3. 6. ev&Efa] con*, ex SV&BLKS D. 8.

6 (alt.)] om. D. 9. rrjg (pr.)] corr. ex

supra scr. D. 12. ET] trjv EF D.13. EF] FB D. oni-Q t'dsi de^ca] supra scr. D 3

. 14. #']

comp. ins. D 3. 15. AT] corr. ex FA D 3

. Post oKj] del.

17D 3

. 17. tjv] r- e corr. C. 18. BF] corr. ex FB D 3. 19.

%ca] ins. D 3. 23. ^4EF] corr. ex z/EF BC 2

.

EF] xj\v ET D.

tr\ D 3. 10.

ia rr\v f)[ifaiav avrr\g vnorftvovtia

xal o'Aov to A4Z TQiycovov, dijjAov 7tl d\ TTJS AFi)&as o'A^g ddo[ivr]s vitoxsirai xal 6 rfjg AE TCQO<S

EF Aoyog b avrbg G)v TG) rijg vnb tr^v dtÂijv rijs

5 AB Ttgbg rrjv vnb rr\v dntki]v rrls BF, ijT AE

6rai do&t6a [dat. 7] xal Aomr} ijZE. xal dia

rovro xal rijg z/Z dfdo^vr^s So&ritiexai xalij

t vitb

E4Z y&via rov E4Z ogfroycovtov xal 6'A^ ^ vnb

10 hoiJtii i]BF' 07tQ fdft, dftât.

6 ABF 1tQtl XVTQOV TO ^/,

avrov tttjg)&G) tgCa Gr]iiia

A, By .T, &6t XaTQaV t&V AB^ AF 7tQl,<pQeiG)V

r

dvai rmixvxMov' xal 7tl T&V

15 fiavo[iVG)v jtQKpQi&v to opoiov VTtaxovfa&G)'

Im&vx&tfGai, ijT dA xal % FB

0V[l7tl,7CTT(06aV XaTfX TO E 6rj[ltOV.

xal

xal

1. seq. ras. 1 lilt. D. 2. zgiyavov] TQiycovovD. Se] Ss nat D. 3. 6] supra scr. D 3

. AE~]seq. ras. 3 litt. D. 5. BT] PE D. 6. ZE] EZ, E in

ras., D. 7. dedo[itvr)s\ alt. 8 supra scr. D 3. 8. yeoWa rov

Ez/Z] om. D. 10. oneQ I'^t de%ai] om. D. 11. ABP]ATE D. Mg. TQLTOV tcbv Kvy.foH&v B 3

. 12. cr\îcc\ 6r]\[Licc,

post r\ras. 1 litt., A. 13. &GXE 15. vnanovsGO'ca] om. D.

13. Supra AT scr. ET C 2. 16. tnifcvtd'Bfate D. FBI

BTD.

,on iGtiv, cog j]

VTCO r^v diitkifo rijg PAagog x^v vitb r^v diTt^v rife AB, ovrcog

rjrE v&tcc TtQbg rfv BE.

opoicog yo\Q TOO itgorspG) A^ftftarlip, lav cbto tcbv Bxccl F a'yd'y&iisv xa&srovg enl rrjv 4A t^v rs BZ 5

xal rrjv FH, serai dux rb xaQKMrjAovs atiras elvai,

<&g ^ FH rtQO$ xrp> BZ, ovt&s r\FE it$bs rrp> EB

[Eucl. VI? 4] CO&TS xcu', cog ^ vitb iv\v dtjrAijv Tr^g FAXQOS rfv vnb ryv dnt^v ri\g AB, ovrcog % FE vtgbg

ity EB' oitQ sdst, defeat,. 10

xccl VTav&cc ds ccvrod-sv TCccQaxoôvd'

j]FB 7tQi(pQicc ôV?; do&rjj xccl 6 Adyog 6 rijg v

rijg FA TtQbg xr\v VTtb rv\v

AB do^, xcclr]AB 7iQi(pBQia dod"rJ6rai.

pay ml rfjg oôtccg xccTCfyQCKprig &tt{&vg$E40tyg rijg 4B 15

xccl xcc&tov a%&far]g iitl r^v BF rijg z/Z ^ plv

1. FA] AT D. 2. ovTcog] corr. ex ov-coo A 1. 4. yap]

om. BC. 6. IWat] om. D. 7. cog] yivsrai cog D. 17 (pr.)]ins. D 3

. BZ] ZB D. wôg tr\v\ TCQOS corr. ex JTÔ D 8.

8. cbg] supra scr. D 3. 10. onsg i'^ft î|at] o>: AC,

7tQicpQiciv comp. B, om. D. 11. ?' mg. A.<5e']

^' D.12. ^] ^ Tf D. ô^^] Sod-sir] D. 6 (pr.)] om. D. 13.

rryg (pr.) SmJLfjv] ins. B 3. FA] -A in ras. A. FA -

14. ^B(pr.)] supra scr. C 2. 13. TIQOS rijv] con-, ex TIQ < D 3

.

14.^JB(pr.)]

etiam in textu C. ô^] del. B 3, do^Tjafrat D.

doQ"iJGT<xi] om. D.

74 KAlATAIOT nTOAEMAIOT

V7tb .Bz/Z y&vi'a rrjv rjufaeiav vnoreCvovGa rijg BF7tQi(paiag farat dsdo[ivr]' xal o'Aov CCQCC rb B4Z

7Ci df %al O r rijg FE TtQOg rfjV EBdtdorau xal ert % FB v&eta, do&?j6rat, xal

ij

5 r EB xccl f'rt (U?? ^ EBZ' nets xat, fad % z/Z

dfdorat^ 60fhfott& xcclij

rs V7tb E4Z YGWLK rov

avrov oQ&o'ycDviov xai Aown) ^ vnb E4B. G)6T xal

f\ABrovrav

10 iitwpv.VBt<t peyfatcdv KVX&COV ttQMpfyucu, &6T fig dvo

rag AB xal AF dvo ygcKpffaag rag BE nccl

Tiiviv aMtffag Kara, rb Z 6qiitov' fara) $

avrcbv ttaGGcov f][iixvKMov' rb d$ avrb xal iitl

r&v uarayQatp&v vitaKovfa&G).

15 AS'^GJ drf) on, 6 ry\g vnb rqv diTt^v rtfg FEcpQiag rtgbg ryv VTCO rr\v dnt^r\v rijg EA Aoyog

GvviJTtrai, ex r rov rijg i)ttb ryv ^nt^v rijg FZagog ryv vnb r$\v diithriv rrjg Zz/ xal rov rijg VTCO

rr}v dntkriv rijg 4B xobg rty vnb r^v diTt^v rijg BA.20 fttrjcp&a) yaQ rb Kwrgov rijg GtpaiQag xal faro rb

H, xal riffiotiav aitb rov H 7ti rag jB, Z, E ropagr&v KVX&CW

ijr HB xal % HZ xal

i\ HE, xai iiti-

A4 MfcfttiJGd'G) ual 6vu,7tiittrci) rri HBxal avrr] Kara rb S GrjUEiov, b^,oiG)g df

2. ago] supra scr. D 3. 3. oQ&oyojviov] Tglycovov D. 5.

0>CT KCCL, STCEi] &Gt' STtSl %CCi D. 7. OQ&OyCQviov] TQiydiVOV D.9. 'frfcbjji^a Kuta, dicciQEOW mg. B. 11. y^aqoftWg] corr.

ex yQK<p&i6ag C 2. 12. GT^JLBLOV'] om. D. 13. sldrrcov D.

] d' D. 14. vifaKovtG&G)'] vnci-Aov^cQ-co T\\LIV D. 16. rrjg- 17. dmtfiv] D, mg. A 4BC 3

, KSL'HI-VOV add. B 3. 16. EA]E4 B, y. so. B 3

. 18. vnb r^(pr.)] bis A. 21. ccnb rov H] an'ccvrov D. B,Z,E]BEZ D. 22.

rj (pr.)] om. BC. xat (tert.)]

$' Y.KI D.

MA0HMATIKHS STNTAJSEBS A'. 75

at 4F xal AT r^ivr(D0ccv rag HZ ncii

HE Kara rb K xal Ara 6> K A

7tl

dia rb v dvtilv

ivai l-jtumdoLS r<p r

rov AF4 roiy&vov 5

nal r(p rov BZExvxkov

, ijns Xi-

fev%&l6a 7tOll t<$

dvo Ev&Mag ras A%al FA diiyyiizvas 10

ras A xal

xata rb K Gyiietov' 6 CCQK rijs FA 7iQO$ AA6vvi\7trKi K r rov rijs ^K TIQOS K4 xal rov

rris 4 TtQbg A [p. 69, 21]. AA' fog [tv ^ FA 15

agog AA, ovrcog f] vrtb rrjv di7tA.ijv rijg FE ngbvitb rqv dinkey ri}$ EA 7tQi(pBQiag^ &$ ds ^ FK

, ovr&s n VTTO rr\v dirtArjv rife FZ 7tQi<pQCa.

vitb ryv diTt^v rfjs Zz/ [p. 70, 17], cbg

, ovrog 3}VTCO ryv dnt^v rfjs 4B 7tQi(pQLag yfQog 20

vjfb ryv dinkey x^BA [p. 72, 11]' xal 6 Ad^o? KQK 6

rijg VTtb r^v 8ntkv\v rijs FE itgbs rrjv vitb rrjv diithijv

rijs EA Gvvijjtrai, X r rov rijs vitb r^v dmAijv rijs FZ1. at] supra scr. C 3

. AP] corr. ex AT C 3. 2. TO]

to. D. GruieiK D. 8v&ia$ yivstca D. 3. Sid] coinp. B,di B 3

. 7. txievxfatocc] ante G ras. 2 litt. A. 11. A]corr. ex OA D 3

. 15. FA] corr. ex Fz/ D. 17. vno] suprascr. D. TTJV] supra scr. D 3

. EA] EA corr. ex Ed B,EA mg. B 8

. 18. K4] corr. ex KA B 3C 8. 19. Zzf]

AT. D. J] AC, corr. ex 4 B 2,A C 3 D. 20. AE -

21. r?)g] om. B, mg. C 3,8(ft mg. B

3. 20. Trfetg^tag] om. C 3

.

21. TTfc] corr. ex TT) D 3. rfjg BA] mg. C 3 alio atramento. 22.

Tfj? (pr.)] om. D. vTto (alt.)] e corr. D 3. 24. Ante E^

ras. 1 litt. A.

nobs rr\v vnb rrjv Si7tki]v rr}s Zz/ xal rov rijs vnb rrjv

dinkey rijs z/JB nobs rrjv vnb ri\v dinAijv rr^g BA.xara ra avra drj xccl (otineo enl rijs smnsdov

xara'yQcc(pijs r&v sv&si&v [p. 68, 23] dsfavvrai,, on5 Keel 6 Tifc vnb rv\v dnt^v ir\<$ PA TCQOS tv\v vjtb xv\v

EA A.6yos 6vviJ7tTai, x re rov T^S vnb

rijs F4 nobs tv\v vitb vfjv dnt^v r^g

xai rov rrjs vnb rqv dnt^v rijs Z5 ^6? ryv vnb

rqv diJt^v rijg BE' OCKZQ nooexeiro

10 id'. JIs^l r&v [israkv rov itiqiisoivov xal rov

Ao|oi) KVKhoV 3tOl(pQSl,G)V.

Tovrov dij rov frscaorjiiaros rtoosxrs&siiisvov noirjGo-

K itQcbrrjv rqv r&v noox6i,[jLSva)v TtsoKpsoEi&v ano-

ovrcog.

15 farm yao 6 di'

rcbv jt6A,G)v rov rs

xal rov dice yitG&v r&v

xvxhos 6 ABF4 xal rb

rov farjusoivov rj[it,xvxA,t,ov rb

20 AEP, rb ds rov dia [isticov r&v

%GtdiG)v rb BE4, rb dsEv\

xara r^v ICCQLV^V

avrcov roily, &6re rb pey B %iinBQLvbv rgonixov ELVCU,

rb ds 4 &Qiv6v, efaijy&a) ds Inl rys ABF

2. TTJS dB 8nt\i]v} supra scr. D 3. ij\v vno] postea

ins. A 1. 3. dij~\ de D. xal co<>-] in ras. A. 4. on] corr.

ex 8i6n D 3. 7. dutlrjv (alt.)] -i- corr. ex

7]A. 8. //Z] Z4 D.

9. TtQQSMiTo] corr. ex nQOHSi-cai TO D 3. 10. i'~\ C, dt,

~

om. AD. nsgi 11. 7teQicpQi&v~\ mg. D 3. 10. rov (pr.)] TOV

re D 3. 12. dj] om. D. 13. rr?Y] om. D. 23. TO] xai to D.

elvui roniKov D.

MAOHMATIKHS STNTASE&2 A'. 77

6 ;rcUo TOV AEF l6r]î0ivov xal eGto TO Zxccl aitfiA.rjyd'G) r)

EH 7tOi(pOicc rov dice [leG&v rcov

XVXkoV T[ir][lKTG)V VTlOXEL^BVYl A, Oi&V 0TiV 6

xvxhog T|, dice ds TCOV Z, H yfypagpO'ca yLsyfarov

XVX&OV JtQi(pQiCC fj ZJFf, Xdi JtQOXi6&G) 1T\V H 5

svêlv. jtQOi^cpd'oo dq xai Bvtav&a xccl

7tl Ttadcov r&v dôiov dsC&ov,f

iva

tavrokoywyiGv , oVt, orccv tag

1tQi(pQiCOV tyV&iG)V

,00G)V

7tl [lV TC3V 1tQiCpQiCOV TOiOVT&V (pa^lSV^ 10

fjrov peyfarov Kvukov rtQi(pQia r[ii][idra)v

T|, 7Ci d r&V V&iG)V TOiOVTCOV, QlKtVJ] TOV XVX&OV

7ti tOiVVV V KCCWyQCCCpfi {IfyiGTCOV KVXk&V iS

dvo ras A2> xcd AE 7tOi(pOiccs y^Qcc^^vca efal 15

dvo ij re Z xai i\ EB rfyvovGcci aMtjAccs Kara TO

H, 6 rils VTtb rr\v dnt^v rr\g ZA Myog Jtobg rr\v

VTtb ri\v diTthrjv r^g AB (SwiJTCraif

x r rov rijg vjib

rr^v diTtAijv rfjg Z ycobg rr^v vito TTJV dirthijv rrjg

&H xal TOV Trjg V7tb tr\v diTt^v rijg HE ycobg rrjv 20

vnb TTJV dixMlv Trig EB [p. 76, 3]. odXr\ [iv rijg

ZA 7tQiCpQlttg SiltM] U,OiQK)V 6TiV ~Q7t XCCir]

VJt

avrr)v v&icc T^îdTCov ^c, ^ d ri]g AB dirtki] xccra

TOV 6v[i7t(pa)vr]ii8'vov [p. 68? 4] v\\jiiv r&v ny ycobg ra

Ta k6yov poiocbv [i ft/3 ^ ? r\d' vit avTr)v Ev&sia. 25

~iwj ha v, xal itdfovr\ pev ri]g HE

6. 8r\] ds D. 9. dctv\ slot in ras. 1 litt. B 3. 10.

ij]

supra scr. D 3. 11. 17 T^Tj/Liaroov] 6 [isyiGTos KVK!,OS

. B, om. C.~

mg. B, om. C. 15. sla~\ comp. B, tfafo D. 16.

EB] BE D. 17. TtQbs vf\v\ TrôJarV D>, post 6 add. G D 3

.

19. <9Z] A, Z9 BCD. 24. nqog] corr. ex n$m C 3.

xa17

VTC avrr^v

fjtdrcov , r\ds r^g EB dntkj] ^LOLQ&V ^r xal

i] vii

avryv v&ia rîrj^drcov QX' ear aga dub rov r&v

QX rtgbg rd ^ Aa vs Adyov dtps^ca^sv rov r&v f ftgbs

5 ra QX, xaTafafastai, 6 Adyog r^g vTtb rr\v diTC^v TY\

Z agog rr^v VTtb rrjv dinkey rr\^ H 6 r&v ~QX

Ta xd Is v. xcct iGiiv 17 plv dmAij xr^g Z

pOlQ&V ^3T, V]$ VII

xalf)

vitb ri\v SuiK^

10 avr&v i6tiv xd Is v. &6rs xalf) psv dinki] rfjs

cbv 6nv xy t-91 v-01

, ccvrrj $j]&H

CCVTCOV Tajit eyyiGrct.

TtdhlV V7tOXl<3&G)fjEH XQl(pQLa

rfbv aU.G)v {IWOVT&V rcbv avr&v rrpj

15 EH yivstifttti UOLQ&V QX, r^v dl viC uvrriv ev&elav

vscy. sav ago, ndkiv dnb rov r&v QX

rdîrj K&. ve hoyov dq>^G)^Lv rov rcbv ^y vs *ty

rd ^Xy xara&i,(pd"tJ6rai, 6 Adyog 6 rijg VTCO ryvZ ngbs ryv vnb ryv dutlijv rrjg H 6

20 r&v ~$x ytgbg rd pf} d ^. XKL 6nv ^ vjtb rr\v

rrig Z r^rj^tdrcov QX' &6rs xalr\

vnb rr\v

rf)g H r&v avr&v 6rat,ft/3

a prj. xal17 p

aga rijg H nsgicpSQsias yioiQ&v iGtiv îd oTrj,

H r&v avrcbv x A -9"

2. git] Q- corr. ex o D 3. vn'] vno D. 3. T^ârcov] -v

supra scr. D 3. 5. xara/Ut'nrfTtu] /tfnrsrat D. 6. Z@] corr.

ex S& D. 7. Is v\ corr. ex iv ~vs D 3. 8. nsQupsQeiccs] -$

supra scr. D 3. d] d' D. 9. T&V] rov C. 10. vgj xg BC,

mg. v B. 11. v&~] vj] D. 12ji] A-9

1 v& in ras. D 3. lyytcra]

in ras. D 3. 15. S] d' D. 18. 6 (alt.)] corr. ex v C. 19.

(9H] 6>- e corr. D 3. 20. ngbg rd] con*, ex n$b GTU D 3

. 21.

mut. in sxarbv SMOGI D 3. 24. T] in ras. A.


rbv ccvrbv di) TQOTIOV xccl lid r&v xara [iQO$

xavoviov t&v xov rsrccgryiioQiov poiQ&v 9

twv oftotov rats &'

KKl S0TLV TO KCtVOVlOV 5

roiovrov '

2. sTtdoyiadiisvoi, sec. -i- corr. ex -rj-, D. 5.

A.

2-

p-aa- as 3. ~J

, .

o o

IS 3.

15^

fl rto to

-8 S.

^ 1? v^cd o So'if ^ '

(M <M ^J^

CQ

1QPM ~ao ^

>XJ3 VfiX ,

|S^^|^

3 53.

'ri

rH W **- "^11

<D <?*. lg

5 ^^

ifV _J . R"j ,H 3 X . 41

%r-, n-.fiP H_>>03 CO

a . 2 ^

MA0HMATIKHS STNTASE&2 A'. 81

*u,x

CJQ.CQ.QQ.5i X X xxx

o a CQ.B-jr? ft"

^ CO.

15r sr xI.

CQ.CQ.CQ.~i

IP IP IP

.XXX II: 1:1

sstS


xa

L<5

f

. IIspl r&v fV og&ijs rijs 6(pcctQa$ avacpoo&v.r

E%ijs dy

av sl'rj6vvanodefeat, r&v rov farjHQi,vov

nQi<pQi&v tag yivoiivas nr]favoryras vnb rcov

yQaq)0[iVG)v xvxAcw did te rcov n62,ov avrov xal r&v

5 di,do[iVG)v rov Ao|oi> xvuhov t[ir}[idTG)v ovro yap

f|ofti/, sv 0716601$ %oovoi,g fayjiEQivois tec rov dice

[isG&v rcov t,G>diG)v rpriiiara diA,ev6rai, rov r îs^rjî-

PQWOV 3tccvra%ij xal rov 7t' oîjg rijg GycciQas doi-

ovrcc di& rb xccl avrbv ror p6vov dia r&v noh&v

10 yQKyfG&ai rov fayiifQivov.

roivvy % 7t

tv rijs EHA dov k'tirco

rr\v E rov faypfQivov itQi-

15 Cp0LCCV VQLV.xara ra avra dy rolg k'p-

7tQo6&v 6 rijs wô tfiv dt,7tki]v

rf}s ZB JtQog r^v vnb rr\v 81-

itK^v ri]S BA Aoyog Gvvvptxai gx

20 r rov rijg &*o r^v dirthijv rijs

ZH xgbs ryv vnb r^v diJtAijv rijs H xccl rov rijs

vnb rr\v dmhijv rijs E itgbs r^v vnb r^v

rijs EA [p. 74, 15]. jAX_ji ^V rijs

dmhij poiQ&v itiriv ohfi 1% y, xal % vnb ccvrrjv

25 r^riîdrov o& /Ltd vy, 17$ rijs BA poiocbv ^ ft/3

st B, om. ACD. GvvctvacpoQ&v D.ov KVV.I.OV A, KVKJ.OV mg. pro scholio BC.. -v sv OJT-] postea ins. A 1

. 19. yldyog]-

1.

BCD, fcrmsQwov KVV.I.OV A, KVKJ.OV mg. pro scholio BC. 5.

ovrcos D. 6. -v sv OJT-] postea ins. A 1. 19. yldyog] -g in

ras. D 3, seq. ras. 4 litt. cvvfjnrcci] cvyKEtTui D. 20. t^g (alt.)

21. H&] supra scr. C 3. 21. ZH H&] mg. B 3

. ngbstr\v\ V.KL TTJS C 3

. rfjg H&] etiam in textu C, H0 in textu B.

xcu] yiccl s* D. 22. @JE] E@ D. 24. vno] A, vn BCD.25. BA~\ BA Sinl.fi V.

ft]corr. ex D.

MA0HMATIKH2 2TNTASE&S A'. 83

xalf)

vrtb avrqv ev&elcc rîrjîdrcov îrj Aa v' xal

7tv,kivj] [isv rijs ZH TtsQiysQSiccg SmKv\ \LQIQ&V QV$ p IK

xal fjvjtb avr^v sv&eta rîrjfidrov pt hoc 7

5 17ds

rijs H poiQ&v xy t,& v& xalfj vjcb avrijv sti&stci

nd Is vj. sav CCQCC aito rov rcbv Q& pd vy 5

ra ^ ha vs k6yov fafdfaapsv rbv r&v ptf Aa is

agog ra xd Is vg, xaratei,(pd">j6T()it, v^nlv 6 rtjs i)Jtb

ri\v diic^v rils E jc^bg rv\v vjtb iv\v diTthijv xv\

EA Aoyog 6 rcav vd v$ x$ agog tec ptf A Is' 6

d' avrbg Aoyog 6zlv xal x&v v$ cc xs xgbg ra ^x. 10

xat iGtiv y [isv dwr/tfj rijg EA [IOIQ&V QX, % d' bit*

avrty ev&sla r[ir)[idr(DV 'QX' xali]

vitQ x^v diit^v

aga rrjg &E tpqp&iaw. rcctv avr&v etinv v$ a xs.

xalfj pev dinAij rijs E 7tQi(pSQias stirat, poi-

ve ft fyyitfcct) f]ds E r&v avr&v xj v. 15

TtdAlV VTtOXSlG&G)fjEH 7tQl<pQia IIOIQ&V |, G30r

rcbv ahkcov iievovr&v r&v avrcbv ri]v [iv diTthijv rijs

ZH tt$L(pQias yiv<5ftai iioiQ&v Qkri v& pf! xal TYJV

vjt avryv v&tav rinqiidr&v gift xy vg 9 ryv d

rijs H 7tQi<pQias [loigcov JLtao 7^ xal rv\v #' 20

avrqv sv&etav riirjpdr&v yifia

jil^.av aga aito rov

rtbv pO- |itd vy ngbs ra ft^ Aa v hdyov acp&G)[jiv rbv

r&v Qi/5 xy v$ rtQbg ra pfi a fZ^, xaraA,icpd"tJ6Tai 6

rijs VJTO rfv dntkriv rijs E ôyos XQOS rr\v vjtb r^v

1. vno] A, vn3 BCD. 2. QV$ ft a] B, ipv s jta A, QVS Ji ft

B 3, pvg fta C, QVS ftg|5 D. 3. vno] AC, corr. ex vn' B, vn' D.4. H&] H nQicp()ia$ dinhcccicov D. vno] AC, vn' BD.

5. lav] bis D, sed corr. e-91

] corr. ex 90 D 3. 7. 6] in

ras. C. 10. %cu'] %al 6 D. xs] corr. ex vy D 3, vy in ras. B 3

.

11. vn'~\ corr. ex an' C. 13. r^rjârcov] supra scr. D 3. xf]

corr. ex vv D 3. 15. Post p ras. 1 litt. D. 20. H} AB 3C 2

D,ZH BC. 7tQitpQEi<xs] om. D. 21. apcc] aga nuliv D. 22.

Id] corr. ex ^^ D 3. Adyovc, a eras., D.

84 KAATA10T ITTOAEMAIOT

rr\g EA 6 r&v $ ft p rtgbg to, Qifi ny vg' 6

$' txvrbg rovrcp Acfyog farlv xui 6 tcbv pa KTJ x

ra0jc.

Hat atfTtv ^ VJTO r^v diitH]v rijg ^cpQiag ev&sia r[ir][icira)v pit' entire xal

fybttb rr\v

5 diicKriv rijg E r&v avr&v fativ QCC mj x. KKI % [isv

E 7tQi(pQiag stitcci, [IOIQ&V gls MJds

v\E r&v afa&v v pd.

)on rb yfev a aitb rov

da)dxcctrj[i6Qi,ov rov diet [izG&v r&v

10 xvxAov 6wy%QOveZ rots rov farftisQivov xara rbv SK-

v r^tjâîv x~v, rb

x& vd, 7ti,dri3tQ a[i(p6rQa' xal rb rgfaov $ dÂovdrt

rats Aomccis ffe tb

15 A/3 T% dt,a rb xai oAov TO rov Ao|oi) xvxhov rrao-

rrj[i6at,ov oAc? red rov far][iQi,vov

rovg dt,a

rbv ccvrbv d?) rooftov rr\ 7tooxi^,vrj defiêi xar-

axohov&ovvrs &Vttoyt4<xp&m xal rag xa6r'fl dfxa-

20 (JLOiQiy rov Ao|oi) xvxAov 6vy%Qovov6ag 7tQt,cpQiasrov i&ftifQ&ov di& rb rag k'ri rovrcov [iMooâfdrfyccs

Lv r&v itpbg oâ^v TCCCOKV-

ovv xai ravrag^f

iva

Kara rb 7iQ6%eigov fyopev, iv otioig %oovotg ccvrcbv

2. J<mV] -v del. C 2. x] D, supra scr. A 1

,in ras. B 3

,

^ C. 5. T&V 6. @E] D, om. A, mg. BC. 5. IGXIV\ecToci D. 6. KQCC] D, *. BC. 8. 8t8emxai\ COIT. ex ê-

SfKZKi C 2. TO] supra scr. C a

. 10. rotg] om. D. 11. tie]

Om. BC. 14. Gvy%QOVLGl] BC, GVV%QOV16SI A, 6VV%QOVi]6i A 3,

cvy%()ovi]6t, mut. in Gvy%govit D. ÔLTtccig] fainovGcas corr.

ex iinovGKis D. 15. rot?] corr. ex TO C 2. 16. 6vy%Qoviv BC.

19. SfnaôiQia] corr. ex dfxaTrjfiopta D 3. 22. TTÔS] corr. ex

D 3. 24. TiQo%iQoxov D, TTô^stôTaTov D 3

.

MA0HMATIKHS 2TNTAEE&S A'. 85

rov r [i6r][if}oi,v6V) 035 (pa^v^ itavra%Yi xai

rbv iit opoHjg rr}s Gtpcciocts boi&vrcc di^v6rai^ rrjv

riv anb rfjs TtQog r& farjufoiva tf^/m'co

flV OVV JtOCOrr] 1t8QiB%l, %QOVOVS & 1<, fj

$ $V- 5

& tf, fj$

ccvrb rov a'

'Y\$ teraQ

81 fxrr 6vov$ I Ig &6rs xcci rov

10

ds fid6[ir) %QOVOVS TAd,L ftj, fj

$ fvdrr) %QOVOVS i VE, fag

xal rov pey rofaov xal nobs tot$ raoitwols 6r][iioi,s

rovs kfi 7$ %QOVOVS., oAov d rov

rovs 9 (Jvôavog. 15

avr6&v cpavfaov, on xal y r&v koiitfov

rd&s n VTI) rvy%dvi ovGcc, ndvrcov

xcctf Ka6rov r&v avr&v Gvuficuvovrcov diet rb rr\v

0(pcclaav oofi-qv vitoKtiGftai,,rovrfanv rbv i6^Qivbv

nobs rbv boiôvrcc. 20

3. TO tGr}[iQivbv Grjpsiov D. deuceILOLQLCCS] post pr. -a-

ras. 1 litt. D. 5. nsQi^si] seq. ras. 1 litt. D. I 17] i'\j]

corr. ex\ii]

D 3. 9. ôvovs (alt.)] -ov- ins. D 3

. tg] corr. ex

ic D. codrf] o>s D. 12. evdtr)] & C, v supra add. D 3. 14.

ScoSmcttriiLOQlovs, -g eras., D. TOVS] om. D. 17. OVGK]om. D. 19. rovrtcTiv] -v del. C. In fine: Klccvdiov

IlTotefiKiov pa.&riiLctXi"A&v (-bv C) a' ABC, T&O$ TOV

mg. sup. D 3.

B'.

Tads V6nv v rc5 p' rqg IIrofo[icciov

Gvvrd,G)g'

5 /J'. yt&g do&vrog rov rv\

aC K7toA,oc[ipav6[ivcii, rov

vito re rov i6r\[iQLVOV xccl rov Ao|oi) KV

avr&v vxoxi,[iVG)v rb ^KO^CC rov itohov

10 didorai, xal rb avdnccfav.

d'. it&s ZitikoyitirsoV) tiGiv xal 7t6rs nal TtoGdmg 6

ijUosf

yCvrai xara xoavytfv.f

. nag KTtb r&v KKiîBV(ov oi /loyot r&v yvwpov&v

jtgbg rag farj(ieftv&g xccl raomxag iv rcclg

15 [ifGyiifiQfaig 6xi,ag Aaiipdvovrcu.

sr'. x&6ig r&v Kara, 7tccodMr]A.ov touopufaanr.

'. 7tol r&v iitl rrjgi

yxxhi,[ivyg Gcpcu'oag rov dice

r&v ^(pdicw xvx&ov xccl rov i6y[iQi,vov

20 vj. xs<5ig xavovi&v

avcctpoQ&v.

_ 1. B'] om. ABC; Khccvdiov nrotepaiov iiaQ'^cixiY.&v D,

{3add. D 8

. 2. rfjs 3. 6vvrdea>] QiQMtp r&v UTotefiaiov

paQ'JULoiTiKMV D. 6. o^tôvrog] OQIÔVTOS V-DU rov D. 11.

riGi D. 15. (iscri^QLvats Gv.iu.is D. 17. lyttextafpfrijc AC.20. Hccvovfov D. SBKccpoiQiav] om. D. 7tccQciM.rj1.ov] -Hov

comp. in ras. B.

KAATA. HTOAEM. MA0HMATIKHS TNTAgES B'. 87

91

'. JtSQi rcbv xara {isgos rats avayogaisfrovvr&v.

t,' . itol r&v vitb rov dia peGwv r&v

Keel rov (i6r][if$()i,vov ywojievovIK' . 7tol rcbv vrtb rov ccvrov Ao|oi) xvxAov Keel rov 5

'. xsol r&v Ttobg rov avrbv xvxhov rov diu r&v

rov bgi^ovrog ywoyisv&v y&vi&v xal

r&v 7tgoxsi,[i8VG)v y&viGbv 10

XCCi TtSOiCpSOSiGJV.

a. Tlegl rijg xcc&6Aov ftstisas rijg

sv r& Ttgcorc) rij$ 6vvrK%s&$ roc rs

ytsol rrjs r&v oAav 6%tiG)s xara rb K<pKkcu,G>8$ 15

Kcd o6cc av ri rCbv 7t 60-iHjg

itgbs tv\v r&v v7toxi,iiVG)v

7tiQa66[Ji9'K Kara rbfijjijjs

xccl r&v

rqv lyxwliyizvriv Gcpccioav ^v^ccivovrcov ra

xvQi(brQcc ttukiVy <$$ Vi ndki,6rcCj Kara, rov sv^ra- 20

vravd-cc (^ ro {ilv 6ho6%QK>s otpatAov TCQO-

i, rovro <5nv, on rijg y^ ?$

1. itccQccKcdovd'ovTcov D. 7. T&V (pr.)] v B. 8. nut] D,xal r&v ABC, x&v del. A 8

. 10. Kara] r&v nurd A. yco-

via>v\ r&v ywvifav A. 11. In fine add. xeqpaXcaa ly D. 12.

ju-atbji^arnt c5i> ^ supra scr. B. a'] B, om. ACD. 14. rs\om. BC. 17. r&v vnoKEiiitvcov] vno%i^vriv D. 18. 177^-caro D. 22. ro] r- in ras. A. blo6%Qt<s B. 23. rovro

lortv] rovrecriv D. rsGGaga] t^GGSQa A, A D.

rraorrjÔQLa ra yivoêva VTCO rs rov Kara rbv

KVKÔV Kal vbg r&v did r&v

avrov yaa(poiiva)v rb t% Ka

vnb rov sroov r&v poofi&v

5 rovro d' av îdhcfra ysvowo cpctvegbv [snl [isv rov

rovrstinv rijs anb ^le^^^Qiccs yfQog r&g

ttccoodov., dia rov Ttavraî] rag &v ral$ faq-

liQiat,$ rav yvcoôvcsv yiyvoîsvccs fU&rjufaiv&g Gxias

XQOS aaxrovs aisl 3toil6&cu ra xooGvevcfeis teal

10 pydsTtore agog [LetiyiipQiav, exl ds rov ntfxovs, rovrstinv

rtjg ajcb avarok&v nobs dvGp&s xagodov, dice rov rag

ccvra$ eKkeityei$, [idfoGrcc de rag 6eA,r]vi,ccxd$) TCCCQCI rs

rots lit* CCXQCOV r&v dvarohMcbv [LSQ&V TrjjgKCC& f}H>&s

ofaov[ivr]s oiKovtii uccl ttccQa rolg in ccxocov rcov

15 dvrincbv Kara rbv avrbv %$6vovitkeov dddsxa Ttyorsoetv rj

vtirsostv (ba&v

avrov Kara [irjxog rov rsraQrr^LOQiov dcodsxacooov

diddrrma itQie%ovro<2 , ETtsid^TtSQ v(p evbg rcov rov

i<5r][iQivov fjuwvxMcov dfpoot&rai,. r&v ds Kara

20 dtpsihovrcov &G)Qr]d'rivai [idfaGr av rig

xobg rr^v ytQoxi^vrjv XQayptctefav CCQIIO&IV ra

j5oaiorQG)v rov

v avrtW]

-v e corr. D 3. 11.

ano] an' D. 12. pdhGra] ft- in ras. A. rag'] om. D.15. SVXM&V] Sv- e corr. A; UVTIK&V C, ^ supra scr. C 3

. 16.

OQtov C. 17. Post rov ins. r^g yfjs mg. pro scholio BC.

rTaQrr][JiOQiov] rraQrr]ÔQiOV rf]g y^g A. Scodwdagov] corr.

ex ^fxacopov A4. 20. pdliGr' av] pdliGTa D. 21. ra\ corr.

ex TO BC 3. 22. TtvxZcov D. 23. xorTa] corr. ex v.a C 3

,xa

corr. ex xcu B 2.

MA0HMATIKHS STNTAEE&S B'. 89

6' ittiV) oôv rs oi rtohoi rijg XQaryg (poQag rov dgi-

frvrog aysGrujxaGiv, i} o6ov TO Kara, xoQvtprjv 6rj[iiov

rov farjpSQivov xara rov (itfr][i{$Qi,vbv xvxkov, xai\

olg 6 ijfaog Kara xoov(prjv yCvtrai, icors xal Jtotidxig

rb roiovro GvpfiaCvGi^ xal rivsg oi koyoi, r&v farjiisgivcor 5

xal rgoitiKcov iv ralg [i6r][i{lQtai,s Gxi&v TtQog rovg

xal mjMicai, rcsv [isyfarcw rj &a%irag fariiLsgwas ai v7CQo%ai^ xccl

rag Kara HSQOS avô^LG)6i^ r&v

In r itQi rs ras GvvavaroAas xal Gwyxa- 10

rov re foqiiSQivov nal rov Ao|oi) xvxAov xal

ra idico[iara xal ra psyiftvi r&v

vnb rcbv xvQiorQCov xal [i&yforcov

do&evros rov rijs iifyiGrrjs fjpSQag 15

ai aitokayifiav6iivai, rov dotôvrog

7tQt,cpQi,ai vjto r rov l0r]îQLvov xal rov

Ao|oi) xvxAov dudovrai.

nQoxffa&G) drj xa&oAov r&v vnodsiyiidrov VKv 6

dicef

P6dov yoacpoiifvog jtaodA.A.rjA.os r& far]iiQivG) Kvukos, ^Qitov rb iikv \aQâ rov TtoAov [toiocbv fariv Ag; f)

df

1. <T] Ss D. Tf] om. D. rov] anb rov D. 3. PostM _

add. aqpf'ffTTjxfv mg. A 1

, aqptcrrj mg. B, ^ <xcpGri]Ka6iv

mg. C. 4. yfyvsrcii D. xca] xal nov V.KI D. 5. roiovrov D.

rives] rivsg re D. 9. avo[ieiwGeis] -v- supra scr. C 2, pr. e

ins. A 4. vv^rjfi^Qcav] corr. ex vv%Q"r\êQiv&v D 3

. 10. GVV-

uvcirolas] corr. ex Gvvavuro7.LV.a,g C 2._ 12. nsQi'] oca negi D.

Post KCCI del. v.ctrd D 3. 15.

j3'J ^ B, om. A CD. 16. at]a- in ras. C. 19. xa-Ooôv] inter duas ras. 8 et 3 litt. D.

20. *P68ov] 'P- in ras. A 1. nagdHrilog} 7ictgdl\r]lo<s xvxAog D.

KVY.3.G) D. 21. ILQI.Q&V} ras. 3 litt. A.

90 KAATAIOT IITOAEMA10T

G)QK>V fayiiSQivcov id/.', xal E&TCO

[lev xvxhog 6 ABP4, oo^ovTog de

XOV r][ll,XVXhl,OV TO

BE4, xal

5 VOV 116V

b[lOLG)g TO AEF,6 ds VOTIOS CCVTOV

TO Z. VTtO-

ds TOV dia

TG)V

TO

VOV TQ07CMOV

xvxhov TSTccgTrjiiOQiov TO

10

TOV H,15 dia T&V Z, HZH. dsdod&a) ds TtQ&Tov TO peyed'os Tr\$

)XCCl 7tQOKEi<5&G) TYJV EH TOV 6()%OVTO$ TtSQL-

EVQEIV.

7tl TOiVVV % TJJS GCpKiQag GTQOCpri 1tQl TOVS TOV

20 l6rm,eQt,vov it6hovg aTtOTefaiTai,, fpavsoov, OTL sv TG>

avTG} %QOVG) TO T H Grjiistov xal TO xaTa TOV

Qivov E^TKL^ xal 6 ^v ait CCVKTO^^

Tijs VTtQ yfiv iiEGovQavvJGE&s TOV H XQOVOQ 6

6T\V V7CO Tijs A TOV i6^^lOiVOV TtEQl-

25 <pQiKg, 6 d' aito T^g vitb yi\v [i6ovQavrj<5EG)g

4. xat 6. AEP~] supra scr. D 3. 6. ART] -P e corr. C.

13. ScvuTsMav C. 17. EH TteQicpfysiccv] HErov OQifrvros D. 18. EVQSIV] add. B 2C 3

. 20.

-st- corr. ex s A 4. 22. ABTJ] corr. ex Tz/, AB D 3

.

IWca] SGzai dr]Jiov6zi Kivovfisvrjg rf}s GcpctLQccg D. Kit']CCTCO D. avccTolris] -lf\- renouat. D 3

. 23. XQOVOS] comp. B,mut. in %o6vovg C 2

.

MAGHMATIKHS STNTABE&S B'. 91

rilS avccroAijs 6 7tais%6iivos vitb rijs F.ds scfnv, on xcci 6 fisv rijs qôKS %Q6vo<3 6

6rlv rov vitb rijs A 7COi%oîvov^ 6 ds rijs vvxrbg

6 diTthcctifav rov vnb rijs F TtQi%o^vov^ eyte^TCSQ

xccl x&gls tu t vitQ yi\v xccl ra vTtb yijv T[iri[iccta 5

rcbv jiaQaMtfAov red i<5rniQivG) xvxA&v rtdvrwv

lLlrai VTtb rov [i6r][if$Qivov.

dltt $ TOVVO Xaifj [lV E

ov6a rov diuyogov rij$ ifajjlkfii

nciQK rqv farjiisQivrjv fita? [iv &QO.Q xal d' ywrai 10

xara rbv vitoxiiivov JtccQaMrjAov, %QQVG)V d dyAovori,

Irj jilf, .fjds Aoirtrj fts rb rfragrrjiioQiov ^ A r&v

avr&v OK T. 7Cidri ovv xara ra avrd rotg

artoddi, /

y[ivoi,s i$ dvo [ifyfar&

rag AE Kal AZ dvo <

yiyoa^vccL ffalv ai EB xai 15

Z rspvovticci, aMijAccs xara rb H, 6 ri\g vitb rv\v

rrjs A jtQog rqv V7tb rrjv dutAijv rijg AEGvvijitrcii, x r rov rijs VTCO rr\v dt,itA.ijv rrjg

Z Jiobg rqv VTtb rqv diit^v rij$ Zif xcd rov rijs

vjfb ri\v di,ithijv rrjg HB TCQOS rrjv vnb r^v diyt^v 20

rfjs BE [p. 76, 3]. cUAo:f\ psr rijs A

ftirw opf} A xalf) VTtb avrqv

~Qi/y Ag vd, ^ ds ri\g AE poiQ&v ^r xali\

2. %QOVO$] mut. in %QOVOVS C 2. 4. Post 7tQie%o[ivov del.

7tiSr] TfSQisjô^vov A. 5. t(n^fiaroi] corr. ex r^Tjârcov D 3.

6. T&V~\ om. D. -Avnlau D. 15. AZ~] corr. ex ABZ D 3.

16. Z@] corr. ex ZH& D. 17. A] -A supra ras. 1

litt. D 3. T?)g(alt.) 19. dmlrjv] supra scr. D 4

. 17. AE~\EA CD 4

. 21. &U' B. Post iti-QL<pQeias una litt. (t?) ma-cula del. C. 22. UTTO] ABC, vn C 2D^ 23. rfji^KTcov

-

p. 92, 1. QX~] bis C, corr. C 2. 23. ]

in repet. corr ex

Jig C. AE] AE Sinlfi D.

VTt ccvrqv v&Za tftrflufacw ^, xal itahiv % plv rijs

,QIQ&V pjr %al % vTtb avirpt sv&eicc

ds rijs 2.H poiQ&v pA/3 it, % xccl % v

jv v&ta rprindr&v Q& ftd vy' sav &QO. artb rov

5 Aoyov n&v Qiy A vd agog ra QX acp&K>iiv rbv rCbv

Q% rtQos tec Q& [id vy, xccTafaicp&riGMcci, i]îv 6

vnb TÎV dL7Cki]v trjg HB TCQOS rj\v V7tb rr^v

rrjS BE Aoyo? 6 T&V ^yy ^vs wy ngbg ta (M. XKL

r\ vrtb ryv dijt^v v^g BE tCSQUpeystegi fad

10 fjLOQiov rvy%KVi) xpvipcatav ^sc* xalfyvnb rqv

CCQCC rijs HB r&v avr&v faxiv ~^y v wy'

yS BHavrr] $

rjBH r&v ccvr&v *

xccl tomy KQCC

HE roiovtcov xatahsiiterai, A, oitov Itixlv 6 b

15 T

y'

'

. Hag T&V avrcbv vitoKi[iVG)v rb k'âg^La rov

didorai xccl rb

dq itdfav rovrov ddoîvov xal rb

rov nohov kaflelv, rovrs'tinv rr\v BZ 7lQi<ptysiav rov

20 ii6r]ii(lQi,vov. yivsrui roivvv Inl rijs avrijs

6 rvls vnb rfv diTtAijv rijs E nobs rr\v VTtb rr\v

1. T[ir)[ictTcav px] etiam ing. C 2. r^g] corr. ex rr\ D 3

. 2.

vno] A, vit' BCD. 3. QJL] corr. ex pop A. __vno]AC 2

,

V7f} BCD. 5. ply] -i- supra ras. 1 litt. D. vd] corr. ex

v\ D 3. 7. rfjs HB~] supra scr. C. 8. y] post 9 ras. 1

Htt. D. xy] B, xy?A, xs CD; sed cfr. p. 93, 10. 11. xy]

%y?A, xg BCD. 12. BH] HB D. poiQai D. 13. xat]

corr. ex i] D 3. 14. 69^001'] -v supra scr. C 2

. 15. OKSQ] suprascr. D 3

. owep ltf det|at] o):oo ABC. 16. y'] y B, om.A CD. 18. dr/ TfdHiv] corr. ex driniriv C. df

fteVov D. 19. BZ] ZB D. 21. E@] E D.

MA0HMATIKHS STNTASE&S B'. 93

rijs A Ao7>0 (fwrfpfdvos ex rs rov ri}s vnb rrjv

rrjs EH nobs rr\v vjtb ri\v diTtAijv rijs HB xccl rov rrjs

rr\v diithijv rijs BZ nobs rr)v vytb rr\v

ZA_ [p. 74, 15]. AA' fj plv dutMj rijs EBAf A xal

r\vnb avr^v ev&sta rîrj^drcjv Ay Ad

de diTtM] rijs &A ILOLQ&V Qpfi A not ^ vitb

T(ir}ndtG)v ~gi/y AJ vd, xal ndfov y per

rfjg EH poiQCbv % xalj\

vjtb avrriv evfteicc

|, ^ d diTthi) rfjs HB poig&v ^ xccl

sv&sta r^^drcsv qy w wy' lav KQO, anb rov Aoyov 10

r&v A^ Ad x/3 agog ra yip AJ i/d dtpeA&nev rov r&v

f ^6? ra oy ve %y, Karuhei(p&ri6er(x.i 6 rife vô ri)i/

dmhijv Tys BZ ytobs r^v vito r^v dtTt^v rrjs ZA6 r&v o Ay syytfra Tfobg rot QK. KKI i<5riv

r\ vTtb rr^v diTt^v rijg ZA jtQiq)Qias r^rjfid- 15

r&v QK' xccl vrtb rrjv dm^v CCQK rrjg BZ rcbv

avrCbv itinv o Ay &6rs xcclf} pv dinki] rrjs BZ

rtZQMpSQstccs farcci noiQ&v o/3 a, rjde BZ r&v avr&v

Ag h'yyi&ra.

itdhv 7tl rrjs ccvrfjs xccrccyQcctpijs dvdrtccfovfj [isv 20

BZ nsisEicc rov sâccros rov it6kov

1. 6vvr](t[ivos] 6 cvvriyfitvos D. 2. EH] HB v.ccl rov rr]s

vnb XT\V dinlfiv tfjs EH BC^corr. B 2. nôg HB] del. C 2

.

4. rf)g(pr.)] bis D. 5. ^] -înras.A1

. vn D. avrrjV]corr. ex nf C. fu-9-fta] in ras. C. 6. vwd] mut. in vn' C 2

,

v?r' D. 8. Ante f ras. 1 litt. A. vn6~] mut. in vxc* C 2,

vn D. 9. Post 1 del. H D 3. HB] -B in ras. B; #M C,

corrigere uoluit C 2. vn' D. 10. sav ago] bis D, corr. D 3

.

13. BZ] ZB B. 14. &7rw>] -v del. C 2, comp. B. 18. sarcti

\L iativ D. o|3 a] a in ras. A, corr. ex o |3a D 3.

20. TTeoff TOV s|a(âTOff rov nolov do&svro$ rb ftgyf-d'Off rijs

(LifyiffTTjg r)(jiQKS SiSorccL mg. pro scholio B. 21. BZ] -Z in

ras. A, ZB D.

psgsias.

nb ryv

^ntKr^v


poio&v A, nQOKi<5&& ds svostv rb did-

A,a%i6rr]g T) ^Lsyidrrig fjfieoag nagd rqv

rovrstfriv rrjv dinhijv trig EroCvvv did rd avrd [p. 74

? 15] 6 rijg vnb

5 dinAijv rijg ZB nsoicpsosiag ngbg rrjv vnb rqv

rijg BA A6yog 6vvr}ii[ivog x rs rov rijg vnb rr^v

dinAijv rijg ZH nobg rr\v vnb rrjv dinAijv rijg Hxal EX rov rijg vnb ^v dinhijv rijg E nobg rrjv vnb

rqv dinAijv rijg EA. aAA' ^ VLGV dinky rijg ZB10 [loiQcov fariv oft xai % vnb avrr\v svftEla r^^drcov

o A/3 y, ^ $ dinhij rijg BA [toio&v ^ xalj] vnb

avrjjv evfrsta r^^idra)v ^ d vg, xal ndAiv

rijg ZH [loig&v stinv pA/3 1% K nalf) vnb

\v sv&sla rpyiidrcav ^^ fid i/y, 17ds

15 H [loiQKtv ftf ft/3 ji xalfjvnb avryv sv&sta

r&v^Ji/ij

A,a vs' lav ciga dnb rov rcov o A/3

9? d vs Adyov dcpE^co^isv rbv r&v pO1

^d vy ngbg

^ Aa v) xaraAsitpd'YJo'erai r^^lv 6 rijg vnb rr^v dtnJ

rijg E ngbg tv\v vnb rrjv dmAijv rijg EA A.6yog 6 ri

20 A Id wy nobg rd 9? d vs. KOI snzidri 6 avrbg

stirlv fyyiGra xal rcbv A^ Ad ngbg rd ^5c, ^ ^ V7t(-

6. >l6yog] Myos 6 D. 8. SinJUjv'] Si,- in ras. A. 10.

D. vn' D. vnb UVTIJV] vn' CCVTIJV corr. ex vnb xr^v

11. y] seq. ras. 1 litt. B, corr. ex A D 3, y 8 AC, 8 del. C s

-UTTO] mut. in vn' C 2,

-UJT' AD. 12. piv\ -i- in ras. A 3.

6nv\ om. D. 9^j3] Q- e corr. D 3. VTTO] mut. in vn' C 2

,

vsr' D. 14. pfl] corr. ex jlv D 3. 15. j*p] -|3

e corr.D 3.

jiZ]

^ D, (i add. D 3. -UT^] mut. in vn' C 2

,VTT' D. 16. y] corr.

ex A D 3, y ^ ABC, sed d punctis adpositis del. AC 2

,eras. B.

7T(>6s] ngbs TO. D. 17. $] postea ins. C. fid] corr.

vd D 3. 19. &E TT)S] mg. A 1

. 20. xy] supra_scr. ^ C 8.

v.ccl inziSri] ensl S' D. 21. TCOI>] 6 TCOV D. W] 'ku seq.

ras. B. 9f] S' D.

rijg EA rîrj^drov <5rlv psc, Gwdystai,

xalYI

vitb rrjv 8i7t^r\v ri\g E r&v ccvr&v Ay Ad'

&6T XCCl J] dlTt&fl rfjg E 7tQl(pQiag fJLOLO&V {IBV

6rai Af A fyyitircc, &Q&V ds far][iQi,v&v fiL'' OTtfo

$1, dft^CCi. 5

XKTCC ra CCVTK d dod"^6rai, xccli]EH rov o^t-

JtQL(pQi,cc diet TO xal tov Ti}$ VTtb ri]v dLTt^v T^g

agog ^nv ô rnv dMki]v ri]s AB hoyov ddo{ivov

[p. 76, 3] x T rov rrjg vitb tr\v dnt^v rijs

Z jtQog r^v VTtb TTJV diitkriv r^ H deSoptvov xal 10

CCVTOV xal % rov x^ VTtb rrjv duit^v r^g HErtfv vitb rfjv din^v rij? EB, 6}6r xal rijg EBlivr]S xarccAirt6&ai, xccl rb rr^g EH ^yf&og.

<pccvobv d',

ort?xav

[ir}rb %i[i()i,vbv

6r][iZov vrtod'G)iLd'a rb H, r&v ahhcov de n rov dia 15

r&v ^(pdi&v xvxAov r^rjîdrov ,xccrcc ra ccvra

XCCTQtt rCOV E XML EH 7tQl<pQElK)V dod"lj-

taofxrid-fiiwav T f)[iZv dia rov rrjg

xccvovtov r&v d7foAaâvo^vov rov

7tOi(p0iG)v vq) xd<5Tov rîtjârog rov dta [ifacov 20

r&v c?dtW xvxl.ov xal rov fayiifoivov ,rovrfanv

r&v oftotov rri H jtoi,(p0La^ xal

3. ftfV] om. D. 4. 07tQ t$i dsi&i] om. D. 6. n&sdo&evtog tov l|<^funro( rov nolov SiSorca r\ (ji8Tcc^v rov kr}-

(jiBQLVOv v.a.1 rov >lo|ou tni rov ogifrvrog nsgirfigsiK rag. B.

9. ,xiqv _ 11. &_] mg . C 2. 10. Z@] Z D. Z 11.

rfj$ (alt.)] om. B. 10. rfjs] om. A. dedopevov v.al ccvrov]om. C 2

. 11. $yi] om. C 2. t% (alt.)] om. A. HE] corr.

ex NE C 2. 12. EB(alt.)] BED. 13. xara^wrfGât] mut.

in v.arKUTtiGâ.1 D. xat] om. D. 15. aHoov] -v add. D 3.

18. nQotnriQ-tpiv&v] -i- mut. in f C 2, TtQOSKrtQ-si^vfov D.

TS] yg D. 20. vcp'~] VTCO corr. ex vn' D 3. to-D] om. B,

add. C 2. 22. TTJ] rng C. TCfOLfpeQficc] 7tfgicpQia)v at D,

ccl del. D 3.

96 KAATAIOT nTOAJEMAIOT

rog [lev avro&ev rov ra vitb rcbv avr&v

yivotisva rîtjâra rov dia

a7t%ovra rov avrov roonixov

Grjfisiov, rag avrag xal iitl

5 ra avra [isoy rov

iioislv rag rov QQi&vrognod ra rcov vvft&yii

l'0a sKarsQa sxaregois r&v

rovrsGrw ra l'6ov

W

10 rov xal ra VTCO r&v focw itao-

aMtjhcov yiVQ\itvu, rovreduv ra faov a7te%ovra rov

avrov faruasQivov 6vnistov9 rag rs rov 6o%ovrog XSQI-

(peaeiag l'6ag sxarsQco&sv rov iGrnasQivov Ttouelv xai r&v

wxfHjflfyaMf svaMa% i'6a ra [leyed"*} r&v avoôCov. sav

15 yao iitl rijg sxjcsiîsvrjg KarayQacpr^g VTtod'&iLsd'a xal rb K%a&' o reîvsi rb BE4 rov boi&vrog

b I'Gog xal ytaQdAkqAog red dia rov Hxal 6vvavaitAr)QG)6a)iisv ra HA xai KM

r[itf[iara ivukKofc, ual i'6a drjkov6r

20 did rs rov K xal rov fiogsCov itokov rb NK$reraorrjiioQiov, i'6ai psv faovrai ^ [lev Arri &r dia rb exarsoav txare'oa rav AHxal MR b[ioiai

slvat,, xaratei,(pd"tJ6rai, ds xal ÔLTtrj ^ E& homy r\

E& fay, ysvtfGovrcci ds xai dvo r

ft&>] om. D. 2. yivofifva] ysvofisvcc D. 7. Andel. rd D 3

. 15. xca] supra scr. A. 16. BEom. D. 17. xca'J om. D. yeaqpop-aW] corr. ex ygcccpopsvov

20. Ante SLOC ins. V.OLI comp. C 2. tb NK1~\ corr. ex r

KB A, corr. ex rb KB B 2;rbv KB C, mg. TOV; v mg. add. C*.

21. tWt] corr. ex i'cc, B 8. ph (pr.)] om.

D^. A\ A D.

C. 22.ti[i\

xai i] Halrna. S-AKTEQU] corr. 62

D. 23. T$] corr. ex rfjs D 3. 24. fffij]

corr. e:

i'crjg D 3. y.at] om. D.

MA0HMATIKHS 2TNTABE&S B'. 97

rcov EH xal EK% at dvo per ntevgal rcclg dvetlv

focu, % plv E rf] E8, n $ H rfj KB, <W ds

XCirQCC TG)V TtQOg roig XCil & y&Vl&V, G)0T Xttl

ryv EH pdfci rfj KE

. H&g titikoyKSreov, xiGiv xccl note xccl

6 ijAios yiverai, tcara nogvcpriv.

ds 6riv rovrcov dsdo^isvcov rb Gvveiti-

)ri<3i xal itore xctl Ttotidxis 6 tfhog XCCTCC

jv yiverai. (pavsgov yaQ ovrog avT6&V, onvnb TOVS ittelov ci7t%ovrccs rov faiftiQW0& 10

r&v r^s oA^g cbrotfra'tffcos rov &SQIVOVsiov poiQcbv wy vcc x eyyiGrK ovd' o^cog

yivexai xccra xogvyijv, rolg ds vno rovg avxb

rb todovrov dcpsdTGJrccs ajta% iv ccvrfi ty ftsgwri

yCverat, KCCI, on, rolg VTCQ rovg sAdtiGovag 15

OIQG)V djt%ovTccg dig yCvrcti, Kara

riv' KCil TO JtOT d 7tQ6%lQOV TtQltlfjTOV KKVO-

VLOV r^g Ao%(D6G)g 'x&6t,g. o6a,g yag av 6

{ivog TtaQdMrjhog K7i%ri rov l6rnneQwo

Ivrbg dri^ovon rov &QLVOV rgoTtinov, rag roGavrag 20

L0vfyxovrg ig ra dvrQcc ft(>^ rcbv tiffodicov rag

3taQccxi,[ivccg civrcctg %. rov rera^rrnLogLOv poiQctg v

1. EH] E- e corr. C. 2. EB] E- e corr. C 3, mg. f

H0] corr. ex HE D 3.

_3.Post r&v del. rotg D 3

. @] e

corr. D 8. Hal B] corr. ex o D 3

. 5. #'] om. AD. xfai D.

6. ylvercu] yive C. 7. im D. 8. TLCL] corr. ex riciv D 3.

9. ya^] del. C a. 10. TOV] rov? A. 12. yC\ supra scr.

AD 3. 13. TOLS] -i- supra scr. D 3

. 14. TO] ins. C 2D 3. &tp-

EGT&GW D. 15.$f}1iov~\ D, 8r]T(.ov6ri ABC. nat] D, xara

xoovqprjv xat ABC. mdoGovccs D. 16.o^t's] corr. ex di6 D 3

.

17. TO] supra scr. AD 3. 18. av] D, sdv ABC. 19. wap-

rjio?] pr. A e corr. A. 21. csliScov D.

rots ito&Tois pistil T&V Gefadicov loî>, o6as dnfycov

6 tffaoS dfp' XKTOOV T&V far][lQiVG)V 6rj[lLG)V tig

XQOS TO &SQIVOV TQOTtixbv KccTa xoQvcpfiv rolg vit*

Xtvov TOV sxKSipsvov JtaodMrjAov

5 &'. II&s dab T&V exxeipsv&v 01 Adyot r&v

povcov 3t()bs fag l6rj[iQi>vtt$ xai rgomxarats [i6'r}[Ji<(lQittt'S Gxiag A,a[ifldvovTcii,.

"On d xai 01 nQOKsCpevoi Adyot r&v Gm&v

rovs yvaiiovas KitkovGteQov â^ftdvovrat,

10 ajtat, rijg T [ira%v r&v TQOJtw&v 7ieQi<pQia xai

rijs [ira%i> TOV OQ%OVTOS xal r&v noAcw, om&g av

tQOV TO E, XCCi V7tOXl[lVOV TOV KCLTO,

15 TOV A diij%d'G) rjAEP did[iTQOS) 17 xobs

v T& TOV ^^^QLVOV fTtiTteda)

drjhovoTt, yivoîvYi TV] KOLV^ Topy TOV

xal TOV [ifGrjupQivov. xal tti o^rj rj

Ccl XVTQOV k6yOV %l 7COO

20 TJJV TOV fjAlOV 6(palOCCV) CD6T ddlCCCpOQtV TO E XVTQOV

Tijs TOV yvcbpovos xoQvcpijS) voi6&& yva)[iG)V plv 6

d FKZN v&icc, ly $v Iv TCCLS

1. GsUdtwv] corr. ex otMdmv D. ajr^cov] corr. ex &n-

i%ov C 2. 2. 6 ijiiog] in ras. A, seq. ras. 2 litt. Grjfisfov C.

4. EMSLpwov] supra scr. D 4. 5.

']om. AC. 7. ntcrui-

PQIKIS D. Happdvovrag BC. 8. of] Sia T&V D. TCQO-

KfipEvoi] -(ifv- supra scr. A, 7tQOKi[iV(ov 01 D. 12. yivoixo D.15. AET] A- in ras. B 2

,corr. ex JET C 2

. 16. FKZN]-N corr. ex H A. 20. adiacpOQtw] fii] dLccytQfiv D. PostE eras. N A. 21. yvmâjv] corr. ex yvapor C 2

. 22. raig}TKIS ri' D.

MA0HMATIKH2 STNTASE&2 B'. 99

rov

ra axaa r&v Gxi&v, xal diri%&G)6av dia rov

Eij

rs farjpEQivri xal ai rgoitixal iiEGrjufiaival dxrtvss.

E^rco ds i6r][iQi,vr] [isv r\ BE4Z, &EQivri dsr\ HEK,

%t,[iQi,vr) dsfj AEMN, cotfrs xal TT\V psr FK &SQIVTIV

yweti&ai, Gxidv, rqv 5

ds FZrfjv ds FNvijv. ETtsl roivvv

fj

[IEV F4 JCSQKpEQEia^

(Mfi iv\v i'Grjv e^YiQrat, 6 10

K

ovrov 6rlv Ag, OL&V 6 ABF [i6r][i(lQi,vbs r%, xaroa

ds rcbv 4 xal 4M r&v avrcbv xy va x, (pavEQOv, 15

ore xal AotJTT? [IEV f\F@ rtQi(pQEitt r^rj^drov Ititai

ifi y ft, oArj dsr]FM r&v avr&v v& VK x. coGrE xal

r&v vitb avrccs y&vi&v, olcov piv EiGiv ai d QQ&al

r$, roiovr&vf) [IEV vnb KEF ycwi'cc 6rlv t/3 ^ ^,

fi_dsVTtb ZEF r&v ccvr&v Is", 1}

d^ vnb NET 6/iOio? 20

v-91 va X, otcov ds ai dvo oa&al rj, roiovr&v7] [isv

vjtb KEF Y&VIK xd 7^ x, $ ds vnb ZEF r&v

ccvr&v o^3, % ds vnb NEF dpoi&s QI& ft/3 jZ.xal

1. diri^mcav} -%- in ras. A. 2. rgoitiKcxL] tgoTCMCti g' C.

4. AEMN] D, A- in ras. A, corr. ex 4EMN B 2C 2. 5.

yiyv6&ui D. 10. f^ttu] D, flrjpTTjrat ABC. 11. poqios A.12. V710Y.8Ultvov] 7lQOKl(lvOV D. 14. fGtC D. 15. TKtV d]

x& N&J C, N e corr. C 2;r&v J D. ity] corr. ex xa C 2

.

17. v& va x] co^.ex ~&v ox B 2

. 18. vd] BC, vn C 2 D.

VJTO avrag] vn' ocvrds corr. ex -UTTO rag A 1. 19. ymvtct

Icrtv] om. D, rV supra scr. D 3. 20. to' (pr.)] ^ 7)

D. JVEr]corr. ex JVT D 3

. 21. ^'] 5' D. at] supra scr. D 3. 22. x]

seq. ras. 1 litt. D.

7*

T&V yQcccponsv&v CCQK xvxA&v TtSQi TO, KEF xal

ZEF xal NET TQCy&vu OQ&o'ycovia i\ psv nl

vf}S FK evfreiag rtSQiysQeia poiQ&v i^tiv xd t K

xalr\

7tl Tils FE, faiitovGa ds EI TO fiiuxvxfoov,

5 T&V avTcbv gve ft/3 [i, v\d litl rijg FZ [IOLQ&V o/3

xcclr\

7tl tys FE oîoios t&v KVT&V ^, r\ds iitl

rfls FN [lOiQ&v ^tO- ft)3 flxal

fjiitl tils FE r&v

st$ TO ÎKVKÎQV % i %. KHSTS xal

sv&eiobv i\FE GwayETa^ otW [iv r\

10 FK etiTiv xs id fty, roiOVT&v Qit, Irj ~vu, oiav ds-^

FZ ndkiv o A/3 5, TOIOVTWV $ d o/g, ol&v ds ^ FNjitg Zg, TOIOVTCQV | LS ^/3. xccl oi&v CCQCC

6 FE yv(6[iG)v ^, TOLOVT&V xccl ^ [isv FKGxia 6vvcc%d"rj6Tcci, tj3 v, fj

de FZ faripSQivii

15 M> Ag, f\ds FN %si,iiSQi,vrj $y % syyiGTcc.

cpavegov ds avTO&sv, OTL ncti dvdrtccfov}xav dvo

povoi, hoyoi do&coGiv OTCOIOIOVV dnb T&V sxx{,[i8VG)v

TOV FE yv&iiovos ngbs TCC$ Gxidg, TO T TOV

k'^CCQlLK didoTCCi XCCi fj flSTCi^V TCOV TQOTtM&V,20 7Cldri7tQ KCcl dvo do&l6O)V QTtOl&VOVV JtQOS T& E

didoTcu xccl ^ howfi did TO l'6cc$ sivai Tag

TOV

2. xat NET r^yoova] om. D, g NET Jj mg. D 3. 4. Ss]

om. D. 5. QVS] seq. ras. 1 litt. A. rfjs] yrjs D. 6. i^(pr.)jadd. A 1

. ^] -r\ e corr. A, corr. ex QX C 3D 3. Si] d' D.

7. gift] griy D, -9- supra scr. D 3. rj]

om. D. 8. |] seq.ras. 1 litt. A. 10. vu] v& C. 11. iF?] corr. ex vy D 3

.

12. tg] corr. ex x? D 3. xat] seq. ras. 3 litt. A. &QCC]

supra scr. A. 15. <jy x] supra scr. D 3, <o

y x D. eyytara]-yiGTct eras, propter figuram insertam et ia mg. add. B 2

. 18.

FEJ supra scr. D 3. 20. ta E] rb e~y D. 22. 04] @A C,

J xat D.

MA0HMATIKHS STNTAgESS B'. 101

6ig avTccg KXQifiovg f'vsxev txslva psvxa& bv vTtsdeiâ^v TQOTCOV, 01 ds T&V

GKiGbv Jtobg Tovg 'yvoDîovccg koyoi, ov%

bpotcog did TO T&V plv farjjisQW&v rbv %Q6vov doQitfrov

xatf CCVTOV SIVCCL^ r&v ds j^SiîeQiv&v T& t&v 5

axga

XCCT& itaQukkrikov ldiG)[idrG)v.

Tbv avxbv dr\ tgoxov rovtoig xal 7tl r&v aMcov

Accflovrss rd 6&o6%SQij T&V BXKSL^BVCOV

tdpTG) pices &Qas fay[iQi,vijs tog avrdgxsi, 10

rag vjtQO%ds rcbv syxAfascov TtaQcivt.rJGavTsg 3toir}6o-

lis&ct TTJV x&6iv avrcov %$\v xafroAov itQO xr^g r&v

xara pfyos ^nL^vâLv6vrov ryv dg^v dnb TOV i)7t

CCVTOV rbv (6rj(jLQivbv rtaQaMtfAov jro^tfcfyifi/ot, bg

TO JtQog [i6r}[i{lQiav psQog TOV 15

%i Tag fipBoccs xccl Tag VVXTCCS Jtddas faces

1CKVTC3V T&V iv Ty Gcpccioa TtaQaMtfA&v TGJ

llQLVG) XVXA.G) TOT [IOVOV Sfytt VTtO TOV

diaiQoviiVG)V) &GTS TK vitQ yY\v KVT&V TîtjîaTcc opoid 20

T dMrjAois slvai xal face Tot$ vjtb yfjv xatf SXCCGTOV^

TOV Toiovrov pi} GviificcivovTos Jtl ^rjdfîccg T&V

dMa povov plv 7td^.LV TOV farjitfoivov

dfycc T VTtb TOV OQÔVTOS dtatoov^vov xccl

1. &dieTdKTa>s BC, corr. B. Mg. rovro TO -9-fo)^ Sice TO

%OQIG to ypa< 6 n/ D. 5. ^ft^fptrcov] ^BI^SQIV&V TQO-v D, TQonmv del. D 3

; rgoTtwajv Halma. 7. 5'] om. AD.8. a mg. D. 12. xa-ihttoi;] -4- in ras. A. 14. og] corr.

ex cos C 2. 15. TO] corr. ex rd D. 17. Ss] d' D. 18. ty\

rf\i corr. ex xr\ A.

rag xar' avrov rjîeoag rats vv%lv faag rtoiovvros

at'cffi-yGiv, end Kal avrbg r&v [teyfar&v etirl

r&v 6s koiit&v eig avitia diaiQovyitv&v Kal Kara rb

ri\g fftiereoas oiKovîevrjs eyxAijia rCbv [lev vonoregcnv5 avrov rd re vTteg yr\v rîtjîara r&v vrtb yijv

xal rds rj[iQas rcbv vvurCbv ($Qa%vreQas

rCbv ds f$oQSi,orQG)v avdnakiv rd re VXSQxal rag fftiEQas nohv%QOViK>rQag.'ds xal afupfaxios ovrog 6 jtaQdMyhos rov

10 rjMov dig Kara xogvytyv rots vit avrbv yivoptvovKara rd rov farjiiSQLwv KOI rov Ao|ov KVK&OV r{MJ-

entire rors povov rovg yvd)[iovas iv ralg [i6ov-

dtixiovg yivtG&ui, rov ds i]lLov rb psvv diaitoQvo[ievov rd$ r&v yvo^dvcov

15 GKidg dnoKMveiv agog ii6rnipQiav, rb ds vonov agog

rag aQKrovg. KaC itirw Ivrav&a, otcov 6 yv&iicov

f, roiovr&v exarsga ijre fteQivr} KOI ^ %ei[ieQi,vrj 6xid

e xa&oAov GKidg rdg ev ralg

20 yivoyisvag Kal &g [tydevl |toAdycj diacpEQovtiag did

rb pri Ttdvr&s ev avraig ralg êtiriî^Qicas rds t ^n~

pSQiag Kal rdg rgoitdg aKQificbg d7toreAet6&at,.

rolg de vjtb rov faijueQivbv Kara KOQvtpriv [lev

yivovrai, r<bv dGreg&V) oôt xar avrov rov

2. aim'] -si in ras. 1 litt. A 1. 4. VOTSLOTSQCOV, -EL- e

corr., D. 6. vvnrwv] bis C, sed corr. 7. dt] corr. ex rs D 3.

9. %GUV D. ovrog] ovrtog C, civ-cog D. Trapa/UTj/lotft B.

10. rots] corr. ex TTJS D4. 11. rd] ins. B a

, supra scr. C 2.

Supra TfiTJârK add. xotva D 4. 15. ngog - - 16. xca]

mg. A 1. 16. ivTav&cc] -a postea add. D. 17. %ai 17 %W-

Qivri] om. BC, post GY.IO, add. C 2. 20. a|to/ldya)] -o- e corr. B 2

,

corr. ex o> C 3. 21. lGr}(iQiccs] -a- e corr. A.' 23. <sr][iQi-

vov\ I- ins. A 1.

MA0HMATIKHS STNTAgES B'. 103

itoiovvrai, rag TtegKpoQdg, Jtdvrg de KOI avarslkovreg

xal dvvovTs (paivovrai rcbv rrjg Gcpatoag Jtoh&v iit

avrov rov OQi&vrog ovrcov xal îrjdsva xvxhov noiovv-

r&v iitjrs rcbv TtaQaMtfAcDV asl (pavfobv T)ael dyavrj

H^re r&v [leGiHipQiv&v x6AovQov. ofatJGeig de sivcct, 5

per vito rbv farj[iQivbv evSfysG&ttC <pK6iv as itdvv

dta to rbv t/Atov ^rs rots xara KOQvyrivTtSi ret,

KV to &QOS fvxQdTov yivoiro^ \Lv\r iv rats VQOitccls 10

rov xccra xogvcpriv, &s p?d rbv

itoielv rtvg $ dtiiv ecu

OVK KV %Ol,[lV 3t7tl,6[lV(QS ^tVrov dvgo rots ano rijs xa& faces otxov-

xal ftxaGi'av n&M.ov av rig-

forogtav fiytj- 15

Gaito ra fayopwa itfgl avr&v. ra [ilv ovv I'dia rov

vitb rbv l<5ruiQivQV 3taQaMijA.ov 6vv^6vn titlv

ravra av fy.

7tQl d rcov AoiTt&V) d(p (bv xal rag oxtj0i,g

rivlg ol'ovrai, xart,Arjq)d'ai,, JIQO^Ô^V ixslva xoiv6- 20

iva pri xa& ZxaGrov ravroAoyapfv, on, r rcav

xd0rov xard xogvcpyv yivvvrai r&v

o<5oi rrv fav 7ti(ELav dc6rxa6iv rov

1. noiovvrca] -vrcti ins. in spatio uacuo 2 litt. D 4. rag]

i/]

'

rag D. iteQicpOQag] corr. ex nsQicpfQEiag D s. 3.

corr. ex Y,v*1.mv C 2,HVHJ.COV D. 4. fityrf] p^de D. cpavfQo* D.

&yavfi\ &- supra scr. D 3. 5. x&v

mut. in TjLtfffrjft^ti;

3 B 2. 10. [lyre D. 13. ov%] o- in

ras. A. n7iiGêv(og\ ns- corr. ex itsx- C 3. 14. [ISXQL] (t-

inras. D. 15. fyriGKiro] ^yrjffaro C 2. 16. rov] raov D. 17.

, -g del. C 2. 22. Ixaarov] Ixaffrrjff D, fxafftot D 3

.

tti rOV did TG)V 7t6A.G)V CCVrOV XVXJiOV, Y^V xdl CCVZOg

6 vitoxsi'iisvog ytaod^rjôg acpsGTrjxs, xccl on cpavsgbg

[iv del xvxhog yivsTcct, 6 jrdAcj per r& flogst(p jrdAo>

rov farjusQivov, diaGrruiart, de rd) rov Jtohov %ccQ[icirt,

xal oi BinteQLââv6^voi vitb tovtov

asl d' acpavrjs xvx&os 6 3t6A,G>

diccdrtfiiccTi, d TG> avr& ygacpo-

xal OL SVTOS rovrov dttsoss del

f$'. devrsoos yivBtai jrapa/UÂog, xa& ov

10 f)iiQa 6rlv faacov toypsfivfttf i/3 d'. o^rog

rov t&fti*Qtvov potQccs 8 ^'. xai yodcprca did TaitQO-

f}dvr]$ rrjs vôv. l6n d xai ovros r&v dyL<pi(5xC&v

rov r\Mov Tt&kiv dig rots vn avrbv ywopwov xara

xoavyfiv xal rovg yvcbpovas v ratg [i6ovQav>j<36i,

15 Ttoiovvros dtixiovg, orav d7td%ri rijg &Qi,vijs roonrlg

z<p xdroct rd iiorj [loi'oag o^1

/.',&6re rdg [ilv ovfr

ravrccg avrov dia7toovo^vov rdg r&v yvoôvovGxidg ditoKMvBiv ig rd vorict, rdg d Aomdg 6cc, elg

rd POQBICC. XKL itixiv ivtav&a, olcw 6 yvtoîcov |,

20 roiovr&v fj [ilv l<5rniQivri 6xid d y' /3' ? i\

xd y', f]$ %i[iai,vri AjS.

1. Sid'] d seq. ras. 1 Hit. B. 2. K^GTJ]V.V D. 3.

nolco (pr.)] woôot, i in ras., A; xeVrô) D. 4. dictGtûxi] -i

corr. ex -rj C. 5. V7CQiôc^^ccv6(isvoi D. 6. $'] f ins. B,

seq. ras. parua C. noloi] om. D, i supra scr. D 4. 8. TOVTOV]

corr. ex rov D 3 et mg. D. &<pavsis] cc- ins. D 3. 10.

lanv D. d'] ins. D 3. OVTOS 11. d'] nag. B,

add. B 3. 11. fKHpag] comp. ABCD, ut semper.

. D 3.Ta- supra scr. D 3. 12. f'ort] -i corr. ex

rjC 3

.

corr. ex OVTCOS C 3, ccvros D. a[icpi6Kicov] -ft- in ras. A. 13.

wr'j VTTO D. 16. ^'] F^^. m] om. D. 18. v6ria\vmrBLu D

;similia saepius. <?a] G- renouat. A, G- e corr. B 2D 3

.

20. rotovTcov] rotov- in ras. A. t(3'] Z^'BC. 21. xa y']

xy a D.

MA0HMATIKH2 STNTAEE&S B'. 105

y'

. ratios ds iGxiv TtaodMrjAos, xa& bv av ywoiro

i\ psyfarr] rjîoa &Q&V i&HpifUf&V iflL'. ovros de

ayt%(, rov farjpSQivov pot'oas rj x xal yodg)rai diet

rov Avakirov xohitov. <5riv ds xal ovros r&v dpcpi-

rov i\Mov dig rots vit avrbv yivoÊvov Kara

xal rovg yv&iiovas iv rats

Jtoiovvros, orctv rijs &Qivr[<s

ra [tEgy [taigas ^ ?<Q0rs ras [lev

ravras avrov diaTtOQZvoyLtvov ras rcbv

aitouMveiv itgbs [iSGrjuPQiav, ras de Aoinas 6%fi 10

agxrovs. nai i6tiv svrav&a, oicov 6 yvcsîcov |,

roiovrov

i$L' y', nd'. rraQros ds l&nv jraâAAÂo^, KU& ov av

ys'voiro ^ [ifyfarrj fjusQa CVQ&V &h}(&Qiv&v ifii' d'. 15

ovros d' an8%i rov farjiteoivov poiaas i${l xal yod-

ysrai dia rov 'Adovhinxov xoAnov. 6n d xal ov-

ros t&v a[icpi,<5xG)v rov ijAtot) ndfav dig rots vitb

avrbv *yivo[ivov xara xoovcpyv xal rovs yv&iiovas V

rats ii6ovaavtf6s6i,v atixiovs noiovvroS) orav a7t%Yi 20

(p xdrQa ra

1. Si IG-CIV} BG-CI D. 2. ds] d' D. 3. cuis%i\ corr. ex

]C 3. 4. Supra Avatirov ras. B. OVTOS] corr. ex

ovrcog C 3, civ-cog D. 5. rots'] corr. ex rccig D 3

. 6. [ifGov-

gavr^GfGi D. 8. Q^rj] -r\ e corr. D. 11. ngos] TCQOS rag D.

12. ^/.'y'] >]/_' y' A; similiter saepe. 13. tt'] A, i s' $' B,

Ts p C, i D. 14. 8] d' B, om. D. IGTL D comp. B. av]supra scr. A. 15. fajpepiyibr] om. D. d'] in ras. D, seq.ras. 1 litt. 16. <T] â| A, in ras. D. 17. 'Adovli-cixov]alt. i corr. ex o D. tcuv D, comp. B. ovrog] post pr. o

ras. 1 litt. A, corr. ex ovrcog C 8, avzog D. 18. VTC' D. 19.

yivoptvoig D. 20. noiovvrog] -og corr. ex -cog C. 21. ra]om. BC.

r, &6r tag plv Qi y' ravrag avrov dtattoomopevovrag rcbv yv&pdv&v Gxiag aitoxfa'vMv agog

rag ds hoijtag 6pd rg itobg rag ayxrovg. xai

wrav&tt, oi&v o yv&n&v |, rouovrovi\ psv

5 6xt,a ly y', i\ds frfQivrj /3, fj

^ êifiBQiv^ ftd g'.

7tttQKkA.rjA.OS) KCi& OV CCV yVOl,TO

rov farjpQWOV ÎOLQCCS tg ^J xal

ys v^Gov. fan $ Xtti avrbs r&v

10 rov fjMov dig rotg vit avrbv yLVO[ivov xara

xttl rovg yv&iiovag v ralg [i6ovQttvrJ66i,v

noiovvrog, orav aite^ri rijg &Qiviis rgonris (p' xccrQKra nfyq ^loioccg fit, Kn5r rag [iv 9 rccvrag avrov dicc-

7tOQvo[iVOv rccg r&v yvG)[i6vG)v Gxiag a7tOKkCviv Jtobg

15 [i6rm,poiaV) rag d Aoijtag ô itobg rag agxrovg. uai

6nv fvrav&a) ol&v 6 yvcb[iG)v |, roiovr&v ^ P&v

va.

$'. sxrog Itirlv TtaQaMrjkog, xatf ov av ylvoiro

20 ^ îyi6rrj r^LBQa coocbv farjiifaiv&v Iy d'. anz%(, (f

ovrog rov fav}pQtvov [lotaag x id xal ygdyfrai, dia

NaTtdrcov. 6n $ xal avrbg r&v &pqpi0xnv rov

1. r*] (boc est %) fo A, lp C, t|3 BD, corr. in TQIXOV B 3.

y'Jût.in F B 3

. 3. r#] r A, i C, 1/3 BD, mut. in r B 3.

5. ju,^] post ras. B, ^ D. 6. icxi D, comp. B. 7. r]fi8Q D.

OQ&V C. 8'] ds D. 8. ypaqpftat] 79- renouat. B 3. 9.

MeQorjs tfjs] -s t- renouat. D 3. V7j<yov] vrj- renouat. B 3

. HGUV D,comp. B. 10. Si's] dt>6 BC. Post yivoptvov 1 litt. del. D 3

.

13. xdg] reels C. 15. xat Icriv] bis D, corr. D 3. 18. va]

v vcc D, ^v aXico fii^Mcd itQOGKSiTcci TOLS vcc xai TO y mg. D 3.

19. ^Tt BD.'

20. 6000V C. ty] -y ins. D 3. <T] 8s D.

21. 5ta] ^ D, ut saepius. 8ict Nandrmv] corr. ex 8t' ccvoc-

Tcdrcov B 8,SLccccvundrwv C. 22. fffrtv D.

MA0HMATIKHS 2TNTAEE&S B'. 107

rjMov rots xar' avrbv dig yivopsvov xara xoavytyv

xal rovg yv&povag iv ralg ^rjôâig dtixiovg

Ttoiovvrog, orav aTtfyrj rrjg faoivrjg raoTtrjg Qr] [lOioag A,a, K>6rs rag pew |/3 ravrag

ccvrov dia7toQvo[ivov rag r&v yv&iiov&v Gxiag aito- 5

xMvsw TCQog ii6r][i($()iaV) rag d% Aomag 6cjrj agog rag

agxrovg. xai i^nv svrav&a., oicov 6 yvcbjiov |, roiov-

rcov17 pv faripEQivri 6xta xft g', ^ $ ftsQwii y L' #'

9 n

7taQdM.rjA.og, xa&' ov av ytvwtQ 10

(bgcbv farftiSQiv&v ~iyll. KTtiyti $ovrog rov ItirjiiSQivov [toioag wy va, xal yQaysrai duo,

Ttocorog ds 6nv ovrog 7taQdAA.yA.og r&v

ersQOGxi&v' ovdsTtore yap roig V7tb avrbv

iv ratg ê^ri^QCaig at r&v yvcoîovcov Gxial 15

Ttobg ii6r][ipaiav KTtoKUvovGw, aW iv \L\V avrfl

rri ftzQivfi rooTtfi xara xoav<pr]v avrotg b rjA.iog

xal 01 yv(b[iovg atixioi, ftfooovvrai,' ro6ovrov

anfyovGLv rov IGVHLSQIVOV, o6ov xal rb &Qivov roo-

Ttixbv 6r][iLov' rov dl aA,A.ov Ttdvra %oovov cci rcbv 20

yvc)[i6v(x)v 6xi,al Ttobg rag aoxrovg (X7toxMvov6iv. xal

oicov b v&Gov ^ roiovrG)v i ev

1. roi<s\ om. D. uvxov] avr&v A. 2. jiSffTjftfJpi'cag] peoov-qavr\Gt6iv D. 7. ot'cov] o- corr. ex t A. 6 yvebfteoj/] corr. ex

z&v yvco(i6v(ov D 3. TOGovrcov D. 9. vrj ?'] corr. ex r[, J D 3

.

10. IGTLV C, comp. B. nccQciUôg] n- corr. ex v A. ys-

tTo] yhot C. 11. d'~\ SB D. 12. ovrog] corr. ex ovrcos C 3.

13. Za3i'v7]g D. ovros] ovrcos C, ovrog 6 D. 14. vno]'

CD. 15. ffxtat] -K- in ras. A, pr. i e corr. D. 16.

<7T^f3(Hay] -G- e corr. D. CCKOKKIVOVGIV C. 19. ant%ovGi D.

22. tanv evrctv&a D. 23. 7) (alt.) p. 108, 1. fort] om. D.

i<5ti. xal Jtdvrsg ds 01 rovrov

p>%Qi tov rr)v rftisrsQa

ovros stsQoGxioi, rvy%dvov6i,v ovrsg' ovdsnore yapxax avrovs OL yvcbpoves dv ratg p0ri[i(lQtais ovre

ywovtai ovrs rocs Gxias itoiovtiiv TtQog [i6r]ii-

aMa itdvrore TCQOS CCQKTOVS, dia rb [tr^de tbv

rtors Kara Ko^vfp^v avrots yiyvsGd'ai.

a& bv av yevoiro

7yl_' d'. Kitiyjti d7

10 ovrog rov farnisgivov yboiQag v^ t/3 xal yQatpsrai dia

IlToA.[iccidos trijs iv qflatdi,) xaAovpevrjs ds'

i^nv evTav&a, OLCOV 6 yvcojKov |, roiovrcovfj

yi'', fj ds farjpSQivJ] Ag/.' y\ ^

od g'.

15 -91

'. SVCCTOS fan 3taQccM.rjA.oS) xa& bv av

rj [isyfarrj ^BQa WQ&V farjiisQLv&v id. ane^st, d9

OVTOS tov i6r][iQi,vov fioioas A KJ5 teal yQacpsxai dia

nils Kates %G)oas rffc Atyvitrov. xaC i&nv

OICQV 6 yvG)[ia)v |, roiovr&v ^ psv frsQivrj <5xi

20 ^ ^ faYHLSQivi} A t/3', j]ds xsipsQivr] ny t/3'.

bv av

id d'. uitfyu d*

1. K6%i6g] &- supra scr. A 4. 5. TTOLOVGI B. 6. TCCCVTOTS]

seq. ras. 1 litt. D. apxTovg] -x- supra scr. A 4, rccs &QKTOVS D.

jitrfD. 7. UVTOIS MOTE xara KOQvcpriv D.

CD. 8. SGTL D, comp. B. 9. d'] 8i D. 10. (JLOLQCCS]

Ss]om. D. 11. sv] sv rj] D. j}paldri C.

mg. A 1. 'EQUSIOV] 'Eg- in ras. 4 litt. A 1

. 13.

14. oiJ] e corr. D 3. 15. WVUTOS C. isnv C. 16.

Ss D. 17. I] in ras. A. did] ds did C. 19. /_']xs D.

20. ifi' (pr.)] i B' BC. ^7] corr. ex Ty D 3.

ij3' (alt.)] I $'BC. 21. ^rt D, comp. B. 22. <T] ^' D.

MA0HMATIKHS ZTNTAEE&S B'. 109

ros rov farjiisQivov H,OIQK$ Ay Trj KCCL

6

,TOLOvr&v fj per frsoivri 6ma t, j]

ds i6t]îOivrj

i<5xi 5rce0aAA7?Aog, xa&' bv av ysvoiro 5

rj \Lyi<5xr\ fiêycc cbQ&v fariiLEQivcbv id/.'. aitE%ei d'

OVTOS rov iGifHLSQwov [loigas Ag xccl ypKcpercct, dia(

P6dov. xcct IGTW sinccvâ^ o'i&v 6 yvthpov |,

de %Bi^8Qivri ^yy y'. 10

/3'. d&dexccTos 0rtv TCa^dîqôg ,jca^' oi/ av

-^ [isyfavn fniQa COQ&V farjiisgwcbv id /_' d'.

d' ovro? roi) ItirHieQwov jioiQag At/ Ac #at

ta ZJ{ivQvr}s. uai i6xiv wrccvd'cc, oi&v 6

|, rotovrcjv ^ iilv ftsQivri GKIK Ts rS, rjds i6r\- 15

y, a %Ei^QLvri Qi_ y i .

TQSMSxcudexccTos fan ^ccc^ctAAÂog, â^1

'

6v av

v\ psyiGxri fmsga WQ&V i6rj{iQi,VG)V Is.

ovros rov farjueowov [IOIQCIS ^ v$ xal

. KO.I i<5xiv evrccvd'cc^ oicov 6 yv&yiwv 20

[iev

2.^f'tfTjg] -0- e corr. A. 3. z] ins. D 3

. /_'] om. D. 4.

t|3']t'

j3'AB 3

,I ^' BC; similiter saepius. 5. ta'] at B.

saviv C. 6. df

] ds D. 9. f) dt i' y'] bis A, sed

corr. fly] ft y D, ^ add. D 3. y'] om. C. 11.

t|3'] |3tB.

^(jTi D, comp. B. 14. ZIIVQVTJS] -s e corr. D. ioxiv\

IX 15. r*] 4 A, ^ B, 15 B 3, rs C, l_8" C 2

,/

ij D.

16.p, %m,Qt,vri\ supra scr. D 3

. 17. ty'] yt B. T^KT-

otat^'xarog^ 19. tf] dg D. ?s] I ts D. 22. 5'] in

ras. A. px] corr. ex ^x B 3

, px C.

id'. r06ao6xaidxar6s dn TtaodMrjAoS) xa& bv

av ysvoiro % iisyfarrj fj[iQa &Q&V far][iQi,VG)V Ts d'.

d* ovrog rov farftiEQivov poiâs ~\iyd xal yad-

dia MaGGaMag. nau <3nv fvrav&a, OLCOV 6

5, roiovr&vi] pv ftsQwrj 6xia %.{_' j/, ^ ds

v/_' y' ifl\ rids ^BI^BQLV^ Qîd.

bv av

ovrog TOV far][iQivov [loiQCis ]Te a xal

10 dlK ll00V JI6vtQV. GTW dl fVTCiV&tt, OIG)V 6

I, roiovT&vfj ply &Qivri 6mb v/y d

r

, ^ d LG^-

rcov avr&v |, rjd$ %i,[jiQivfj QV i$ '.

xxcu,dxaT;6s i6nv nccQccMyAos ,xa& bv av

V} [ifyfarr] Îga fagcav L6i

YîQivS)v t L' d'.

15 ait%i ds o^tos rov far][iQLvov poiQas ^ va xal

ygd(prai, dia rcbv nrj'y&v rov "I6roov jcoraîov. <5nv

dl Ivrav&a, OLCOV 6 yv&ii&v 1, roiovr&vf) [iv

6xia xsi', $ Se forjiifOLvfi %yL' y' ifi', n d

20 i% . 7traxaidxar6s 6riv 7taodMrJ.og natf bv av

ywoirodf ovrog rov farjiifaivov poiaas ^YJ A/3 xal yod(prai,

1. id'] 81 B. t66UQi<jY.uiSmciTos CD. 3. (IOIQCCS] om.

AC. ^] corr. ex I B 8C a. 4. Matftfa/Uas] pr. G in ras. A,

dice ^vâvriov mg. A 4, Mccccdfas BC, pr. a corr. ex IK D 3

. 5.

x] x C, x|3 D. 6. pp] Qii S' EC. 7. IF'] EL B. IGTL D,

comp. B. 9. a] 1 C. 10. j&s'ffov] -v supra scr. C 2, [itsov

TOV D. I'ffrt A, comp. B. 12. t/3'] corr. ex 18 C 2.

13. 15'] gt B. Ixxa^âtrog] AB, E^xat^f'xaTOg B 3 CD.

SGTIV] comp. B, Ss SGTI D. 14. tGTfpSQW&v] om. D. 15.

8t] 8' C. xal yâqpfrat] bis D. 16. TOV "/CTTÔV] "IGTQOV

rov D. 18. |yj ||5 D. 19. poor] mut. in ^>odB3

. s'] mut.in ^5" C 2

. 20. *n ^ B. iffrt D, comp. B. 22. 8f] 8' BC.

MA0HMATIKH2 2TNTASE&S B'. HI

dia rCbv Ixftofaav Boav6&vov$. i'tiriv ds eweav&a,

OIG)V 6 yVO)[lK)V ,rOiOVrOV

T] [lV &QIW?I 0XLCC

,xcc&' ov av

ywoiro fj pfyfarr] r^SQcc ngcbv farjiisgivav Tg 6'. 5

d' ovro$ rov far][i()ivov [loigas v d xccl yQK-ia ^6rjs rifc Maicbndos Mpvqs. ftinv $ v-

OICQV 6

10'

ov av

fj psyfarri YI^QK COQ&V faruiEQiv&v Ig/.'. an-

d ovros rov faripZQivov ponces VK[! g' xal ygd-dia r&v voTi&Tccrav vys BQTTCCVICCS. Z<5nv dl

,otov 6 yvaiicov 1, roiovr&v

i\ ^lv ftzQivii 15

Ace'

i' r d

av yevoiro

ovros TOV tGrftLSQivov [loioccs vfi v xccl yQayercii dia, 20

r&v rov 'Ptjvov txfiok&v. fariv d vrav&a, OLOV 6

roiovr&v i ilv ftfaivr Gxia k r $

1. 6s] d* D. svtctvd'K] -K e coir. C 2. 3. %ei(iQivrii A.

Q7t D.' Mg. 79. y B 3. 4. IT?'] Tjt B. IGXI D, comp. B.

nagdJi\ D. 6. 8'] 84 D. v 8] C, ~vS ABD. 7. MaionSos C.

_^] 8' D 9. r*] fo in ras. A, r BC, r D. 10. ^ y']

tfTjy D, -r] e corr. C 2, supra y' add. o B 3 euan. (mg. r B 3

)et

eo C 2. 11.

i-fr'] -9-t B. 8vvccKaiSeKctT6g~] pr. -a- suprascr. D 3

. IG-CI D, comp.^ 13. 8s ]j^_C. s' xat] g% D

(h. e. Mat'). 17.(jxfl-] GH^ post eras, crx-d

1

y D. Supra y'add. r B 3

. 18. tcyrtv C, comp. B. 19. 8'] 84 D. 21.

fdTt A, comp. B. 22. Supra y' add. d B 3.

xa'. Eixotirbg TfocjTog EGxiv Ttaod^rjôg ,xa& bv

av ydvoixo q \Ltyi6xv\ fftLEoa &Q&V farjiifoivcbv it,.

aitB%t, 8s ovrog rov idriÊQivov [lotaag vd A xai ygd-

<pxai dice, r&v rov Tavdidog fxfioA&v. ftiriv d v-

5 rav&a, OLCDV o yv&îov f ,roiovtnv

?? plv6xia A.d i' y t/3

r

, f}$ faripSQLvii jr/3/.' t/3', ^ ds-

/' JB>'

6or] L -

xfl'. SiKOGrbs dsvrsQog fan 7tciQccA.A,r]A.og, xct&' ov

av ysvoiro fj psyiGrr] r\^BQa caocov fayiiSQiv&v i^ d'.

10 aitiyti d' ovrog rov farjiieqivov (lotgag vs xcci YQK-

(percci dia BQiyawtiov rqg [iyK&rjg Bosrraviag. stiri

ds svrciv&a) OL&V 6 yvcoîcov |, roiovrcovi] pv ftsgivri

6xia fa d', ^ $fa'iW>EQi>v'fi

X r^, T]df %iiiQivfi rdL'.

ny'. ixo6rbg ratrog 6rlv ttaQcckkrj&og, xcc& ov av

15 yeVotro f] {ifyfarrj fftLZQcc (boobv for)[iQLva)v tj/.'. ait-

d' ovrog rov far][iQivov {loioag vc; xal

[i6r]g rijg ii/

ydAr]g [email protected] v&KQv roiovr&v

20 xd'. Eixotirbg rtraorog 6nv jr(>aAÂog, na& ov

1. sttiOGTOs itQ&z6s &>ttv] TtQ&TOS *v.l efaoGtos D. 3. ds]'

C. T] A, K BCD. 6. y'] corr. ex t D. t^'(alt-)]om. C.

8. flnoGTOS SevrsQOs] devTsgos xal efaoGTOg D. 10. ^']

^ D. 11. BQiraviccs D, t corr. in a D 3. &mv D. 13.

d'] ins. A 1 ante ras. 1 litt. Tte] corr. ex ny D. p^j r A,

IS C, f BD, corr. B 3. /.'] s

rD. 14. r^trog xat fôffrd? D.

SGTI D, comp. B. 15. a.7tE%si] 8t,%si, C. 16. ^'] fo' D.

17. BQETTCCVLOCS] rfjS BQsrrccviag A, rfj$ del. A 1

; BQfrccvviccg D.

*'] ^ D. _ 18. if] -^ e corr. D 3. r*] -^ ins. A 1

, y BC,corr. B 3

;r o D, o del. 19. y'] om. D. jff*e B extr. co-

lumna. -rAf] rêD. 20. TSTCCQTOS v.ai ewoGtog D. $GTL D,

comp. BC.

MA0HMATIKHS STNTAgEQS B'. 113

av yevoiro r\ {Lsyfarr] qpSQcc agcbv

aTtiyî ds ovrog rov farjpfoivov poiQag vt, xccl

dia. Karovgaxrovtov rijg B$rraviag. l6xi ds evrav&cc,

ot&v 6 yv&iicov 1, roiovrcovfj [lev ftfaivfj Gxia A-fr y ',

^ ds farjusQivfj 9/5 y' t/3', ^ df isiptQivri TOft if} '. 5

its'. stxoGtbg Ttepitros ttirlv nccQccMrjAog, Haft' bv av

ydvoiro fj peyfaTr] quGQcc ctigcbv i^r^L^QLvCbv Irj. aTtijjti

ds ovrog rov iGrftLSQivov {loiaccs wj w& yQKtpetat, di,a

voti&v Tr}$ [iMQag BasTTccviccg. 6nv ds evrav^cc^

6 yv&pcw 1, roiovrcovfj [ilv fteaivr} 6xicc ji r, 10

$1ds fariinsQivfi 9?, ^ df %iiioi,vrj vtO-

ifi

'

.

Kg'. SixoGrbg exrog 6tlv TtccQaMrjAos, KK& bv av

yivoito r\ \jLtyi6tri rj[iSQa COQ&V forjpsQivav njL'- ax-

ds ovrog rov fayiieQivov poiQag v&L' xctl yQaysrat,

a rfbv iifa&v rrjg P,IKQK$ B^rraviag. 15

OVK r6di&a d vravfta r rov rrdrov r&v

i r r

rovg ytaoa^^ôvg xal rrjv r&v âQîdrcsv diayoaav

o^rjg poiQag (fwdy&f&cu, xal dia rb

lv 7tl r&v t'ri, ftoot,orocov Jtoo<3ijxiv 20

dib xal rovg rcov Gxi&v agog rovg

yv&povag Myovg &g iitl oupwaitinwov rox&v itQi,66bv

2. 8e~\ 3' C. 3. KCCTOVQCCHTOVIOV] rov GCCKTOVIOV D. BQST->Cug\ -rcc- in ras. A, BqetrccvvLas D. Saxw D. 4. y'] s D,

supra y' scr. g B 3. 5. rof5] roq D. t/3'] j- D, r supra

scr. B 3. 6. 7[{jL7tTo$ Y.oc.1 sfaocrog D. sort D, comp. B.

nocga.M.r\lo<s\ pr. I e corr. C. 9. Bgsravvias D. 10.ft]

ft ft D. r^J -R AD, in ras. B 3, p C, supra scr. quaedam

uan. C 2. 12. sxrog xal F^xoCTOg D. ari D, comp. B.

14. 8] S' C. 15. jâxâg C. BQsravviKs D. 16. fV-

Tfu^fO' D. rfr|Ta^TOv D. 17. re] corr. ex da' D. yCvtcfrKi C.

21. fê^ya^fff'O'at D. 22. &cpoqLGîv(ov CD, corr. D 3.

Ftolemaeua, ed. Heiberg. 8

x'. xccl onov [ilv roivvv % {ifyfarr] fftiEQcc GOQOJV

&, Xivog 6 naod^rjôg dnfysi rov

noioccg 1-a xccl yodyfrcct dice rfbv POQSI&V

rijg iiixoag Bofrrccviccg.

5 xr}''. onov der\ [isyforr] f][iQcc (tiQ&v itixiv farj-

'i KtVOS 6 JtCCQCchhykoS KTcfytl XOV 107]-

xccl azrai, dia r&v

defj \ji,yi6rv\ ^socc COQCQV stitiv

10 iiSQiv&v Jc, Metros 6 TtaoecMrjhos artfysi rov

xal YQacpsrcci, dta &ov^g r^g

K' . OTtov df ^ \LByi6xvi rîeoa faocbv i<5xiv

Kivog 6 ytaQccMrjAog uitiyti rov

.' xccl yodspsrai, dia Exv&ix&v e&vcbv

15 Aa'. ojtov dsrj psyfarr] ypsQcc caoav itinv farj-

xfl, sxeZvog 6 ^âAAÂo? d7ts%i, TOV farj-

y, Xtvog 6 xccQccMrjhog ditfysi rov i6r}[ioi,vov

20 iiotoccg gg.

Ay', onov d% y [L&yfarrj fniQcc ao&v 6nv

xd, Xtvog 6 jcccQdM.ijhog dn%i rov

poiQag Jg rj ji. Tto&rog d 6rtv ovrog rfbv

xccra yag povriv rqv &Qi,vriv raonqv ^ dvvovrog

25 fast rov qMov at 6xi,al r&v yvcopovcov 7tl ndvrcc ra

4. BQtravvlas D. 7.fi] -ft

e corr. B 3. 10.

corr. ex IGTI^QLV&V C 2. 11. ^y] t?$-L- D. ovZrjs tfjs

VIJGOV] corr. ex CKvowav eovtov ayvwGTcov D, cfr. lin. 14. 12.

isnv tGj][LEQiv&v] om. D. 14. Sv.vQ'iK&v] Syi.vQ'r^&v C, corr.

ex GMOIY.(QV D 3. s&v&v] corr. ex eovoov D 3

. ctyvcoGtav]

corr. ex ccyvrnGxtoG D 3. 16. x|3] ttnoGidvo D. 19. xy] stv.o6i-

D. 23.?] ft] ? D. */j ^

J

D. 25. TO] om. B, add. C 2.-

MA0HMATIKHS STNTAEEaS B'. 115

TOV baftovrog [lEor] rag ifao<5vv0i,g itoiovvrcu. xai

ffSriv vrav&a b [LEV &EQivbg rgortixbg jrapaAAÂog del

<pavo6g, b ds ÊtîSQtvbg rooitixbg del dcpav^g^ did TO

diMpoTsoovg evakkat, EfpditTEG&ai, rov boiôvTog. yive-

TCU ds xal 6 Ao|6g xal di,cc psti&v rcbv ^cpdiwv xvxAog 5

6 ccvrbg rco 6^tjoi/rt, orccv avrov TO IKQWOV

si tie rig a/Utts ftsMQiag f'vsxsv xal itey! r&v en

eyxlfasov sitifyroir] nvk rcbv bAo6%Q6-

TQO)V 6Vll7tTCQ[ldTa)V, BVQOL V, OTtOV TO f^CCO^CC TOV 10

POQIOV 7t6fov flOlQ&V StiTW |g fyyiGTCC, Xi ^dvvovtiag o'Aog Tag etp xaTQa Tqg ÊQTOV dia {I,6G)V T&V t,GtdCc3V XVX&OV pOlQttg 18'

TJJV yLsyCdTriv fipfyav xal T^V T&V Gxi&v 7tl ndvra,

TK pfyrj TOV bgCôvrog 7tgtayco'yriv 6%dov prjviaiav 15

b'Grat, ya^ xal TavTa vxarav6r}Ta dia TOV

xavoviov r^g Ao|c6^C3g* o6ag yao av

VQG)[iv TOV farjjjisQivov jioiQag TOV itaadMrjAov dn-

%ovra rov dnoâ^dvovra Myov svexfv 9' xdroa

TOV TQOTtLXOV 6r][llOV [lOLOag t,/

yiv6^lVOV $ TOT r\%0l 20

dfl (pavfobv 7)dfl dytavri, {iTa TOV aitoââvo^vov

TinjpaTog TOV did {ifa&v TCOV tydicov xvx&ov, ratg

roGavTaig poioaig drjAovort, faifyEi T&V TOV TfTaorrj-

liooiov r^'Yi^drov 9 TO âoâ TOV POOELOV

1. ^97]] /*- in ras. A. 3. TO] om. D. 4. svcddi- D.

6. tcrHLSQWov] om. C, supra scr. B 3. 7. avccrsUrj] B, ava-

rsUH D, bvctx&ri A, fa&liii C. 8. IS mg. D 3. 9. lyx^t-

Gfcov] corr. ex ov Y.IIGSQ> D 3. 10. W'] B, om. ACD. 12.

dvvovaas] -o- in ras. A 1. 14. tj\v (pr.)] rrjv re D. 16. yi'yvf-

6ai D. 17. &v\ D, sdv ABC. 19. $<p'] T&V tcp' A, corr. A 1.

20. ytyvoftfvov D. TOTS'] om. D. 21.r/']

ins. C 2,

f^ D.

23. JLetyet] Jl- e corr. C 2. 24. Tfirjfidrmv'] -T\- in ras. A,

-v supra scr. D 3. jfogclov] -t- ins. D 3

.

8*

Aa'. xal oitov plv roivvv rb âoîa rov jrdAov

dvvovtiag

[loioag A*

0%sdbv itl [irjvag fyyidra dvo rtjv re

5 JHIQCCV xal rovg yvafiovas 3tQi,6xiovs

Ag'. oitov dl rb Capita rov itohov poig&v i<5tiv

oy y\ *xl av rig VQOI pr} dvvovGccs rag Ifp

rijg &Qiviig rÔTt^g {loioccg jZs* &6r rtjv r

fj[iQav xccl rovg yvcoîovag Xfoidxtovg inl

10 fyyiGra 7taoarivi,v.

),' . onov de rb fâoîa rov rtohov IIOIQ&V i(5tw

orj y\ Xl av rig VQOI pri dvvovdag rag (p xdrQcc

rijg avrijg rooitrig {lotoag |* &6r

r^v re [i<

yi6rr]v rj[iQav xal rr^v r&v Gxicbv

15 aTtorffotGd'ai,.

Ay'. OTCOV $ rb Zâoâ rov noAov HOIQ&V <5rw

Jtd, Xl av rig vooi \L^ dvvovtiag rag <p xdrgarijg ftfowfig roonrlg poioag of* KH5r Tffvra^rjviaiav

itdhv 6%dbv rqv ^yie'r^v fipfaav yivEG&ai, xal rovg

20 yvapovag rbv faov %oovov TtfoiGxiovg.

A-01

'. OTCOV $ rag oAov rov rfraorrjîooiov poioag

9 6 fioQEiog Ttohog aito rov 6aiovrog f^Qrai^ Xt rb

plv ($oQi6rQov rov i(SrîQivov rj[it,xvxA,iov rov dia

lisGov r&v ^G)diov ohov ovdeitore vjtb

25 rb df vori(brQov 6Aov ovdfaorf vitfo

1. te"\ add. D 3. 2. IGTI D. 5. ytyvfffât D. 6. Is']

add. D 3. 11. ilQ add. D 3

. 12. oFq] -TJ renouat. C<y' Jxft] corr. ex ys-nsi D. 13. 3>6ri\ cb? D. 16. Zij']

add. D 3. 19. G%s8bv nccUv D. 21. rds] zccvrag D. olov]

corr. ex 61?; D 3,deinde ins. td? D 2

. rT<xQrr}iioQiOv] tert. t

supra scr. A 1. 24. ytVsrat] ytyv

tat D. 25. y^v] yfjv

D.

MA0HMATIKHS STNTAEE&S B'. H7

fjusoav sxdtfTov eTovg ytyvstiftccf) [itav de vvxTa,

xaT8oav eyyitircc Qaiirjviai'av, Tovg $ yv&povag ndv-

TOTS TtsotfXLOvg Tvy%dvew. i'dia ds teriv xal Tijg

TOiavTrjg eyxMds&g TO re TOV fiogsiov noAov xaTa

xogvcpfiv yCyved&ai xccl rbv forfl&Qivbv rtjv re rov 5

asl yavsQov xal rr\v rov ad a<pavov$ xai STL rr\v rov

S01V KTtO^a^KVSLV f)7tQ y^g [IBV TCOLOVVTCC

TO POQSIOTSQOV SCCVTOV ndv ffltttyafytoV) vitb

TO VOTKDT8QOV.

Usgl T&V iitl Trjs syxexAiiievys 6<paiQccs tov 10

xai TOV

$rj T&V xa&oAov itSQi Tag

avsl'rj dt|at, rt&g av

IxdGTrjv EynlLGw xai oC Gwavacpsgoiisvot, TOV 15

XQOVOI, Talg TOV dia pfa&v TCOV Z&

xvxhov nsQiysQstaig, a<p &v xal Ta aMa ndvTa

xaTa ptQog axoAovd'&g ^iv nffrodzvfrfideicti, xaTa-

XgrjGoiisd'a [isvToi Talg T&V Z&di&v 6vo[ia6iai,g xal

jr' avT&v TCDV TOV Ao|oi) xvxAov d&dsxaTrjiiOQicav xal 20

ag T&V ao%c!)v avT&v drtb T&V TQOTtix&v xal farjiiSQi-

v&v Grjiisiwv Aa[i/3avoii8VG)V) TO [lev dnb Tijg tagivrjg

1. ytVttfohu CD. 2. ^yytcrra] eiTiGrct D, r\roi D 3.

\ alt. v ins. D 3. 3. sen, D, comp. B. 4.

om. D. 5. yiyvscftcii] A, yhssO'cii BCD. 6. ccyuvovs] &-

ins. D 3. 9. voTeiooTtQov C, corr. C 2

; voteioregov D, VOTLOTS-

QOV D 3. 10.

'] I BC, om. AD. lyxtx^f'g B. cyai-cg] GtpaC- e corr. D. 12. 6vvKvcc(pOQ&v~\ -o- e corr. C. 13.

ing. A. 14. civ HapfidvoivTo] ccvcdctpjidvoiVTo D. 17. rcc

Ua] A, raUcc BCD. 18. r]piv axoXov-O-cog D. 20. T&V]TOVTCOV D. xai] om. D.

is to, sitopevK rijjs r&v oAov

Koibv xaAovi/rsg, to de dsv-

rfoov TavQOv, xal iitl t&v %rjg coGavrog xara rijv

TtaQadsdoiiEvqv v^nlv ra&v r&v i$ tydi&v.

5 dsfeopsv de TCQ&ZQV, Qti a[ faov axfyovtitti, rov

avrov iGripsQivov GYHLBIOV 7t8Qi<pQeicci, rov dtu

XG>V tydfav xvxhov rats i'ticus asl rov

xvx&ov ytQi<pSQSicu$ dwccvatpegovrai,.

i'titG) yaQ iisGyppaivbs {lev xvxkos o

10 %ovro$ d^ vîiKvxîov rb BE/d^ rov ds far][iQivov rb

AEP xal rov Ao|oi> xvxAov

dvo ruijuara r6 re ZH xal

rb K) a)6r zxdrfaov pwr&v Z xal GripEC&v rb xccrti

15 rv faivv fariQiav V7to-

avrov

6ag ras ZH xal K dia rcbv

K xal H 6rniLG)V avacpQ0d'ai,.

20 A^yo, on xal at fxarfya avrcov 6vvava(poo^vai, rov

i(5r^LQivov 3tQi(pBQiai, rovr&nv ai ZE xal E,i'Gat, efaiv.

yao avrl r&v rov faqpfoivov TtoAcov ra A

2. KQLOV] comp. B, ut semper in signis. 4. i$] A, 6m-6ey.cc BCD. 5. Ifjfifjiu a mg. B, a Hfjmicc mg. C. dstôfisv

SB] om. B. <?] drj D. tinszovocci] -at in ras. A."

6.

avrov ai](jLQi,vov] faqiieQivov rov ccvtov D. 7. tai$] on rctig D.8. 7tQi<pFQica C. 12. ZJf] corr. ex ZE D. 14. wC\

om. D. 18. xat] om. D. 19. v.u.i\ om. D. avacpEQS--i/a- supra scr. C 8

. 20. at] supra scr. D 3. ovvavava-

svai, D. 21. xal @E] E0 D. 23. iffrco] mut. inA 4

. avri] del. A 4. r&v] om. B, supra scr. C 8

.

rov] om. D. nolov B.

MA0HMATIKHS STNTASE&S B'. H9

xccl M Grjiieta,, xal yeygdyftodav dt' CCVT&V

xvxk&v T^îccTa to re AEM xccl A teal en r6 re

AK xal ZM xccl MH. eitei ovv toy e(Svlv % ZHTi] K, xccl 01 diet T&V K xccl H yocc(p6[ivot,

aHÂot l'6ov aiCBiovdiv <p' exdreoa TOV

G>6re xal T^V [i^v AK rij MH yive6&Ki fav\v, rfv de

EK rri EH, faoxtevoct aoa yiv&tui TO plv AK@V& MHZ, TO de AEK T& MEH. xal

'

$ Îv vxb

KAE aocc y&via L'6rj efalv T% vnb HME, r\de VTCO

KA o'Ai? T% vnb HMZ oty' &dTe xccl Howr} ^ vnb 10

EA Aowrf/ Tfi vnb EMZ fay e'tirai. nal (Id6i$ aocc

y E (Ideei, TTJ EZ fay itiriv' oneo edet, dei%cu.

ytdfov de defeoyiev, OTI ui avvavacpegoiievai, TOV

tGYHieQivoi) TteQiytQEiai Tcctg focus xcci i'Gov anexovGcuc;

TOV KVTOV TOOTtMOV 6rHLiQV TOV ditt {leCf&V TG)V fC3- 15

dfov Kvnkov GvvKiKpoTeocci, 6vvcc[i(poTeQai,s CCVT&V Talg

lit 6od"f}s Tils Gyatocts avacpooccis fam d6iv.

yap 6 ABF^J [ie<5r]ii{lQi,vbs nul tcovri[ii,-

TO Te BE^J TOV OQLÔVTOS xal TO AEF TOV

,Kctl yeyodtpfrcoGav dvo l<5ai Te nccl faov 20

TOV %eiêgivov Grjiietov TOV Ao|oi) xvxlov

1. xat^pr.)] om. D. di' UVT&V] corr. ex diu r&v D. 2.

to TE (pr.)] om. D. xt (pr.)] AK e corr. D 3. xal tti

3. ZM xca] MZ D. 4. dice r&v] corr. ex 81* ccvr&v D.

%at(alt-)] om - D- 6 - ^H MEND, del. D 3. 7. iao-

Ttlsvga} corr. ex loonfovgov D 3. AK~\ -& e corr. D 3

. 8.

AEK] EAKT>. MEH] -H in ras. A. 9. yom'a CCQCC D.10. (Ufl] om. D. 11. EMZ] AC 2

,MEZ BC, corr. ex

HMZ D 3. 13. Ifiwa $ mg. B, JT lr\â mg. C. Ss] Sij D.

16. Gvva^cpotBQcei] ccl ovvupcpotSQUi D.

rats] supra scr. ^-a-y B 3. 17. avarpogcci D. facet] LGJ\ D,

supra scr. $ B 3. 18. ABTJ] ABF D. 19. rov (pr.)

AET\ mg. B 3C 3. TO (alt.)] om. D. 20. facet] supra scr. D.

XQiq)Qi,ai, ijr ZH rov Z vrtoxi[ivov

xalYIH rov vnoxsiiisvov eaQivov

xal to ftev H Grjtisfov xoivbv rrjg avaroA.ijs avrcbv

Lvai xal rov 6o%ovrog dia, rb vitb rov avrov

5 aAAÂov xvKkov rc5 farnneQivK*

TtSQiAaiifSavsGd'ai, rag ZH Kal

H TteQiysQSiaS) GvvavcKpsQS-

cf&ai, de dôvon rqv [lev Erri H, rty de EZ ri] ZH.

10 tpavsgbv ovv yivercu avro&sv,

on xccl olri v\EZ fay <srlv

rats rt' OQ&ijs rijg Gyaioasr&v ZH xccl &H avayoQaig. eav yaa v

vonov rov Gr][iQivov jrdAov rb K15 dt' ccvrov xal rov H yLyi<3rov xvxhov rrccorri^6oi,ov

rb KHA faodwccpovv r& iri OQdijs rr\$ Gcpaioag 6pt-

r H rijs

ZHi\

dl AZ ^ Gvvccva-

xal 6vva[i(porQccg

20 rag &AZ GvvaiHporfycug rats EZ faag r slvai xai

vjfb [nag xal rijg avrijs Xoi,%(j&ai rr^g &Z'

xal yfyovtv

fvbg povov25 xara [iaog Gvvavayoaag

dia rovrcov, on,, xav g>'

rag

,7too6an;od-

4. vnb rov] vn B. 6. vat] om. D. 8. 0E] E@T>. 9.

- e corr. D. 13. xat] om. D. H] corr. ex N A.

vno&ffievoi] v- e corr. D. 16. tcoSwaôvv] -v add. B 3C 8.

*rjs] om. D. 17. TJ (alt.)] ins. D 3. 18. rjj] corr. ex ro D 3

.

19. ZH] H Z D. wars] corr. ex re B 3,rs C. 20. Ante

rds ras. 1 litt. C. <9EZ] 0- e corr. D 3. 21. onsQT D. 23. ^' Ini D.

MAGHMATIKHS STNTASE&S B'.

%o[iv xal rag r&v Aomcbv rgi&v

121

rovr&v ovv ovrcog %6vrov vf

P6dov itaQakkrikog ,OTtov

f\

fanv far][iQi,VG)v id L'I b ds

Ag, xal 6rco

nafav 6

Ttohog

[ilv o^toiog

rov 5

6

to BEA,dl to AEP, rov de

rcsv tydicav TO ZH0ovrcog %ov, &6T to H vito- 10

Xt6d'ai, rb WQivov GVHLSIOV. xal

kqyd'WTOs rov oai'ov nohov

rov farjufoivov xara rb K 6r^-

yieiov yeyQKy&a) di? avrov xal

rrjs xara rb A roping rov r 15

dia {LBGcw rCbv ^cpdC&v xvxkov xal rov bgi^ovrog

psyfarov xvxkov rsragrruioQiov rb KAM. rtooxffad'G)

$ ryg HA 7tQi(pQiag do-O-ft^g tr[V 6vvava(pQOiivr)v

rov far][iaivoV) rovr6nv rr\v EH^ VQelv xal

Jto&rov ^ HA rb rov KQLOV d&dfxaryiiooiov. 20

7ti roivvv Ttafav iv xaraygatpri ^yfar&v xvxAcov

stg dvo rag EF xal FK yfyoa^^vai, itilvij

rs EAxal

fjKM Tu,vQv<5ai aAkij&ag xara rb A, 6 rifc vnb

rr\g KA Jtobg rqv into rqv diitki\v ri\g

re rov ri$ VTIQ rfv ontv 25

4. ftf'v] om D. f][ieQa] j\- corr. ex v A. 5. (3o(uog A.

D, e)QTi]Tca ABC. 6. teT] -s e corr. C 2. 7. iv

'om. D. 9. picmv] -co- e corr. A.Sic* rov D 3

. 15. re] TB dt D. 16. uvnlcov D. 19. avty]bis D, corr. D 3

. 22. xcu] om. D. i rs 23. 1 at E4 D.25. ^T Pz/ D.

14. di' avrov] corr. exuvnlcov D. 19

ij rs 23. 17] at

rijs KA Ttgbs ryv VTCO r^v dijthijv rijs AM xal rov

rijs vnb rrjv dirtAijv rijs ME ngbs rr\v VTtb rqv. 74, 9]. AA'

rj plv rijs K/l 8ntô/3 xal

f)vn avryv sv&sla r[ir][idrG)v o A/3

5 ^ de rils F4 poiQ&v Qrj xal q vnb avr^v sv&eia

(jidfcov c,J d v$) xal vtakiv % plv dtÂiJ rijg KA p

Q&V QV% pa xcdfj

VTib avrrjv sv&stcc rprj^dtojv QI Aa

f]ds 6inkvi rijs AM iioig&v uy tO1 v%" xal

i\vnb

sv&eta rp'rjpdrcov xd ie v^' lav aga axb rov

10 o A/3 d itgbs ta c d vs Aoyov g>Aco^v rbv r&v

(>tj Aa Is TCQOS ta xd Ie v, KarakeKp&riGBrai 6 rijs

i)7tb rr\v 8nt)^\v rijs ME ngbs rfjv VTCQ r^v diTt^v

rijs EF ^6yos 6 r&v Ty o 7- ngbs ra QX. nai itiriv

fjvitb rrjv diitlijv rijs EF rprjpdrcov QK' v\ aga VTtb

15 ryv din^v rijs ME r&tv avr&v stirw Irjo . tiers

xalr\ y&v dtJtAi} rijs ME iteQUpegeias [ILOIQ&V h'tirai,

, avrr\ dsf]ME r&v avrGbv

t] Ay. AA7

i\ HM jtsQKpsQSia rfj HA sn' og&ijs rijs cftpai-

GvvavacpeQsrai) r&v TtQoaxodsdsi'yiievcov [p. 84, 11]

20 <Srl [lOLQ&v x v' xal Aoiicr} aga ^ EH

4. 3] mut. in y" B 3. 5. 8ft ds SinJifj D. vno] vn D.

6. rg] v?" e D. 7. â] p$' D et, (3in ras., B 3

. M]vn D et corr. ex vno C 2

. 8. vno] vn D et e corr. C 2. 9.

ir^<W A._ J^ 8 (pr.)] y" in ras. B 3. 11. Xo] ta' D,

corr. D 3. *8 Is v\ renouat. B 3

. Is (alt.)] MJ' D, corr. D 3.

6 rf)g vno'] renouat B 3. 12. ME] ME loyog D. 13.

EP] E- renouat. B 8,ut in seqq. complura. Ir\

o s] corr. ex

t fl ffO- Ir\ Is D 3. 15. o i] corr. ex Zs D 3

. 16. totcci] Ictiv D;deinde del. Izvs~jJip. 17. tg] add. B 3

,om. C. Xij] ^ B.

18. 6^73] e corr. D 3. HM] corr. ex M C 2

. 19. cvvavcc-

vacpSQSTcci D. nQoanoSeSsiynsvtov] post -a- ras. 2 litt. A.

20. loriv D. 21.iJ3]

t- in ras. B 3, x|3 C, ifi supra scr. C'.

MA0HMATIKHS STNTABE&S B'. 123

xal GvvanodsdfLXTai,) on xal TO psv t&v'

dodsxccTrjuoQiov rots avTols %QOvoiS GvvavcccpSQercu,

id1

t/3, xaTQov ds TO TS Tijs HaQfrevov xal T&V Xrjh&v

rotg fafaovtiw els TYJV dwrAiJv T% lit' dg^s Tijs

avayopav %QOVOIS AS m^' oney edsi dti^cci,.

itdhv v\HA itEQiyeQSia 7tQi,s%eTG) T&V dvo dco-

aTrftioQiov TOV TS KQIOV xccl TOV Tavgov ^Loi'^ccg |*

dy TCL {jitOKEipeva T&V akkov HSVOVT&V T&V CCVT&V

$1 per diTtfa] T^g KA (loiQ&v yCv&tui Q^ v&^Lt/3

xal

fjvitb avrfv ev&stcc TIIYJIIKTGJV ()tj3 wy vg, ^ $* diit^ 10

TVJS AM pOiQ&v fta & wj xalrj

V7t CCVT^V ev&eZa

tpYilid't&v pf} a prj. sav CCQCI ncttiv aito TOV xtibv

o A/3 d Jtgbs Ta QJ d v$ hoyov atp^o^ev TOV tS>v

gift ivy vZ rtQO$ TK ftj3a jiu?, XKTcdi<pd"tj0Tcu 6 Trjg

vxb Tijv di,7tA.r}v Tils ME rtgbs TYJV vitb TVJV dinKr^v 15

os b t&v A/3 Ag d ngbs tec, QX. XCCL

iv\v diTthijv Trjs EF TjirjiiaTcw QX' r^ O.QK

v Tils ME T&V CCVT&V tetiv Aft Ag

xu.1i} psv dunki] Tils ME TtSQitpegsLas poig&v i<5nv

Ace A/3/

yyi,6Tcc, avrri derjME T&V CCVT&V Is p. 20

arjME <ttrj xaTa TK KVTCC TtQOKjtedetx&r] [p. 84, 13]

vt, p8' xal Aoiitri ago, v\HE poiQCbv fativ

vv\. 6 CCQCC Kgibs xal 6 TCCVQOS avccysgovTai 6vv-

sv OVOIS cc v G)V 6 Kib

1. cvvavccrtoSedfwTcci D. 2. cwavatp^Qerai] post pr. aras. 1 litt. A. 3. xat] xal TO D, r6 ins. B 3

. 4. -nfc(alt.)]om. D. 5. oiiSQ s^ft delicti] om. D. 6. vcov] om. D. 9.

yivsroci, fioLQatv D. ^TJ] QVT\ D. 10. vno] VTI D. 11. JIK]

-u renouat. C 8. ^] ABD, o A 4B 3 et in ras. C 8

. 21. f)]

xal i] D. 22. HE potQ&v SGTLV] EH D. 23. cvvccfiapoTsgoi,

Jv] 6vva(icpots(>ois D. 24. cvvavacpSQOpsvos] D, corr. ex GVV-

ois AC, Gwccvarpsgo^svois B.

%a6voic; i& ifi- xal povov ccacc TO

Tavoov dodsxaryiioQiov GvvavcupeQSTKi, %Q6voi x/5 jitsv

dia Ta avra de xdfav xal to (iv TOVr

Tdorj%6ov

d&dsxatrjpdQiov GvvavV%d"ri6Tai Tolg foots %o6vots

5 x(i jiHf,xdToov ds r6 T rov AZOVTOS xal TO TOV

Tots fairtovGiv Eig Trjv diit^v TJJS

avcupoQccv %QOVOI,S Af /3.

ds xcclvj ftv yLEyiGTri rjîsocc, fag&v itixiv farj-

id L\ fjds eA.a%faTr) &

/.', dijAov, OTL ncti TO

10 [ilv alto KKQKLVQV [iXQi> TOV TOÔTOV i

fj[ii,xv%A.iov 6vv-

avVxd"*J6Tat, TOV far]iiQi,vov %g6voi<s 6it> A, TO d%

cforo AlyoKfQG) pfygi 4idv[i(QV %QOVOLS QpP A. &GTB xcct

XCCTQOV {lV T&V XaTQG)d'V TOV fCiOWOV 0rj^lLOV

TTKQTrHLOQiG)V 6VVCCVVX^t]6TCCl, %()6vOl<S OK If, XttT-

15 QOV $ TG)V XCCTQG)d'V TOV [JiT01tG)Ql,VOV

V0t,$ ~QTJ jl. Xal kOLTtOV [lV CCQCC TO T T&V

HCCi TO TOV Afy6KQG3 dcotifXCCTTJllOQlOV XKTOOV 6VV-

avV%&Yi6Ta,i %QOVOIS x& it, Tots tefaovGiv ei Tovg

TOV TfTaoTrjiioaiov %o6vovs 'oa tf, Aotjrov d TO T TOV

20 Kaoxivov xal TO TOV TOÔTOV XKTaov %a6vois A Is

Tots teinQvGi ndkiv fig TOVS xal TOVTOV TOV TTaoTr]-

q)CCVQOV) OTL TOV CCVTOV CCV TOOJCOV TOVTOIQ

3. 6s] Srj D. 'TdQwoov] A, comp. B, v8qt%66v C, V$QO-

%6ov D. 4. 6vvctv%ftrlGtai B, Gwccva^r^cttca D, corr. D 3.

Ante rots del. o D. 5. gxarfpov] -o- in ras. 2 litt. A. 6.

rr?s(pr.)] CD, rot? AB. 8. 6s"] corr. ex Srj D 3. 9. 6s*]

6' D.10. TOV] om. D. 14. 6vvccvavt%fti]6tTcct, A, supra scr. vs A 4

.

If] corr. exir^

D. 15. -QOV ds r&v Ixar^-] mg. A 1. 17. cvv-

ctvavfx&riGtTKi, AC, corr. C 8,vs supra scr. A 4

. 19. rov (pr.)]

om. BD. 20. rb rov] BD, rov TO A, TOV C. 21. teinovGivCD. TOV] om. D. 23. uvrov] bis D, corr. D 3

. TOVTOIS

TQOTtOV D.

MA0HMATIKH2 2TNTAEE&S B'. 125

xal Tag T&V B^KTTOVOV T^ri^KTov TOV dt,a

T&V <pdiG)v xvxhov GwavctTohcig.

(f av v%or]6T6TQOv xal ti&odi,XG)T()ov avTccg

*a xal ovT&g.

6TG) yap itQ&TOv [isGriiiflQivbs xvxkog 6 ABF4 5

xal OQôvTog [lev fipLKVKhov TO BE4, farjpfQwov

ds TO AEF, TOV d dia fisdcov T&V fydicov TO ZEHTrig E Toping KKTK TO SUQI-

vbv 6r](iiov vitoxi,[ivr]g. xal

Jt aVTOV TfJQ 10

ETOV dia TOV

TG)

TOjfiT,

xal

Tog TOV A itokov TOV 16^8- 15

CCVTOV TTccQTrjîoQia p,eyi6TG)v

TO A&M xccl TO AKN xal E'TI, TO AE.

<paVQOV TOIVVV KVTO&SV 0TiV,

OTi TO ETOV dia fifVov TCOV Jwdtcov ml pv oQ&fig Tijg

ty EM 7tQl(pQia TOV l<3rHLSQI,VOV 6VVKVa(pQTCCI,) 20

7ti $ TYIS yxxki,[ivr]g Tr\ fay TTJ NM, litBidr^nsQ

f) fJLV K TOV TCCCQCi^ÔV 7tQHpQLa, 6VVO.V(X,-

<pQT(U TO E T[JLrl[lCl, 6[IOLCC 0Tl T% NM TOV l6V\-

[JiQLVOV) CiC d' OÎOICCL 7tQl,(pQlCCl, TG)V 7tCCQaA,A,rjA.G)V

Iv faoig jcavTccîj %Qovoi,g avacpsoovTcu. xal r EN 25

2. cvvccvKCpOQcig D. 3. noi ptQ'oMwtQOV\ mg. A 1. 5.

mg. BC. 7. ÊF] corr. ex. AEF D 3. 10. ccno-

C. 14.-xvjtlov D. 17. to (pr.)] r6 rs D. 20.

EM] ENM D. iteQicpfQslas D. 21. eyKhpevris A, corr. A 1.

NM] MN D. 22. K&] OK D, 0K D 3. avvuvava-

D. 23. icriv D, comp. B. 24. 8'] dt D. TTKQ-corr. ex 7tuQcd1ii]l.oLs D 3

.

126 KAATAIOT I3TOAEMAIOT

<5rlvfj

7tl

rov E rpijfiaros uvuyoQa rife id

0<pcu'oa$, dedsixrai Tf, on xal 3ca<9-oAov, eav

nv<s ovr&s 3tai(pai,cci, [isyfatcov xvxhcov cog rj

5 rb EN rpriiitt nsQis&i, TJJV V7tQo%Yiv r&v siti rs

teal rr\g 'yKKîfjivrjs GcpaiQccg avcctpogibv

rov dia ILSG&V r&v t,G)di(av nvxkov

3tQltpQSl,G)V i}Tt6 T tOV E XCci XOV yQCC(pO[lVOV dlCC

rov K10 rovrov

p6vcQV rov r

rov far}[iai,vov ûtxvÂtcov, xctl

dia rov Z voriov 7t6Aov rov

fariiLSQWOv yyQd(pd'G) dvo re-

15 rccQrynooicc n&yfarcov Kvnk&v

ro r ZH xal rb ZKA,ds rb pev H 6rj-

rb xotvbv rov di,a rov

xxi<5&G)

v xccl r&v rov xal

20 *yQccq)0[ivov Jtccoa^tjôv xal rov opt'fovrog, rb de Krb XOLVOV rov yoa(po[i6vov dt: rrls dox^S Aoyov VXV

1. ^/larrcov D. 2. GcpcciQcts] GtpuLQK$ uvucpogd D. ccva-

om. D. TTJ

] ini D. 3. on xal xa-^d/lov] xcct xa-91-

6/lov on D. SKV] corr. ex &va D 3. 4. TtSQicp^QEiai, ovrcog D.

me ^ AC, A&M supra scr. A 4, i] A@M xat post tog ins.

mg. C 2, obs ?j ^1M in ras. 7 litt. B 3

, wg 17 A&M xal ^ D.

yfKN, ro] xal ^ ^^JNT" ro mg. B 3. 6. xat] xal int. D. 8.

E xat] corr. ex EX C 3. 9. oTrcp ZSei ^r|at] om. D. Deinde

? ^ xaraypaqDT? D (fig. in eadem pag. est). 11. ^6r\^-

D 4, ^ D, f D 3

. TOO*] om. D. 12. TO] rcov roi) D.

D 4, ^ D, ^ D 3

. 14. forêtvotT) D 4,

f?\ D. 16.

TO rf] ra D. xal TO] om. D. 17. ft] di? D. 18. â] 6? t-

a D. 20. xal tov oôvrog] om. D. TO 8s K~] rag. A 1.

MA0HMATIKHL 2TNTAEE&S B'. 127

i&v 'Iftdvov tjxal aMov Tivbg TCOV TOV

T^^LCCTCOV dfdopwov. etg dvotfi)

ndKiv [isyforcov xvxAcov

3tQicpQiag rag Z xal E ysyguppivai fidlvij

TS

ZKA xal17EKH TtpvovGat, aUtflag Kara TO K, xaC

6 xris vitb TJJV diTChfjv rr\s H itgbs TT\V vitb r^v 5

rrjs ZH Adyo? 6 Gwrjupsvog sx re rov rfjg VTtb

TYJV dinAyr ryg E agog tv\v vnb TJJV dtjrAijv rijg EAxal sx TOV rils VTtb rr\v 8iitKr\v rijg KA TCQOS TYJV

tr\v dnt^v Trig KZ [p. 74, 9]. AA' iv TtaGaig

ijTS dt?rA^ T^g H TtSQiyegsias fj avri\ 10

ttiriv yaQ r\ psTa^v TCOV TQOTtLX&v xal dia

TOVTO xal koiitri % dmMj T^g HZ. xal bpotcog mlr&v avT&v TOV dia \ni6&v r&v Jcodtcoi/ rpyâtfov ij

TS

rijg AK 7tQiq)Qiag dutkij xaTa naGag Tag dyxAfafig

i&ilvv\ avTî xal didoTat, dia TOV Tijg Ao%(b6G)g xavo- 15

Wov, xal koiJtr} dta TOVTO itakivj] diithi] Tijg KZ'

&6TS xal TOV Tijg VTCO TYJV dtjrAijv Tijg E 7tgbg Tyv

vitb tr[v diTttfjv Tijg EA xaTateiittf&ai Aoyov TOV

CCVTOV v TtaGaig Tatg iyxkfatfw litl T&V avT&v TOV

TTaQTr){lOQlOV T{ir]lldTG)V.20

lav drj TOVTOV ovT&g fyovT&v Tqv Tr^g KA rtQi-

y>Qtag diafpogav dia 8dxa T^îaTov TOV aito Tijg

farjiiQiag fag xgbg TO %i\iQt,vbv TQomxbv

TTaQTr)[lOQLOV 7taQaV^0CO^LV Tijg pfyQl TCOV

JtQt(p()t,G)V diaiQ0COg aVTCCQXOVg XaTCC 25

Tijg

1. rov'] om. D. 3. nctl] om. D. ij rf] at D. 4. nctl

om. D. ccUrjlcus C. 6. ZH] HZ D. 6] om. CD.8. KA] AK D. 15. dido-cat] -o- corr. ex -i- in scr. C.

17. -Ttlr\v 18. diTtirjv] mg. C 2(alt. -itlfjv etiam in textu C).

19. h] 8> D. 26. H] corr. ex &E D.

fôpsv TtKVtote ÔIQ&V [it, [ifi ~p nut rrjv vno

ccvt^v Ev&slccv TIWIIIKTWV pr] Aa vs, rv\v ds tr\<sHZ

A/3 it> % xai rr\v VTCO ccvtqv sv&stccv

[id vy. ctidavr&s de xcd tTtl [ilv TTJ

5 dsxcc[ioi,Qiccv ctTt%ov6rig rov eccgivov Gijpstov o>g ngbsrb %em,SQivov tQOTtinbv 7t8Qi,cpQSiKS tv\v [iv rvls KA

\ y ~i$ ual rv\v VTCQ avr^v

v\xe A#, tqv ds rrjg KZ dtjc^

QOCC vS [id xctl ryv vitb avrrjv sv&slccv

10 QL& ft/3 id. ml ds rri<s

7tQi,<pQLccs iv\v [iv Tijs KAxai TJJV VTtb avrfv v&tavds Tr}s KZ diTt^v HOIQ&V ()|d vd nccl

ccvrqv sv&slav rîrjîdrcov git] v ftf. itl d rijs A

15 ponces art%ov6ris 7tQi,<pQ{ccs iv\v [iV rr}s AKpOlQG)V Wy l& VTJ KKl TrjV i)7l

Twv xd L v$, rrjv d rijs KZxal rqv VTtb avryv v&lav r^r^Krc3v QI,

Aa T. litl

d rrjg fl iioigas <x7t%ov6rjg jtQi,(pQias tfjv [iV trjs

20 AK diit^v pOiQcbv A ^ ^ xal tfjv vitb avrr^v v&iccv

1. (ioiQ&v] sic ACD. vno] vn D. 3. vno] vn' D. 5.

rag I ft D. cog] corr. ex COGTO D 8. 6. rv\v\

corr. ex rrjs D 3. KA] AK D. 1. TJ y] rjy AD, corr. D 3

.

ff\v\ fn(i. B. vn6~] vn' D. 9. vno] vn3D. 10. enl]

corr. ex sn C. K (JLOIQCCS] slnoGtrjc ft D, ei'-noGi p D 3. 11.

xr\v] -v ins. D 3. KA]_AK D. 12. *ca] ins. C 2

. vno]vn 3

D. tg] corr. ex /Is D 3. 13. vno] vn' D. 14. TJMI;-

fiara D. 15. AK] KA D. 16. vjj] j]BC. ^7 xat]

NH SV

_D. vn6] 81 vn D. 17. Is] id' D. _ QVS] QKS D.

ft |3] pp D, fia ABC. 18. vno] vn' D. ia] A, o suprascr. A 1

,US C. Ts] i D. 20. AK] KA D. dtTr^v] -v

ins. D 3. i

jj] Jiij D. ^ (alt.)] om. C. vno] vn' D.

MA0HMATIKHS STNTA3E&S B'. 129

ce IK jity, rr\v $ ri\g KZva v(l xal rr]v i)itb avri]v sv&stccv

1

. eitl d rf$ v

vi)v [lev rijs AK 8nt'kv\v [IOIQ&V Ag sjiZg

xal rr\v vitb

&VTTJV sv&Elctv Turjuccrov Af T A#, r^v ds tys KZ 5

Qpy vd td KKL xv\v vitb avrrjv sv&stav

s ftd. sid ds rijs f iioigas fateffyfaift

v pw rtjg AK diTthrjv poiQcbv ]IK o1/tj

Kal rrjv VTtb ccvrriv sv&iccv rîrj^ccrajv pfl a pij, rr\v

$1 r^s KZ dnt^v [loigcbv ghrj v& pfi xai rr\v f)itb 10

ccvrfjv v&tav T^rjîdrov pt/3 wy vg. iitl df rijg o

Qi(pQtas rr^v [iv rijs AKji %$ xcci rv\v vitb avTrjv SV&SIKV

g 7^, n)v dl rijs

xal rrjv vitb avrr^v v&iav rîiccrcov 'giv& ftf. 15

AK diit^v [lOiQ&v jZ? vS A/3 Kal rr}v V7tb avtijv

ft ;i, tyv $ rijg KZl rfjv vitb ccvrrjv i)&lav

d Tsr. 20

xal 8ia ta itgoKSLêvcx, ,eav aitb rot) rtjg t>^6 ri}v

b$ rrjv i)7tb tr\v diithijv rrjs HZAdyov, rovt6Tiv rov t&v

^LTJAce v agog ra Q& pd vy,

fxatirov r&v Kara

2. vno] vTt D. QLS] QI& D. 4. xr^v (pr.)] -v renouat.

B 3,corr. ex -a D 3

. AK] KA D. te] -g renouat. D 3. vno]

vn D. 6. vno] vn D. _7. F] e corr. D. 9. VTTO] -yjr' D.

10. xfjs] trfv D.^/Irj] >l7]

C. vno] vn' D. 11. r^rjficc-

roov] -j]- corr. ex v in scr. A. 13. vno] vn' D. 15. VTTO]

vn D._ i^] corr. ex ve D. 17. ytX] ^^1 D. vno] vn' D.

18. /^(ali)] jl seq. ras. 1 litt. C, om. D. 19. vno] vn D.

20. <H 8] QI$ ABCD, similiter saepius. 22. HZ] ZH D.

Ptolemaeua, ed. Heiberg. 9

rijg VTtb ri]v diithijv rijg AK Jtgbg rv\v vnb rr^v

rijg KZ Adycoi/, xarakeup&riGsrat, rîiv xal 6 rfjg vnb

rijv diTtAijv rijg E Jt^bg rr)v vnb rty diithijv rijg EAAdyog Kara xdiSag rag fyxMtisig 6 avrbg r& rcbv | iicl

agog ra & A^ ?fal de rijg x itgbg ra Irj vg, iitl $\

rrjg ~K Jtgbg ra MJ a, snl ds rqg ft Ttgbg ra Ag Ay, enl

ds rijg v ngbg ra [id t/3, iit\ de ri\g | ngbg ra v ftd,

iiti ds rrjg o xgbg ra vs ft, iitl de rijg it agog ra

10 vrj vs.

tpavegbv de avr6&V) ori, xal xa& Ka6rriv rcbv

iBvriv fyovreg ri)v diitM]v rijg

, fat&tiifctff rotiovrcov farlv poig&V) otfoig V

rr)v Aa%farr]v r^^Qav fj t^/Ltf^tv^, xal

15 rfv VTtb avr^v v&iav rov re Adyov ravryg rbv ngbg

rv\v vjtb ri)v diTthijv rijg EA, fôîsv xal avrr^v dsdo-

xal xv\v diithijv rijg EA 7tQi<pQiag, rjg rv\v

)rovrsdnv avri]v rqv EA, 7iQi%ov6av r^v

[p. 126; 5] vjtQO%i]v acpekovrsg aitb rcov

20 in OQ&ijg rijg dyatgag rijg xxi[i8vrig rov di&

7tQi,(pQLag avacpOQ&v rv\v xara rb V

rijg avrijg 7tQi(pQiag avatpogav

1. T7)s(pr.)] rbv rijs D. 3. Ttgog EA] om. D. 4. ra]r&i corr. ex rot C. 5. div,u poiQas] dsKccpoiQias B. Iqpafitv]

I- e corr. C 2. 6. #] corr. ex o D 3

. Ay] corr. ex \r\ D 2.

itgbs ra] om. C, ngos D. 6s (alt.)] 9 ins. D 2, 9 D

3. 10.

vs vi]' D. 13. tart D, comp. B. 15. vno\ vn D. 16. -bito]

-6 e corr. D. vnb rr\v] om. C. 17. Trepiqpf^fto; D. ^g]corr. ex slg C 2D 3

. 22. Hie des. fol. 42r col. 1 in A uacante

plus quani dimidia parte, in qua KVCOi\ secrecygacpt] ; fig. initio

columnae 2 est.

ya.Q vnodsiyârog svsxsv ndkiv

rov dia 'Podov TtaQaMrjAov, XK& ov % psv dtnîj rijg

E 7tQi(pQiag ILOIQ&V stinv A A, 17& ît avrr]v

v&ta r^îdrcov A?? Ad syyiGru. STtsl ovv 6 avrbg

Ao'yog 6rlv r&v f ngbg ra Ay Ad xai r&v [isv 0- Ay 5

ra f 17, r&v dl Irj i/f ytgbg ta i$ ta, t&v dlwrjaT<X

1/rj o, r&v ds Ag Ay nfpog r& xy x&, x&v ds

pd i/3 TCQog rot, xrj sci, t&v ds v ^d jrpog ra A/3 AJ, TWV

df vsji JCQOS ra Af v/3, TV df v^ v rtgbg ra AJ v/3,

yivsrat, xai fj JIGV vnb xr^v dfjrAiJv rijs EA 7tQi(p- 10

r&v df'xa poiQcbv viceQO%Ktv r&v

r^^drcov^ i\d fmfafia rijg vit

avr^v 3tQi(pQiaS) rovrfarw avrrj i\ EA^ ILOIQ&V Inl

filv rrjs TtQ&rrjs dsxaîoiQias /3 v^, sitl ds rrj$ dsvrsâg

v, iti ds rrjs rgfarjg r] A?/, litl ds rijg rsragrris 7a tj, 15

7tl ds rrjg Jts[ntry<s 1/y ^t/3,situ ds rr^g sxr^ Ts

^ts", itl

ds rrjg spdoprjs i>t, fcd, sill ds r^ff 6yd6rj$ ITJ xd, xal eid

rrjs tvdrrjs ds dÂovdrt avr&v rcbvl/tj /If. &6rs

7tidrj [p. 84, 15] xal tri OQ^S rijg 6<pKiQK<s 17 pev

fi

r

%(>t rijg TtQ&ryg dsxafioigtag jtsQL<pQSi,a 6vvava- 20

(psgsrai, %QOVoig -9* t, rjds p>%Qt> rrjg dsvrsâg Irj x,

17df p%Qi rijg rQir^g xv, fj

ds IIS%QI* rijg rsragryg

1. fVexfv ndUv] XKQLV D. 3. EG] 9E D. A] seq.

ras. 1 litt. D. <?'] <?e' D. 5. #] corr. ex o D 3. 7. o]

in ras. A 1

;b B, ut semper fere. xy] -y in ras. C 8

,x^ B.

it^] x^ D. 9. jig It] bis D. vjj] v- e corr. C. 11.

(jiOLQ&v] post p ins. t D 3. VTCEQOI&V] VTISQOZ B, -j]v add. B 2

.

15. Fv] ~iv D.TJ] corr. ex r) D 3

. ^] i- euan. B. 16.

?XT7jg] ? AC. 17. Y.8 (pr.)] xrj^ A; x$ D, r\ supra scr. D 3; XT?

BC. 18. ds] om. D. 20. dfxftot(>mt(i D. 7CSQicpQicc<> D.

_ 21. Z, T)] convex T^ AD 3. dfvrâg] ^ D, {3

D 3. 22.

v, f)~\corr. ex v?j C.

A A, f)ds PE%QI, rife Tti^Ttr^ [i^xy, $ de Ê%QI rijg

vt, ftd, ^ df ft(> rife

T^g oydd^g o#, 5

rots oAov roi) TetaQtyiioQiov XQOVOIS 9 ? (pccvegov,

5 ort, ^v oupsh&iisv atp' SKaGrys rcbv EKKBI^VQV iit

rils 6(pciiQccs ctvKcpOQGbv xr\v ofaeiccv

s xattx trjv EA neQi<pQwv vneQO%i],

xal rag w r& vnoxstÊvc) xârt r&v ccvr&v avcc-

10 EKapoiQias TteQicpegsia rots AoiJTotg ^povotg

t/3, ^ d ft^pt r^? TSTccQTqs MS

Ay jitg, ^ de ^^t rij

rijg Endows v vd, ^ d ft^t T% oydd^g f

15 ^ df ^^^ rtjg Evatrjg, tovtEtitivrj

oAov roi)

f'x rijg fi[ju<f{a$ rov ^sysd-ovs tfj$ q

QOVOIS oa Is. xal ccvrcbv KQK r&v dexa-

Vfj {LEV XQ&TV} 6VVKVEVE%%"lfl6Ertti %Q6vOi<3 ff fcd,

^ d dEvtEQa S UK, i]df rptTT^ g A, ^ df

20 ^ df TtEyMtri Ay, ^ ^ ^^ ^ ^/5, ^ df

^ ds oydorj & fc^ 9 ^ df Evdtri I Ad.

1. Post^ del. rjD 3

._ 2. gxrijg] TTTTJS D. ^] -5

euan. A. |rj] corr. ex 77D 3

. 3. e] ins. D. 5. cup'] &nb

Tfjs cp' D. synsLfisvmv D. JJT'] snL D. 7. vTrsô^?)?]corr. ex vnego^v D 3

. 9. (TvvavavfVf^rjaeTat D.17 f*^]

corr. ex jyiiv D 3. 11. dfvrâs] p"'

AC. 13. jxg] |tiyD.

16.(3 linnet mg. C. 17. cvvccvacpfQo^svoLS D. ôvotg]

corr. ex ôvos A 3. %at] xat r&v D. ^sxafiot^cov D. 18.

tfvvavaîbfaetca, supra scr. f, D. 19. fa] af D, ^,' D 3.

20. gxrrj] s' B.

MA0HMATIKHS STNTASESS B'. 133

<bv aitodeSsiyiisvcdv avro&sv 6ovrai> Jtdfav dice ra

tivvaitodedsiyyisvai xal ai r&v konccov

Kara, TO axoAov&ov avayogaC. rov

TQQTCOV

G)v ftp' xcc6vr]v

ye rqv nag' waGr

ravrag xavovix&g 7tQO$ r^v 7tl ra

iev CCTCO rov vn avrbv rbv l<5v\-

, cp&dvovrfs d ^%Qi rov Ttoiovvros COQ&V it,

v, xal r^v naQavt.rjGiv avr&v 10

7toiov[ivoi dia TO pr] a^Moyov yCvsG&ai

r&v fira^v rov fifMOQfov jcaoa ra bîaâ dia-

TtQOTaâvTfg ovv ra rov uvxhov AS dfxa-

3taQad"tJ6oiiv IxaGrr] Kara TO eîjs rovg re rijg

avacpOQ&s rov xMpaTos %QOVOV$ nal TYJV iiti- 15

v avr&v rbv TQOTIOV rovrov.

-at corr. ex a) D 3. 5. qp' xa-

supra scr. D 3. Ante avKcpOQag del. xa-O1

'

waGfriv D 3.

6. oWug] ovs D. 8. vn'] corr. ex In D 3. fcripSQivov]

$, D. 11. inLKQQiG) itoiovpevoL] r](iLCQQi,a67ioiov[ievoi D, a mut.in co D 2

. ysvtG&ui C. 13. nqoGTa^ccvtsg D, corr. D 3.

In extr. col. del. navoviov T&V nata SS^KÔLQLKV avucpo-o&v D 8

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137

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u>^j a. ^

a. ^ 5*

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UJ 005

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MA0HMATIKH2 ZTNTAEE&S B'. 141

if- a

^2*2*2 S 5-S

w

I

^5-s.?*

>i SH

05 2 . % .g- O 80

o.S

ft ^ g g

a* ($!~3 C6 I 1

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,

8 n' <N^-: .so

ft

-&'. Iley! r&v xccra [ISQOS rats avacpogals

"On tie r&v avacpOQix&v %poVoov rbv

rgoitov f\iiiv xr&ei,[iVG)v evArjjtra ra hoiita jtdvra

5 yevrftferat, r&v els tovro rb [isgos Gvvreivdvrcov, KOI

ovre yQaiipix&v deiêcov agog exatfra avr&v dsyGdiisftcc

ovrs xccvovoygaqjiccs TtegiGGils ,di avr&v r&v {)7to-

tfv yap 1% do&*fai}S fiptQas fy VVXTO$

10 fa[i{lccvTai, rb /Ltf/f-O'og fyiftprfolmow r&v XQOV&V rov

otxsi'ov xMnaroS) sitl plv rijs tfiiEQccs r&v anb trj$

polices l*>%Qi> tils dtaftcrôv^g wg sis v&

ccnb rrls diapergovGrjs tbv r\kiQv en ccvr^v

15 iiotgav ttibv yaQ 6vva%d'VTa)v %QOVG)V rb plv nevre-

Aaflovrfs o^v, odcov eGrlv fagcov farj-

rb {)7toxt[ivov $i,K6rr][icC) rb de d&dexarov

f|oftv, o<?cov %QOVG)V 6rlv

rov avrov diccGrrfpccros-

20 evQitixerat, $ xal 7tQO%ei,Q6rQOv rb co

Acciipavo[Lvrjs ex rov TtôxeLêvov r&v avatpoo&v xavo-

viov rrjs VTtego'xfis r&v 7tccaaxi[iva)v

fjlifyccs [ilv rri rjfaaxfi fiotâ, vvxrbs $ ryev re r<p vnb rbv l^êgivbv TtaQcdAriAq) xal iv

1. -91

'] om. AD, mg. BC. 2. anolovd-ovvTcov D. 3. &vcc-

Kov XQOVOV D, sed corr. 7. vno8ei%&'riGoiiivcov D. 9. r[\

D. 10. &9tpf2&&r D, roov supra scr. D 3. 12.

ABC, [toig (^ D. 15. [loiQav] ABC, om. D. 16. lap-D. 17. 8] om. C. 18. AajSovrf?] om. D. 20. Postadd. Y,ctiQiy.6v B

3. 21. 7iQoJ,K(ji^ccvo^vr]s D. 22.

A, corr. A*. 23. [IOIQCC] AD, comp. B, ^VQKI C.

24. rov} -6- in ras. maiore A 1. rw (alt.)] bis D.

rov vyfoxi^vov xârog' rfjg ydo vai6xo[ivr]g v

ox'fjg to $' Aanfidvovrfg xal ml [isv rov f$OQiov ^1-xvxfa'ov ryg l6vr]Vy^vrf g poioag ov^g 7tQ06nd'vrgavrb rotg rr^g farjiiSQivrjs piag cogag is %a6voig, itl

ds rov voriov ayxugovvrss &ftb t&v avr&v Te %qovG)v 5

rb jrAtjO-og rcdv XQOVCOV TVJS

$ rag plv dfdo^vccg xa,iQMa$ &gcx.g ccvcc-

ig foqpQi#ct$ xoMcvtAaGidGccvrfs rag plyfill rovg rqg fniQag fafivrjg rov olxsiov xM- 10

parog cbQicciovg %govovg, rag df vvxrQivag iitl rovg rijg

vvxrog' r&v yao 6vvcc^vrcov rb is' kafiovrsg

hoar foijiitQiv&v* avdnafav ds rag

ag cogag dva^v6o^v stg xaigixag

avrdg inl rbv is xal ^BgCôvreg eig rovg vito- 15

xi[ivovg rov oixsiov dia^rârog foaiaiovg %Q6vo.vg.

do&tvrog rîlv %QOVOV xal cooag bitoiatidTenors

xo&rov [ilv IT\V dvareMovtiav rors poigavrov dia pte&v r&v Jcodtov xvxAov ^rjôîfd'a itoM.a-

itka<5id<3avrg rb Tt^ôg r&v &Q&V fmfyag plv r&v 20

aito dvarohijg tyfao, vvxrbg $ rcbv dnb dv6og 3tl

rovg oixiovg faataiovg %g6vovg' rbv ydo

g'] fXTOv D. JLapfidvTfs A, corr. A 1

; \cc^dvov\ D. 3.

j? C; ffofvrjy^f'vTjs D, post etc- ras. 2 litt. 5. Te~\

D. XQOVCOV] -<ov e corr. D 3. 8. didonsvas D.

fv C. 9. noKTiCi'jtlaGia.GCiV'i D. Post \t,iv del.

ovv D 3. 11. mgiuiovg\ -i- ins. A 1

, seq. ras. 5 litt. D. 12.

if'] iff ABC, TttvrsHccidfxaTov D. 13. ifep&ra&Mr] corr. exD 3

. StSfoîvag D, dsdopsvccs D 3. 14.

6idovTeg D. 15. TOV If] r&v dsKcmsvre D. 16. eapcaovg C.

17. oiaaS^nors D. 18. (loigav'] corr. ex wguv D. 20. nlf]-

-og renouat. B 3. x&v (pr.)] r&v Se&mpbrca* D.


dlEXf$a&OV[lEV f\llQag {lV CiltO TrJQ fjkLCCXijS

vvxrbg de artb ri\g diapergovGrjs &g ig tec

jt6[iva r&v cjdicov Kara rag rov VTCOKEL^VOV K^L-

parog avatpogag, xal ig r^v d9

av xarccvrtftir]

5 6 aQi&iioSi KiVYiv (ptftioiisv TOTS rv\v [Lotgav

sav ds trjv iiEGovgavovGav v7tQ yi

rag naiQixag &Qag itavrors rag ano rr\g

reg sitl rovg oiKtCovg wgiaiovg %Q6vovg rov

10 aQi&pbv tKfiakovpsv ajtb rr\g Ûag% poiQag stg ra

srtopsva Kara rag cV OQ^g rijg Gyaigag avayoQag,xal slg $v av K7t6rj iiolgav 6

rors vitEQ yY\g iiEGovQavtftiEi,.

byioi&g $ ccjtb {lev ri\g

15 pEtiovQavovtiav VTCSQ yijg A,r]il>6[iE&a GxstyaiiEvoi rbv rrj

avarskhovtiri itaQansinsvov rr}g

v r& rov olnsCov uMfiaro

an avrov itdvrors rovg rov rfra^rrjôQiov %Qovovg Q

rfjv TtaQaKEiyLZVYiv r& aQi&iiG) [loigav x rr\g smtivv-

20 aycoyrig rov it' o^îjg ri}g Gtpatgag eskidiov rors vitsg

peGovQavovGav SVQÔ^BV. avaitafav 81 aito ryg

yijv iiEtiovQavovGyg rrjv avardMovtiav itakiv Ay-

a 6xipd[iEvoi, rbv rr\ [lEGovQccvovGrj poiya

tfg eTtiGvvay&'yrig aQi^^bv iv r& ri]g

25 Gaiag GEfadiG)' rtQ06&vrg a avr& Ttdvrors

1. TJJUxTjg A. 3. TOV] supra scr. B 2. 4. %at] om. D.

6. Ante yf]s ras. 1 litt. A. 8. do&ficris] do&L6ris WQCCS D.

9. G)QUXLOV$~] corr. ex xmqiafovg C 2. 11. Tag] rfjs B. &vcc-

cpoQKs] mg. A 1. 12. &v] D, sdv ABC. 16. fatccrelwoffj} C.

17. ohsiov] pr. t e corr. C. V.KVOVI D. 18. arc'] seq.ras. 1 litt. A, aito D. 22. ncchv'] om. D. 23. [IOLQK]

ACD 3, p B, ôt'pt D. 24. Iv] om. C.

MA0HMATIKHS STNTABE&S B'. 145

ccvrovs 9 %$6vovs tiutixstyoiisd'cc x rijs

rov vjtoxf,[ievov xMparoS) Ttoict fiotQcc TCCCQCC-

xsttcci, ro5 aptttywp? xaxivrjv rors Kvar&hovGccv evQij-

<}0[lV.

(pavQbv $ xat, on rots pw vitb rbv avrbv peti- 5

otxovtiw 6 ijfaos ra$ faces faitft6Qt*$t

rijs [isGrjiipoias ty fov neGovvxtiov, rots

VTCO rbv avrbv [i6r][i(lQi,vbv rotiovrois farjiisgivots

oticus &v [loiocus 6 [istirHiflQivbg rov

nag exccrsoois dicccpsor]. 10

i. Ilspi r&v vrtb rov dia [isGcov r&vxal rov ps6r]iif$Qi,vov yivo[ievG)v

AOITCOV dl ovros sts tnv vnoxsc^svrjv ftsogtccv rov

rbv itegl r&v y&vi&v TtoiriGaG&cti koyov, Af'yco ds rcbv 15

rbv dice petfcov rwv ,G)diG)v xvxhov yLvoîevov^

on, ooftriv yovCav vnb psyfarcov xvxhcov

#9t^jr0#af, orccv x6A,G) rr\ nowy ropy rcbv

xccl diatirtjuan rv%6vn yQcccpsvros xvxhov %

vrj avrov itSQiysQeia vjtb rcbv rqv ycwiav 20

3tQi%6vrG)v rprjpdrcov rrccQrr][i6oi,ov rov

2. vrtOKSititvov ] corr. ex eitinsiiiEvov D 3. ju-orpa] B;

fiA CD, ut solent. ,5. (JHXVSQOV jttfV] supra scr. D 3

. 7.

rots] COIT. ex TOV$ D 3. 8. (lEGri^Qivov^ jx D. 9. oWtg]

ccts corr. ex olg D 3. ftoiât?] om. D. 10. nag'] fiotât?

nag' D. diacpsQzi, B. 11. t'] om. AD, mg. BC. r&v (pr.)]

corr. ex tov B, corr. ex rov D 3. 12. xvxôv] om. D. pBGrip-

PQWOV] jiD. 14. oVrras C. 15. r&v (alt.)] rov B. 16.

yLyvofisvcov D. 18. Xf'yojttEv] -v supra scr. A 1. 19. ypa-

ysvrog] corr. ex ygcccpovres D 3.

xvxAov itoi^ xa&oAov ts, ort, ov ccv %?] Aoyov fj cbro-

voiivr} 7COiop0t,a Ttobg rov yoaywra xvxAov,

ov lQtjxa[iv rgoftoV) tovrov %i rbv Aoyov rj

7tQi%0[ivr} y&via VTCO rys xM<5a)$ r&v

5 agog tag t66a()a$ OQ&ds- &6*>) 7it,dri

oticw ccv

xaifj {>7tOTivov6a avrqv ycovia, oicov

ri [ILCC oQ&rj g.

t&v dfj agog rbv AO|OJ/ xvuhov

10 cci iiafoGtci %QrJ6i,[jioi, Jtybg tv\

Xivat ffaiv ca t vitb rijg To/&ijg avrov xal rov

psfSruifiQivov 3tQi%6[ivai, xal at vitb rijs ropfe avrov

xccl rov oo^ovros MX&' mdtirrjv &6t,v xal dpoi&s ai

VTtb Tys TO/iijg avrov xal rov dia r&v nokav rov

15 6(){ovro$ ygacpoiiwov ^yfarov nvxhov

rats roLCivrcag y&vicus xccl r&v a

rovrov rov xvxAov ytotfpOLG)v VTCo r

xal rov %6Aov rov 6oiovroS) rovrztirw rov

xara xoavcpyv 6rniiov. f'xatira yao r&v xxi^ivov20 drtodi%d*vra agog rs rr\v ftf&Qiav avrr^v Cxavcordrrjv

%d)Qav xal Ttobg rd stfol rdg 3taaaA,A.d,t,s rr^Q

rb ittelGrov

3too%G)Qtv dvva-

avv ri}$ zxeCv&v TtQodiKAtjfa&s.

25 7Cl d xal r66aQG)v ovGcbv ycovicbv r&v

1. noiEL B. 6V] corr. ex o D 3. &no^K(i^Kvofisvri\ pr. o

corr. ex s A 3. 3. fyei] corr. ex fysw D 3

. 4. vno\ om. D.5. &GX' D. IneiSvi'] corr. ex snidij A 3

. 6. vQiOKr)i;ai]corr. ex fv07J<>xr]Tca A. 9. #77] de supra scr. D. 11. rov- 13. *al (pr.)] supra scr. D 3

. 12. cu] om. C. 17. vno]v in extr. lin. A, no add. A4

. 18. xat] KVTOV KKL corr. ex

Y.KL D. 22. GvdttsTca C.

MA0HMATIKHS ZTNTASE&S B'. 147

vitb Tils r&v dvo xvxh&v roiifjSi rovrttirw

dlCC [l6*G)V T&V fydlGOV Xal VOS T&V dV^TtêXO-

avrcj, rt$l piac* rijg Kara rr\v ftiGiv 6[iotas for

Aoyov 7tot,i6&a(, ^fAAo^ti/, TtQodiOQiersov, on xa&ohov

rfbv dvo ycovi&v rcbv jcegl ir\v ito[i8vr}v tr\ xoivrj topi] 5

TG)V XVXA,G)V 7tQl<pQl,aV TOV Sia î(3G)V TG)V

x^v an? CCQXTCOV vitaxov6roV) &6TS ra ^v^xal ras xrjfaxorrjTas tag ajtodfi^riô^vas dvai

y&vicbv. a7tA.ov6TQas

fOV {l6r]ll(lQl,vbv XVXA.OV &G)QOV[lVG)V 10

rov Ao|oi) ycovi&v anb TOVTCOV a^6îd'a xal

)on, ra i'Gov drtfyovra rov avrov

rov dia [i6G)v rcov

ycwias I'tias j

t6rnLQwov yikv 15

ART) rov d

rCbv tySi&v rj

d rov i^-rb Z 6rj[ilov, xal

l,6G)V l'0K)V 7tQL<p- 20

Qici)V r^js rs BH xal B

(p xdrQa rov B faring i-

dia rov Z TtoAov xal

V XVXA&V 7tQl(pQiai

xvxhov ras

dia

vov 0r}[iiov

^@

3. Post pi&s ins. C 2.

6. 7tQt,(pQt,Kv^ mut. in

corr. D 3. 7. T] ra ^

9. K7iA.ov6rQccg] -ov- e corr. D. 11. a X^fifta mg.mg. B. 12. fcrjjufîi/oij] comp. D, ut saepius.

Jiicp&tG(bv A. 21. B] T?fc 6) D. 22. E] supra scr. D 3.

24. Ante xvxZcov del. TCOV D 3. nQi(pQicu] -i in ras. C.

10*

5. ya>vi&v r&v] supra scr. D 3-

C 2; 7tQl(pQ8t.CC V.U.C D?

D. 8. rds (alt.)] om. D-

. C, paragr-20. ano-


% re ZKH xal r] Z&A. Aêo, on, fay terlv y vxb

KHB yewLK rfj VTCO Z@E. KKI 6nv avro&ev yccve-

faoyaviov yaa yivsrai, TO BHK rafafovaov r&

7tidrj7tQ xal rag roig xfavQas rats rQitilv

5 itkevQtti$ i'6ag lî sxaGTyv sxaGtrj) rrjv plv HB rfjjB

,

rfv ds HK ri] A [I, 15], ryv deBKry BA [p. 118, 5]-

dsdsixtai, yap ndvra ravra iv rolg [ntQo6&v' xal

ycovi'a aga v\btto KHB y&via ry vnb B@A, rovr-

10 rtdhv dsixrBov, on r&v rb i'ôv aite%6vrG)v

rov did [i6'G)v rcbv ^wdiwv xvxhov rov avrov rgo-

at TCobg rov

yco-

viai 6vva[i(p6rQai, dvalv OQ-

15 &ai$ fcai, sltiiv.

rov dia

ABT rov B

20 xal ctTtokrifp&EiGcbv iy xdrQa avrov rtQi,cpQi,(bv i'G&v

ri\g r B^d xal rijg BE 'yfyodcp&cdo'av did r&v z/

Kttl E GrjiiEiov Kul rov Z itohov rov ItirnLEQivov [i6-

7tQL(pQi,ai, fjT Zz/ xal

fjZE.

1.j\ re] KL D. xai

rf\ om. D.L'GYI\

i'- in ras. A. 2.

Supra Z&E scr. E&A D 3. 3. Icoyoviov A, corr. A 1

. ytyve-XCCL D. 5. endcr?]] om. C. rf?] corr. ex rfjg D 3

. 6. tj)

(utrumque)] corr. ex rrjs D 3. A~] A D. 7. TCCVTCC ndvra D.

8. KHB] corr. ex KBH D 3. B@A] corr. ex B@A B 2 C 2

.

9. Z(9E] -E e corr. D 3. ont-Q i-'dei $*%ai] om. D. 10.

pucc mg. B, ^ Ifiâ mg. C. Post L'GOV ras. 8 litt. B.

13. (isGrj{iQi,v6v] comp. D, ut saepius. 14. cvvctficpoTSTEQca A,corr. A 3

. 18. fj] corr. ex v A. 21. trig TS rfjs] t&vB4 D. 22. xat ("pr.)J om. D.. 23. $ rs ^] ZJ D.

MA0HMATIKHS 2TNTASESS B'. 149

onrj

rs vitb Zz/5 ycovia xccl ^ vyt ZETdvGiv OQ&CCLS facet, i6w. 6ri ds KOI

rovro dôv avro&sv. 7cd yao rcc A xal E GYHLEIK

faov Kit8%i, rov avrov rgoitwov Gypst'ov, fay stirl xccl

fjz/Z 7tQi(pQia rfi ZE" xccl yovia agcc rj

vitb Z/IE 5

ycovia TV} vnb ZEBi'tirj

fariv. dM.ar\vnb ZEB KOI

ZEF dvelv oQ&als facet, efaiv xal % vnb Z4B apa

rijs -bnb ZEF dvtilv ogftccts fo<u efaiV OTCBQ

rovrov rtQorf&fGOQqptvcov &rco

6 AETd, rov df dia pfacov rcov ^codicov

xvxfaov rb AET rov AILGIOV V7tOXi[JiVOV rOV

QLVOV roonixoV) xal ifoAa) rw A,

dia6rij[iccri $ rr\ rov rerga- 15

ycdvov TchsvQK/

y'y()d(p&K) rb

BE4 rjiiixvxfaov. 7td roivvv

6 AETA yL6rnifigivb<s did re

r&v rov AEF Ttoôv xal

dice rcov rov BE z/ yfyytaCfftt) 20

rrctQrr}[ioQiov 6rlvfyE4 7tQi(pQioc [Theodos. I, 9]

*

KQCC 6rlvr\

vTib dAE ycovicc. 6^0'^ d did ra

deiyiLtva, [p. 147? 11] xal f}

vnb rov fteQivov rgo-

Ttixov 6ir]iiiov yivoîdvY]' oTtSQ edei dft^ca.

1. ZJS] corr. ex 4ZB D 3. j) (alt.)] om. D. 2. elaw

D. 3. xat] om. D. 4. sGrtv D. %<u] om. C. 5.

ZA D. ZJB] JZB B. 6. for] x<| mg. D 3. xat']

?j VTCO D 3. 7. dvciv~] -I- in ras. C. daiv facet D.

Z4B] -4- e corr. C 2,ZAB B. 8. dvatv] S- in ras. C.

OTCEQ tdfi dfiâi] om. D. 10. (isv xvxAog] om. D. 13.

rov] om. D. 14. TCO] corr. ex TO C 2. A] corr. ex nym-ccp D 3

.

19. nolcov] -v ins. D 3. 23. nqoa.nodf8Eiy^vu D. rj]

add. D 3.

24. CTjftftov] om. D. OTIEQ edei Ssi^ca] supra scr. D 3.

15

0TK> n&r)iiflQt,vb$ per xvxhos b ARTA,farj[iQt,vov ds finixvxfaov TO AET, xod ysyQdtp&G) TOV

diK {LSGov Tfbv a)diG)v TO AZT fipMvxkiov ovtog,

TO A GrjiifZov slvKi TO

TS TK> A xccl diaQTrâaTi

TOV TSTQaycbvov Ttksvga ye-

TO BZE4 fjiiixvxkiov.

dice TK O.VTK dy, titsl 6 ARTAdid TS T&V TOV AET Keel dt,a

10 T&V TOV BEA nohcov yiyQCMTui,

<5TlvijT A Z KOLl

I TO lV ZTO îîQiVO

[p. 81, 50]

fjZ

ds vttb 4AZ yoviK TOLOVT&V gl/y me, oi&v 6Tlv

ilia OQ&ri 9. dice d TCC HQodedeiyiiEVK [p. 1487 10]

KKL i] VltO TOV EttQWOV far][IEQLVOV 6y[lEiOV

covicc T&V AOLTC&V ig *&S ^vo OQ&ag20 [loiQ&v Jg #.

6 AETA xccl

TOV df dlCC [l(5G)V

Z 6r][liOV VTfO-

TCEQlCpEQElKV

ZEwy ~VK

TG)V

6TO)

16YI{lQLVOV {LV ri^LiKVK^LOV TO

TG)V ^G)diO)V TO -BZZ/, CO(3T TO

TO yiSTQ7tG)Qlv6v, T^V df

1. ^ffTco] corr. ex l<jm> in scr. C. 4. catfrt] corr. exSre C 2

. Gripsfov] corr. ex GJI^LCOV C 2. 5. ra] corr. ex

TO C 2. A] corr. ex itQwrw D 3

. KKI] om. D. 6. Try] ds

ry D. 9. dice, (alt.)] Sid re D. 11. SGTLV] CCQK ZGTIV B. 13.

TQOTCIY.OV] -ixo- in ras. A. 14. syyiGtcc] alt. y corr. ex i in

scr. C. 16. i] vcc] om. D. 20. %f (H add. D. 21.

piv\ om. D. 22. del comp. ins. D 3. 23. BZJ] corr. ex

BJZ D 3. ootTTf] to? D.

MA0HMATIKHS 2TNTABE&2 B'. 151

irov vg TOV rijg naa&Evov xal TO Bde

TO) rov

TO H&EK iiyiixvx.kiov ,xal 5

Tqv VTCO KB y&-

VQiV.TOLVVV 6 ABF4 [l0-

did T Tcbv TOV

AEF xccl dice T&V TOV HEK 10

xd6Trj yiVETcu T&V BH xal B xal EH. dia dl ri]v xccTayQcccprjv 6 rijg vitb TYJV

Trjs BA TCQOS TJJV vitb rv\v dijcîjv Trjg AHGwfptTKl X T TOV T^S VTtO T^V diTt^V Ti]S B Z 15

r\v vjcb Tr\v di7cKi]V Tijs Z xctl TOV Tijg VTCO

v rij? 0E yfQog T^V VTCO T^V ^ntl^v Tijs EHTV\V

[p. 747 9]. AA

5

^ ftfv diTtArj rijg BA dia TK

poiQ&v fanv xy x xali\ VTCO ccvTqv v&tcc

xd Z?, 17d dmhij rijg AH [LOIQ&V ovz ft 20

xalr\ VTCO avTyv v&la T^YI^KTOV QL^ Aa, xal

?] plv diTcki] Trjs ZB {loiacbv | xali] VTCO

1. TIUQVOV C. %at ro] TO $e D. 2. !!KQ-a.

ftevov] naQvov D. 5. H0EK~] corr. ex &HEK D 3. 9. rov

AET xat] supra scr. D 3. 10. SLO. %5>v\ om. D. HEK]

mut. in H0EK D 3. 12. xa! E xai] jB D. 13. ds] corr.

ex Tf D 3. 14. Ante rrjs (pr -)

eras, rfjg vnb rr\v Sm^riv A.

15. GvvfjTtTUi] 6 Gvvruiptvog D. 16. @Z] Z6> D. 19. x]om. BC. vn6~] vn' D. 20. tg] corr. ex ^,g' D 3

. QVS~] -v-

corr. ex 77in scr. D. 21. vito] vn D. fu^fta] v- e corr. A.

â] ô"i? D. 22. rrjs] r- in ras. A. ZB] BZ D. |]ioriv | D. -yjro] vn

3

D.

v&icc Tiirjpdrcov , fjds dmhij rrjs Z

xcclrj

vrtb avrrjv sv&eta rîrjîdrcov lyy ve wy. eav CCQK

7td2.iv anb rov r&v xd 7g agog ra QI ha Aoyov agp&co-

pw xbv r&v | JtQOg ra ^y ve wy, xccratei,q)d"ij0'ccct, 6

5 rvjs vjtb rv\v diTthfjv tij$ E 7tQO$ rr^v tino r^v dntK^v

TJJS EH Aopos 6 T&V pfl vrj fyyiGTa 7tQO$ to, QK. XCCL

etitivfj

VTtb r^v dirtAijv rye; EH rîrj^drov QK' xal

f\VTtb TJJV diTC^v KQK rrj$ E rcbv avt&v i(5tiv

[ifi vrj.

K>6re xcclr\ psv dt,7thi\ rijg E [toiQ&v stirw

[ij} syyiGTct,

10 ccvrfj dsfj

E r&v avr&v xa. xal oA^ [isv CCQCC fj

&EK avrtj rs xalj]

VTtb KB yovicc IIOIQ&V EGTIV

dia ds ra TtQoajtodsdsLy^vcc [p. 147, 11] xal17

vnb rrjs KQ%fjs rov ZKOQTIIOV yivoîsvrj y&via. x&v

facov <STCCL JIOIQCOV QLK^ EMttga [p. 148, 10] drj

re

15 vnb rils ccQX^S t v TCCVQOV xccl rijs (XQ%ijs

t&V

itl rijs avrijs xarccyQcccpijs q ZB XQt,(pQi,cc

VJtOKfa&G) dvO d&dfXCCTrjUOQl&V) K>0t TO B20 elvKi ryv KQ%YIV rov Asovtos xal r&v avtcbv

riv jiv diit^v v^g BA ILOIQ&V slvcaficc

xal

vnb avr^v v&tav r^^drcoAH poiQ&v pA-9

1 xal rr\v vnb

*d, xal itdfav rrjv pw SmKrp rijg ZB

1. 8ntKfi~] -i- corr. ex rj D. _ Z6)] corr. ex 30 A. 2.

vito] vn' I). xy] om. D. 4. xy] om. D. 6. fyytcrra] syy-in ras. A4

,e corr. C 2

. 7. ft om. D. 8. SGTL D. 9. @JE]corr. ex M D. 10. rj E] e corr. C 2

. 11. @EX] -Kin ras. B 2 C 2

;corr. ex E, KA D 3

. ienv] om. B. 12. ngo-

D. 15. r&v] -&v in ras. A. 16. vo\ A, ^ BCD.sdei dtt&L] om. D. 19. dwccTruiOQicov D, corr. D 3

.

21. dinlfiv] -v ins. C 3. 22. rr\v (pr.)] corr. ex xa>v D 3

. vno\vn' D. 23. vno] vn' D. 24. ZB] EZ D.

lioiQcov OK xal rr^v vitb avri]v v&tav rfirjfjidr&v

^y ve xy, rr)v d di3tA.ijv rijg Z UOIQCOV xal r^v

vjtb avri}v v&iav rprjiidrcQv |. av aocc ita'kiv dnb

rov r&vji/3 ft itobg ra gift xd Adyov d(pJ.G)[iv rbv

r&v ~gy r ivy xobg ra 1, xaraA.i,(p&ri6rai, 6 rijg vitb 5

rijg E agog ryv vitb rfjv dnt^v rrjg EH6 r&v x vy rtobg ra ox' fj

aoa vnb r^v diithijv

rrjg E yCveroii rcav avr&v xs vy. &<5rs xalv\ [iv

^tÂ-fJ ri]g E ^LOIQ&V h'&rai x ZyyiGra, avri] $f)

E riibv avrcbv ipL'> ofy [iv aoa rjEK avrtj rs 10

xalrjvnb KB y&vta poiQibv 6nv gPL', di& ravra

$ xalfj plv VTcb rijg do%ijg rov To%6rov 7tOL%oî8vr]

r&v i'ticov oj$l_\ fxarsoa $rj

r vitb rijg do%ijg

didviacav xal rijg do%ijg rovr

Tdoo%6ov rcov Aot-

ig rag dvo ogftag IIOIQ&V of/.', xal dedixrai, 15

ra 3tooxi^va rijg pw avrijg 6o[ivrjg

xal ml r&v b'n [iixgoiifofGrzocov rov Aoôv

aTtaQxovGrjg d' &g Jtobg avrriv ri}v rijg

xal rijg xa& exatirov r&v dwdfxa-

20

1. vno\ vn D. 2. QY v ] eras - propter fig. D, posteaadd. eadem manu. xy] om. D. 4. TOV\ rov re D, TS e

corr. D 3. 5. xy] om. D. 6. <9E] corr. ex EH D 3

. Deindeadd. Aoyos D. Ttgog EH] supra scr. D 3

. 7. Adyog]om. D. 17] corr. ex ty' D 3

. ^x- r[\BC 2D 3

, ^ ACT).

9.6Tiv_D.

10. //] ins. D 3. Mrf] s ofy D. 11. ^f]

corr. ex gift D 3.

/_']in ras. B, î D. TKVTO] TU avtd B,

rctvTcc CD. 12. Ss] D, ^' ABC. TOV] TO D. nsîsô-pevr) ycovid] corr. ex 7feQi%o[ivrjs yavi'as D 3

. 13. /_'] ins. I)3?

i Icrrtv D. 14. a^^^g] om. BC. 15. [IOIQ&V] om. D./_']

4i Iffriv D, i tcTiv D 3. 18. d

3

]Si BC. 19. rcov] supra

scr. AD 3.

ia'. Ilol rcbv vitb rov avrov Ao|oi> xvxkov xal

rov oQiôvrog yivoptvov y&vi&v.

'E(p%ijg $ dsfeonEv, rt&g av â^dvoLêv itl rov

vov xMparog xal rag xobg rov bot&vta rov dia

r&v t,G>diG)v xvxhov pivoê'vag y&vtag cbrAovtfrc-

Qav xal avrag s%ov6ag rqv [i&odov r&v koiitcbv. on

fiV ovv ai Ttobg rov î0r]^^QLvbv yivopsvai ai avrat

fttiiv ratg xobg rov lit* oa&fig rijg

(pavsgov VXv $ rov xal rag lit

10 Gyaigag kaiLpdvsG&at, deixrsov it&Kiv Ttacbrov, on ra

i'6ov vLTtiyovxct, 6rj[ita rov did [iGa)v r&v

xvxhov rov avrov I0rjîoivov tir][iiov rag

7tgbg rov avrov boi&vra yco-

viag i'Gag dhhrihaig TCOIZI.

15 fGrco ydo ii6r]ii/3oivbg xv-

6 ABF^J xal l6rjîQi,vov

Yiiiixvxîov rb AET, oQi-

t,ovrog d rb BE4, xal y-/

yod<pd'G) rov Ao|oi> xvxkov dvo

20 rîtjîara r6 re ZU xal rb

KAM ovrayg fyovra, &6re exd-

rQov [iv r&v Z xal K Grjî&v vitoxBlG&ai rb [iro-

jt&Qivbv toypAQLVOV, rqv d Zfl" 7tot,cp0Lav rfj KA

1. IK'} om. D, mg. A 4 C 2,

at, mg. B. 3. 9s] Sri D- v

Zcc{jificivoi[iv] corr. ex avcdccfjipdvoifisv D 3. 4. diSopEvov] SL-

corr. ex n- in scr. D. 7. ywoêu] -at supra scr. A 1,corr.

ex yevopsvai D. at] supra scr. D 3. 8. efaiv] -v del. C 2D 3

.

9. TOV] supra scr. D 3. syy.SY.kiiLevY] A. 10. A7)fifia a

mg. B, a IfippK mg. C. 12. ar^LfCov] supra scr. D 3. yivo-

liivag] ^yxfx^-tftfVag D. 22. otat] om. D. 6r}piov C. (isro-

no)Qiv6v] -x- corr. ex ft D. 23. ZH] ri]v ZH D: KA]corr. ex KJ B 3 C 2

.

faqv. kiy&, on xalfj

vitb EH y&via far] 6riv rfj

VTtb 4AK. xa stiriv avrd&sv dqhov' ttioy&viov yaQytuhv yivsrcci rb EZH rQiittevQOv r& EKA, itd dia

ra itQodedeiyiLSVK xccl rag rgsls itfavQ&g rats VQrtl

faces %ei, xa6rr]v xa6rr]^ rv\v pew ZH tfj 5

, trjv ds HE Tr}s topils rov optfovrog r EA,ds EZ rijs avccyoQ&s ry EK [p. 118, 5]. fay &QCC

xcil ^ [isv vTtb EHZ y&vCa rtf vitb EAK,ds

rji>7tb EH AoM-fj rfi VTtb 4AK l6r\ S&TIV

idei drgat. 10

da, on xccl r&v

V\tOV

Toov avarohwri H.STK tfjs

rov tregov dvnxfis dvtilv

far] fatCv. sav yap 15

bgC&vtK plv xv-

rbv ABT4, rov ds

&v r&v ^cpdCov rbv

AETZ, rfyvovrccg aMr]kovs xarci ra A xccl F Gr}-

ftfta, 6vraiKporQcci plv ijrs vxb ZA4 xal % vitb 20

4AE dvtilv doftals l<5ai yivovrcci. far] 6*i] VTCO ZA4

1. ioxLv] -v del. C 2D 3. 3. ro5]]corr. ex x&v A, corr. ex

TO D 3. dice] corr. ex 8r\ in scr. D. 4. nQocdsdsiyiisvci D,

-a- del. D 3. -ratg] D, om. ABC. 5. lxa<ytr^] corr. ex

l-AK6xr]v D 3. 6. HE] corr. ex NE B 2 C 2

. E A] -A e corr. C 2.

7. rf|] corr. ex rfj$ D. 8. iavfv] -v del. C 3. EAK] corr.

ex ERA D 3. 9. EH} EH- e corr. C 2

. 4AK] corr. exJKA D 3

. far] 10. d%cci] om. D. 9. i<rtt A. _ 10. s'Ssi]

-- in ras. A. 11. dt] S' A. JUjfifia p mg. B, ^ l^ppa C.

14. dvTiKfjs] -v- e corr. D. 15. i'arj IGXIV} ABC, foai

IIGIV D et supra scr. C 2. yap] AC 2D 3

,om. BCD.

^

17.

TOV (alt.)] renouat. C 2. 18. fifdcov] -v ins. C 2

. 19. ripvov-IK<S] r- in ras. A. xa] corr. ex TO C 2

. wat] orn. D. 21.

EA4 D, -A- renouat. D 3.

156 . KAATAIOT HTOAEMAIOT

rf] vnb Z-Tz/' coGrs xccl 6vva[i(porQces rrjv r vitb

xcel rfjv VTCO 4AE dvo oofrdg noiEiv OTCEQ s'dsi

r rovrcov ovras Eôvrcov,

[p. 154, 10] xal rcbv faov ditEftovr&v rov

5 cevrov i6r}[iai,vov Gruisiov at Tfobg rbv cevrbv QQiôvra

&Ecoaov[iEvai, y&vCcu, facet,, rb xcel r&v rb faov ceit%6v-

rcov rov cevrov roonwov Grjiistov %j\v rov roov dvce-

rofaxrjv xal r^v rov srEgov dvnxr^v 6vvce[icporoa$

dvtilv OQ&CCIS faceg stvai. &6rE xcel dice rovro, sav

10 rcc$ KJtb Koiov ^%oi rcbv Xrjhcbv yivoîEvces dvarohxas

', (SwcertodEdEiyiiEvcei Etiovrai, xal at rov

)v fiiiiXvxA.iov dvcerohixcel xccl En a[ rcbv dvo î-dvnxcei. ov ds rooitov dEixvvrcu, dice fiaa-

rj<5d[jiEvoi xdhiv VTCodsfy^Lceros EVEKEV

15 ro3 avro3 jrapaAAÂca ,rovr6nv xce&' ov 6

%ilQrcei rov

Agi

ai {LEV ovv vrtb rcbv ,

w GriiLEi&v rov did

20 <7tov rcbv ^Ktdicav xvxhov

rbv oQi&vrce yivoîEvca

vicei 7tQO%Ei'aa)s dvvcevrca

EKV y&Q

jiEV xvxAov rbv ABF4, rov ds v%o-

25 xEiîEvov OQiôvros rb dvarokixbv f)[nxv%A,iOv rb AE^J

2. ortfQ idsi dsi^KL] supra scr. D 3. 3. STficv[jipi]6STca'~\ -i-

in ras. A, rt CVÎJGSTCCL D. rs] supra scr. D 4. 6. TO (pr.)]

T D, del. D 3,om. B. T&V} corr. ex rov C 3

. 10. T&V\ om. D.

Xrik&v} Xj\- supra scr. A 1. 11. Gwanod^Ssiy^svcii] G- corr.

ex o A, GWKTioStdtiptvKi C. Deinde add. 8s D, mut. in 8y D 3.

12. *a~\ comp. ins. D 3. 15. voinieziv] -v del. C 2D 3

. 16.

A. In fig. a polo ducta est EK in AC.

xccl rov lilv farffUftvov reTKQTrjpoQiov rb EZ, rov

6s diet pea cov T&V tydicov dvo TO rs EB xccl EFovrcog tyovrcC) K>6r rb E 6r]îtov nobg fwv tb EB

OElG&at, yLSTOTtOQlVOV , TtQOg df TO EFxal rb ^lv B yivtti&ai yti^BQi

rb ds F &Qiv6v, Gwdysrai,, on, rr\g plv z/Z

ysosias V7toxi,[ivr]c; poiQ&v i/d, xarQccg d r&v BZxccl ZF T&V fo&v wy vcc fyyiGra, xccl

f) \L\V

rb E x6hos 6rlv rov ABF ^rj^Qivov^ xccl ri\v

vxb 4EF ycwCccv r^v yivQ\LivY\v vxb rrjs

KQLOV roiovrcov dvai A #, ol'cov <5rlv i\ [itcc

vnb 4EB r^v yivQîvr^v vitb ril

Tcbv ccvrcov o vcc.

LVCC df xcclfj

T&Vr

cpodos cpccvsocc

7tl

plv 10

rov

j 9,

T&V

Aoi- 15

TCCl,

rog

vCccv vjtb rijg

TCCVQOV xccl rov

vov 20

[lV

xvxkog b ABF4, rov d' vitoxEipwov bgôvrog rb ccvcc-

rofaxbv yuixvxfaov rb BE4, xccl yzyQKy&G) rov dice

2. ET] TO ET D. 6. TO 8s\ Ss TO D. T] supra scr.

C 2,E B. oTt]

f

o B. 7. BZ] corr. ex EZ Cl _ 8. xi.'(PrO]

om. D. -Aui f) [isv Tz/] bis C, corr. C 2. 9. I &] corr. ex kfr

C 2D 3. CO(7TF D. lO.JrW C. JlECJl^QLVOV

11. Z/ E T]

supra scr. D 3. 12. I #] corr. ex ^ D 3

. 13. 8t] 8s df-vrs-

QCIV D, rr\v add. D 3. 15.

17] om. D. ZotTrwv] koin&v r) D.

19. Ante y.aviav ras. 1 litt. A. 20. vno] vno re D. 22.

h D. 23. <T] 3s D. TO] om. D.

r&v ^(pdicsv rb AET i^Lixvxîov^ cadre rb E 6r[-

rrjv KQ^V elvai rov Tccvoov. xccl eitel ev rovrc*

i& xUpart, rijs da%ijs rov Tccvoov KvarsMovGrjs petiov-

QccvovGiv vnb yv\v aC rov KCCQXIVOV poiQat, 1% jiZer

5 dedsfyaiiev [p. 144, 6] 7^^, itcbg ra roiavra %

di& r&v

yverat, ^

G) drj 3t6kG) re? E xccl dt,cc6rij[iccri, rr/ rov rsroa-

ytovov Tttevoa psyiGrov xvxhov r[ii}[icc rb HZ, not

10 3tQo6avci7t7tA,rjQG)6d'G) ro rs EFH rrccorr]n6Qi,ov xal

rb EA. yivsrai de xccltf

re z/TZ xccl $ ZH&xar

f

acc rfrccarrjiiOQiov did rb rbv BE b^Ct,ovra did

r&v TtoAcov ivcu rov rs ZJTz/ [i6rj[ji{$Qivov xccl rov

ZH& neyfarov xvxAov. ndfav fael cc[ plv rov KCCQ-

15 xivov 1% ]LCC [LOiQcu uitiyjQvGw rov fay[iQLVOV itobg

rds ccaxrovg till rov did r&v noAcov ccvrov iieyfarov

xvxAov iioioas xfi jL' xr&i,rcci, [p. 81, 32] ydo t\\jiiv

xccl rccvrcc' b df t&HUQivhg uTtiyti rov Z nohov rov

QQitpvros Bill rijs ccvrrig Xai(paLccs rrjs ZJTz/ ôCgas

20 ACT, GwdyErcii xcclfjZF itQt,(pEQt,cc {loiacbv vvj p.

rovr&v dri dofrwrcov yivzrai hontov did rrjv xara-

iv [p. 767 3] 6 rr}s VTtb ri\v ntkv\v rrjs F4 Jtobg

vjtb rr\v dtÂijv ri\<s z/Z Aoyog b 6vvr][jL[JiEvos ex re

2. Ante *at ras. 6 litt. D. 4. pec] corr. ex Â? B 3. 7.

B. 9. vtlevQ&, a renouat., C a. HZ] ZH D.

10. TO] TOL A, sed i eras.; corr. ex TOO D 3. 11. Post EJ0

ras. paruaxn C. Ss] 8ri D. 13. (jiSGrjêGrj^QLvov C. 14.

snel at] corr. ex Int D 3. 15. ccniôvGi BCD. 16.

om. D. 17. xfl]- in ras. B 2

. ^xT&fctrai] -r- alt. in ras. A 1.

20. ZT] TZ D. 21. 5rj 9o*tvcmv\ AD, S^co^vrcov BC.22. -cfjs (alt.)] corr. ex xrjv C 2

, TTJV B, om. D. 23. re]

om. D.

MA0HMATIKHS STNTAgESS B'. 159

rov rrjg vitb ir\v nt'kv\v rijg FE icgos rr^v vnb rrjv

d(,itki]v rils EH xal rov rijg vjtb rr^v diitA,i}v Tys

H Ttobs rfv vnb rv\v dntki]v rij$ Z. aMa did rd

7tQoxei^va rj [iev diithii rijg Fz/ yiOiQcbv i&nv |/3 t

xal % VTIQ ccvrriv sv&sta r[irj[iKTG)v |/3 xd, 17de

rrls z/Z [loiQ&v ^Jt xcclr\

vnb avrqv svd'ela

rcov ^x, xccl itdkivr\ [isv diitAij ty\g PE {IOLQ&V QVS x

xalfj

VTtb avrr^v sv&slcc r^rîdrov QI^ td, ^

rijg EH poiQcov ^Jt Kal r\vxb avri\v ev&elcc

Tav ^3c. sav aQtt ccTtb xov Myov rcov |/3 xd JCQOS TK 10

QX ayeA&iisv rbv r&v git, id xgbs ra

Gstcci, fftitv 6 rrls vjtb tr[v di,7tA.ijv rijg

v%b rr\v ntKv\v tij$ Z Aoyog 6 r&v |y v(l itgbg ra

^x. xcii i$rivf] i)Jto rr^v 8ntk;

v\v rijg Z r^îdrcsv

QX' xalYJ

vttb rriv diit^v aga r^g H t&v ccvr&v 15

etinv %y vfl. GHSTS xal % per Sinki] vys H poiQcbv

iGxiv %d x, f\ ds H avrtj re xal % vxb HE y&vfar&v avtcbv A/3 I' oitsg sdsi, Sslât,.

6 d' avTog TQOTtoS) tW[iri

xa&' f'xaGrov ravro-

iyxvv&nev rbv vjtoîvriâr^^bv rrjs 6vv- 20

,xal iitl rcbv koLTt&v dcsdsxarô^cov re xal

cw v\yiiv v

3. Z0] Z D. 5. ^6] i>n' V^ ds] r C. 6.

vn' D. 8. vno] vit D. 9. QTt] $r) A. vno] vn' D. 10.

r&v] rov T&V D. 11. xara^gj^fffTat C. 12. @H] ABC,H D et supra scr. C 2

. 14. <9Z] Z<9 C. 15. H&\ corr.

ex II A 3. 16. lmv\ A, om. BCD. 18. onsQ ZSei defect]

om. D. 19. d'] om. BC. fvcc iWcrroy] bis D, corr. D*.

20. vTTOftvrjiaTtaLtdv -a- e corr. D.

ifi'. IlOi rcov ftobg rbv avrbv xvxkov rov

r&v Jtohcov rov ooiôvrog yivo^VG>vXal JtQig)QiCOV.

AfiJto^vrjg drf rijg (p6dov, xa& r^v av

5 xal rag agog rbv dice rcov noAcov rov boiôvrog

exdtirrjv lynkiGiv xai KU& ixddrrjv ftitiiv

rov diet psGcav rcbv tydiov uvxhov yavias tivvciito-

cos efpaiisv, xa6ror xai rf\g ebroAafi-

QHpQitt$ rov dice r&v 7t6&G)v rov 6oi-

10 frvros xvxhov V7i6 r rov Kara xoQvcpijv (Sr^neCov xal

rijs ytobg rbv Ao|6v uvxhov avrov ro/iijs, Bx^riôêâ

xal ra ig rovro rb [iQOg 7tQoA,a[ipav6[iva xal

no&roV) on x&v faov a7t%6vrG)v rov avrov

6r][iiov rov dia pfacov r&v ^cpdi&v nvxhov

15 6rjtiiG)v fcovs XQOVOVS axohaiiflavdvr&v l<p xdrQarov iL6rj[i{loivov ,

rov psv nabs avarohds, rov d'

irfyov TCOOS dvGpdg, ai re anb rov xara xoovcpijv cV

avra nOi(pOiai r&v pEyfarcw xvxh&v faai aMrfhais

i0lv xal at nobs avra yivopwai y&viai, xa& ov

20 di6riA,d[Ji&a ro6jtov^ dvtflv ooftais i'6ai.

0rco yao ii6rjnf$Qivov rîrlîa rb ABF, xal vrto-

xi6d'G) 7C avrov rb [iv xara xoovfp^v 6rj[iiov rb

B, b dl rov farj[iQivov 716^0$ rb P, xal /

yi

yod(pd'a)

rov dia [ifacov rcbv ^codicov xvxhov dvo

1. t|3'] mg. C, om. AD, |3t mg. B. avrov] lo%6v BC,mg. IQ^QV pro scholio C. 4. dij] Ss D. 5. r6v\ suprascr. C 8

. 7. Post nvxAov ras. A. 12. xal ra] xa, xat D.

rovroi] corr. ex rov D 3. 14. rpojrntoi;] -i- corr. ex o in

scr. D, supra pr. o ras. 1 litt. /Uyjuâ a mg. B. 18. T&V}om. D. I'cai] slalv foca D. 19. f^fftV] AC, comp. B, om. D,-v del. C 2

. ctvrov D. yivopEVKi] yivopccvai, A, mg. e.

MA0HMATIKHS B'. 161

TO rs A^dE xal rb AZH ovrog sftovrcc, coo'rs ra Axal Z 6rj{isicc l'6ov rs K7te%Eiv ccnb rov avrov rgoitwov

xal faces K3toAa(jifldvi,v 3tQi,cpQias rov <Jt' avr&v

TCCCQCC^riÔV (p' K(X.rQK

H rov ABF [i6r][i(lQ(,vov. 5

Zk- -*^>^ ysyoKwQ'GMSav ds xccl

7tQl-

dia rav z/, ZKTtb plv rov r

rov farjiieoivov 10

re F4 xal $ TZ,ebro ds rov B rov xarcc

xoovcprjv GriiLsCov ijrs EA xccl

fjBZ. AeyG), on,

rj

ply BJ rtSQHpeQEicc ry BZ fcq stitiv, i\81 vnb B4E

ynvia îsrcc rijg VTCO BZA dvtilv QQ&aig for). 15

yag ra z/ Kal Z (SrîEia ['Gag rov di ccvr&v

rov ABP ^6ri^QL-

far} 6rlvrj vjtb BTd y&via r?] vnb BFZ. dvo

6rw ro rs BF4 xal rb BFZ rag dvo

rats dvtil ttfovQttZs foag %ovrcc sxaroccv sxcc- 20

rsoa, rty ^lv FA rfi FZ, xowijv ds rijv BF, Kal

v ynvi'a ryv vnb r&v i'ticov jtkfVQ&v

v V7tb BF4 rf] vitb BFZ' xccl fid6iv aoa rqv

rfi BZ l6r\v Z&i xal y&viav xv\v vnb BZF rr^

1. rd(pr.) TO (alt.)] ra A4E D. 2. xa] om. D. 3.

corr. ex ccnolaâvo^vriv D 3. 8i~\ ins. D 3

.

6. 8s] 1* B. 10. rov] corr. ex TO D. 11. ij FZ] at

TZ, FJ D. 13. 7)(sec.)] om. D. 14. BJ] zJB B. negi-D. 15.

t'<J7j]mut. in IGKL D 3

. 16. %at] om. D. 18.

] -Z ins. postea D.~

17] om. D. BTZBTZ] BZT D. 20. SVGLV C.

ex T7]v A. 24. BZT] BJT DPtolemaeus, ed. Heiberg.

19. SGTIV~] om. D.

fysi D. 23. r%] rrj corr.

r$] ycovicc D.

11

vit

[p. 148, 10], on T&V faov a7ts%6vTG3v TOV CCVTOV

KOV 6r][iiov aC Jtobs rbv dta T&V yto^cov TOV farj-

pSQivov ytv6(ievai ycovtcct, 6vvaî(p6Toca dvalv ood-atg

5 facet i6w, 6vva[i(p6Taai, ccocc y T tixb F4E xalfj

iwb PZA dvelv oQ&cct$ faat, d<5iv. Idsfyfrri de xal

ilvjtb B4F rfi VTtb BZF fay xal 6wcc(i<p6tQtu

77r VTtb B4E xccl % vTtb BZA dvtilv

10 rtdfav drj dsixrsov, ort r&v avrcbv Giftisi&v rov

dia [teGcov rcbv ^coduov xvxhov i'Govg %QOVOVS

(p XKTQK tOV ^LS^r^l^QLVOV Ctl T CCTCO TOV

xoQvyrjv fit' ccvra yQctcpo^vcci [ifyforov xvukcav TCSQL-

<pQiai, fcai, aMtjtyis siGiV) KOI ai agog avtag yivv-

15 iiwai, ycoviai GvvayifpoTZQai ijr ngbs avarohas xal

f} agog dvGptts 6v6i rats vjtb TOV ^6r]ôtvov nobg

TO CCVTO Grjiitiov yivoptvuis facet i6iv^ OTKV (p* xcc-

TOCiTI

VOTICOTSQK TOV XCCTCC XOOVCpV 6r][llOV TWy%(XV<fl.

20 XO&TOV d' VltOXMtidCi) K^g)OTOOC VOTLCOTfQtt, XCti <3TG3

TO ABF^J^ en CCVTOV d TO

TO F, jrdAog d TOV

1. B4r~\ seq. ras. 1 litt. B, EZT D. 3. at] euan. D,

rov] mut. uoluit in rcov C 2,

corr. ex t&v D. 5. LGKI\ corr.

ex I'euis C 2. EIGLV} ACD, comp. B, -v del. C 2D 3

. ij re]at D. %ai

i] vno} om. D. 6. ogfi-ai D. 7.l'ar]~\

corr. ext'cat D 3

. 8. ij re] at D. vno (pr.)] supra scr. C 2. %at 17

vno] om. D. dpâtg] -g ins. D 3. slew facti D. 9. onsg

%dL SeiâL] supra scr. D 3. 10. Mjiipto ^ mg. B. 13. nsgi-

cpi^BiKi tfeai] -t t- corr. ex IV A. 14. ttfftV] comp. B, -v del. C 2.

16. i]\ om. D. 17. TO avrb ffrj^ftbi/] mut. in TOO avTw <nj-

ju-fto)A 4

. ytvojLtfcVat?] -g e corr. D. 19.7) voticorzQK] corr.

ex 'j]v on STCQK D 3. 20. d'] 8s D.

du CCVTCOV

MA0HMATIKHS ZTNTASE&2 B'. 163

TO z/5xal y^Qafpfta) dvo T^TfjîaTa TOV dia [i6cdv T&V

xvxhov TO T AEZ xal TO BH om&gTO E 6YjHtov xal TO H TO avTO

(p' xaTQa TOV di avTov TtaQakkrikov itQi-

cpQi,av a7te%iv 5

TOV ABFA \LBG-

H[\ ~~~~^-^ rujL&owov. xal

10

CCTIQ [lV

TOV r TO T PExccl TO FH, aitb

$ TOV <4 TO T

xal TO AH. dia Ta avTa drj TOIS ^7tô0d-vf15

jtl Ta E, H 6rj{iZa TOV avTov itoiovvTa,

faag avTov rtQicp()tac; (p' xaTQa noisi TOV

PQIVOV, iGoitfovQov T xal faoy&viov yivsTai TO

T& TdH, &6TS xal Tr\v FE Tfi FHtipa) di} 5

ort xal 6vva.yi<p6TQKi ijTS vnb 20

FEZ xal % vnb FHB dvtil Tats vnb 4EZ, AHE

7tl yaQ i] {L\v vttb 4EZf] avTrj i<5nv TTJ vnb

4HB, % d V7tb TEA for] tetlv t^ vnb AHF, xal

1. ptcov C. 2. TO (pr.) TO (alt.)] tec AEZ D. 3. tfrj-

om. D. v7tOKi[i8vov TO amo D. 4. di' avtov] diet,

V ccvr&v D. 12. TS] corr. ex TO C 2,om. D. 14. TS] om. D.

15. SLO] 8ia 8ri D. dri\ om. D. 17. Trotrjffft D. îGr]^--v- in ras. C. 18. yfvsTai] om. D. 19. Post FJH

B 3. T^] T^V C. ^Gr\v\ -v

-v- corr. exju,C 2

. 21.

JEZ] corr. ex EJZ D 3. 23.

I B, ut saepius. 24. ZGXI B.

11*

supra scr. f-r (h. e.

supra scr. D. 20.

FEZ] corr. ex EFZ D 3.

JEZ] corr. ex 4H D.

vitb FEZJHB facet

aQce ijT vitb FE4 xcel % vitb FHB

facet ffalv TTJ vitb 4EZ' co6T xal 6vvce[i(p6Tocei ij TS

xalfj vitb FHB dv0l Tcets vitb 4EZ,

'

01tQ $t dfl^Ki.

avTa T[iri[iceTce T&V X-

TO T ATO B floQtoTQce

/

ytv<5&cet TOV FTO avTo xcel ovtog

TOVT0TIV

ra

10 GvvaiKporsQtti jT vnb

KEZ y&via xal % vitb

AHB dvtil Tats vnb

4EZ foal i6W. Xi

yap [ilv vitb 4EZ15 ^ aVTtj 0TIV TTj Vitb

JEK Tfi vjcb

xod olri agcc r\vnb AHB far]

T7] T V7CO jdEZ xal Tfi

20 a[i<p6T()ai, ijT vnb AHB

vitb 4EZ facet sfaiv.

'

co6T %al 6vv-

V7fo KEZ dv6l

TO {lV TOV CCVaTOhLXOV T^tj^iaTOS {l(}OVQaVOVV

TOVT0TiV TO A, VOTIG)TQOV lVCii TOV JT XCCta KOQV(pr\V

1. y ri\ at D. v.ai 7] vno\ om. D. 2.

-v- corr. exju,

C. tf] om. D. 4. AHE~\ corr. ex HE C 3.

-X D. 5. ).fj(ifia y rag. B. nv.liv\ di]

BD. 13. JHB mg. A 4. 15. fGnv]

18. AHB] corr. ex ARE B 3 C 2. tW BD.

Gvvcc[i(poTQtxis] 6- e corr. D. 20. KEZ] corr. ex KEB D 3.

22. ^rj(i(icc d mg. B, a IfjinpK mg. C. faefafrm C, corr. C 3.

drj] om. D. 24. rovrsonv'] -v del. C 8.

D. 9.

-v del. C 2,iavi B.

MA0HMATIKHS STNTAgES B'. 165

>v, TO $ TOV Ttobg dvGpas Tûarog [LSGovgavovVj

TOVT6TW TO .B, (lOQflOTfQOV TOV CCVTOV. Af/GJ, OTl

GVVCCllQpOTfQCU rjT VTCO

, FEZ xal f} VTCO AHBdvO TG)V VTCO 4EZ {lL- 5

dv<slv do&ccts.

fj [lV VTCO

far} 0TLV Tf} VTCO

4EF) GVVKlLCpOTfQCil, d

ijT VTCO 4HF xcd

fj 10

VTCO AHA dvGlv OQ&atsfaai i<5iv, Kai 6vvct[i<p6-

AEF xcclr\

VTCO AHA dvtilv bQ&a,t$

d KCil f] VTCO

KQO, ijTS

i6Cv.

VTtb A'HB' ci)6T xccl 6vvaii(poTQas rtfy rs vitb FEZ 15

xal rr\v vnb AHB 6vva{i(porQG)v rcbv VTtb 4EZ teal

g rig vn^ êovag ivcci,

t vnb 4EF xai rr\ VTCO dHA,tfalv dvtilv 6o&at<3 facet,' OTCBQ sdei delicti.

<T, oittQ vitoksiTtsrai^ Kara r^v oîoiav 20

TO [iv TOV XQOS Kvatoka$ T^tjâTos {i6-

ovoavovv 6y[itov TO A J}OQIOTQOV yivoyievov TOV

viv v .

v\ -v del. C 2.

\v\ -v ins. C 3.

C 2D. s-

2. rovrsGTiv] AC, Tovtecri BC 2 D. 5. JHB mg. A 4,sed

del. 6. slaw] -v del. C 2; comp. B, ut uulgo. dvaiv] dvo D.

8. IffttV] -v del. C 2. 10. T}]

om. D. 12. elcv -v del. C 2.

13. rj] om. D. 14. tanv] -v del. C a. 16. rr\

xat] om. D. 17. TovTeCTiv] AC, TOVTEGTI B

ova C. 18. 6vvce(ji(poT()ct$ D. 19. flair] comp. B, -v

del. C 2. 8vav] dvo D. 6g&de D. onsg Zdei SE^CCL]

om. D. 20. Ifjuiia s mg. B, y JLTJPIIU mg. C. d'] drj D.

21. TO] mut. in TOV C 2. rov] om. C. T(JLIJIIUTO$] pr. ja

supra scr. D 3. [IEGOVQCCVOVV] corr. ex ^GOVQCCVOVGIV C 2

. 22.

TO] ov TO D. Fig. e corr. A 4,

litt. in ras.

JT, TO d TOV itobg dv0îag TîtjâTog psGovQavovv TO

B VOTICOTQOV. AsyG}, OTi 6VVCt[l(p6TQai ijTS VTtb KEZ

xccl ^ V7tb FHB dvo TCOV VTtb JEZ shaTTOvs'g sltiiv

dv0lv oo&atg. dta

5 TCC avTa yag net-A

l /Q

xai V7tb FHB

10 TS vjcb 4EZ Kcd

Tij$ vnb A HB,TOVTS6TLV dvO TG)V

V7CO 4EZ, &KT-

Tovsg yivQvrai 6vvan<poreQcci,s tr\ TS vitb 4EK xal rf;

15 VTtb 4HF' avTCiL ds dvtilv oo&ats faai dt,a TO xal

6VVCllL(pOTQCC$ [ISV T1JV T V7CO 4EK KCil TJJV VTtb

4EF dvalv do&cclg fcag slvcu, fcyv ds xal TTJV vnb

on ds IK 7too%ioov dvvccvTai, A.cc[if$dv6d'cci, T&V

20 yivoiidvov V7tb TOV Ao|oi) xvxkov Ttobg TOV dice TOV

xaTcc xoovtpfjv 6r][iiov yLtyiGTov xvxhov ycovi&v TS

XKi JtQl,(pQl,G)V ,KK& 0V SL^KK^LSV TQOTtOV, KL TS

7tl TOV ILStirinfiQlVOV Xttl STtl TOV OQÔVTOQ

avTO&sv av OVT&S ydvoiTo di]kov. sav yao25 iis6ri^QLvbv Kvukov TOV ABT^d ncd OOLÔVTOS

1. to (pr.)] TOV BC. 2. jj] corr. ex a in scr. C. 3.

sldTToves] -e- in ras. A 1. slaw] -v del. D 3

. 4. dvalv] dvo C.

5. ydg] om. D. 12. TOVTSGTLV] -v del. C 2,TOVTEGTL D. 15.

Sia] nod did D, corr. D 3. xat] om. D. 16. cvvccîcpOTSQccLs D,

corr. D 3. 17. i'^v] far] D. TIJV~] i] D. 18. onQ edsi] a

D. 19. at TrTjiUxoTTjrfg ante T&V ins. mg. A 4. 20.

D. 21. ycovycoviwv D.

MA0HMATTKHS ETNTAgESS B'. 167

TO BE4, rov ds dta pfa&v rCbv fcodtW

xvxhov rb ZEH ditoGdrjitors %ov, orav psv dia rov

{i6ovoavovvros avrov 6r][iiov rov Z vocbpsv rov did

rov A xard xoovcpyv Giftisiov

yQacpoyiGvov peyiGrov xvxA.ov, 5

6 avrbg ysvijtisrcti, rco ABF4^<?^/fyn>c5 ,

xal 0rat,ij

rs

vnb 4ZE y&via avro&ev

t\\Liv dedojievrj dia rb xal rb

Z 6q[itov xal rrjv nobs rov 10

liEGrjpfiQivbv avrov yivoîevrjv

y&viav [II ? 10] dedoG&ai, xccl

ccvrrj i]AZ itsoHpegsia diK rb %sw rîa^^ rto6ccg

IIOIQCCS Bid rov ii6r][i(lQivov ro rs Z Gqiistov Kitiiî

rov i6ri^BQivov xal 6 farjiisoLvbs rov A xccra xoovcpyv 15

<5iflH,8iov. orav $ dice rov dvarilMovros ccvrov

rov E vocbpsv rbv dia rov A /

yoccg)6^vov

xvxkov cjg rbv AEF, avr6&v xal ovroog

n q [iv AE 7tQt,cpQia ndvror

dia rb rb A 6r][ilov noAov fivat rov 20

BE4 doiôvroQ. OQ&YIS d oijtfrjs dfl dia rqv avri]v

alriav ri] vnb AE4 ywvCag xal ddo[ivrjs tr}g rov

/lo|oi) xvxhov Ttobs rbv dot&vra, rovr&riv rijg vnb

4EH, do&riGBrai xal 6'A^ vjVTtb AEH ycovta' OKBQ

r

di dtfâi. 25

2. xvxZov] om. D. ZEH] corr. ex ZH D. 3.

gavovvrogD. 6. ABT4~\ ABT D. 8. JZE]AZED. 10.

%at] nutd D. fr\v\ corr. ex rov D 3. 13. avrrj r]~\ KVTTJV C,

ccvrriv TIJV D. nQupQLccv D. 15. 6] ins. D 3. 16. did]

mg. add. D 2. 19. AE navrort] in ras. A. 20. TO (alt.)]

om. C, corr. ex ?- D. 23. OQL&V D. 24. 4 EH] 4EHD. OTIEQ Zdsi ^ft|ort] om. D.

)on rovrcov ovrog fyovr&v, av

(p'

rag ngb rov [isGrjiifigLVOV [tovag

y&viag T xal it()Lq)QLccg xai [lovcov r&v aitb ri\<s

KQ%fjS rov KCCQKLVOV ^BIQI rijg ttQ%ijg rov

5 dcodexarrjiiOQicov STtiA.oyiG&iisd'

%o[iv [p. 162, 10; 160, 13] xal rag re pera rov

Kvr&v y&viccs rs xcci rtSQicpzaeiccc; xccl k'rt, r&v

rag re TCQO rov iisGrmfiQivov ual rag pera rovf

iva ds xcti inl rovrcov

10 &B6iv h'<podo<s (pavega yevqrai,,

svsxev sx&rjdotJisd'a rr\v faop4vrfv xa&oAov dslîv

evbg &0)Qriiicirog vjto&fyevoi xara rqv avryvrovreanv XK& v 6 floQeiog itoAog rov ogftovrog

B^Qrai [loiQctg Ag, ri\v KQ^V rov KO.QKIVOV loyov

15 yj&Qiv [itccv &QKV t6rîQivriv aite^LV

rov [i6rju,pQivov ,%&& yv &6t,v iv

[i6ovQctvov6t,v [iv aC r&v z/tdtfytoov potoai,

avccr&AovGiv de aC rijs naQ&vov poloca t AJ.

ai,vbg xvxAog 6 ABP4 xal OQI-

20 frvrog {iv fiiiiKVKkiov rb BE<d^ rov de dia pfaovr&v t,G)diG)v rb Zif ovrag %ov, (o6re rb [iv H

1. f'qp']litt D. 2. xJU'fffoos D. TKS] e corr. D 3

.

corr. ex itgos D 3. 4. xapxtV D, supra add. D 3

. Alyo-

KEQCQ] ros supra co add. D 3. 7. I'tt] corr. ex snC D 3

. 8.

Post kom&v add. TK$ TE ngb (hue supra est ras.) rov fifffrjfi-

@Qivbv KVT&V (o supra scr. D 3) ycoviccs rs V.CLI TttQicpSQtias v.cxl

sni r&v HoLTf&v D, del. D 3. rds T] supra scr. D. 10.

9eaiv] om. CD. 11. dfiîv] d- corr. ex I C 2. 12. fl-ecDî?-

juarogj -rjfi-- e corr. D. 13. rovrsori D. ^f^Qrat rov OQI-

ovros D. 14. iijQrai] -rui in ras. A 1. As] rQiuy-ovraQ D.

16. ?jV] riv St D, fy dri D 3. tv] corr.

ex^hnv D 3

. 17.

HfGovQctvovat, D. 18. ctvur&lovGi D. A] corr. ex 1%' C.

19.Srji] D, de ABC. 21. ovroos] ante r ras. 2 litt. A.

6r}u,iov rr\v aQ%f}v sivai, rov Kaoxivov, TO ds Z iiti-

3 rb ds

did re rov A Kara

Kal dia rov H rye;

rov Kaoxivov yisyiGrov 5

rb AHEF, TCQO-

v rv\v AHVQtV. (pCiVQOV

on, f\ inly Z 7tQi,<pQia

v fariv w K, 17d HS 10

anb rov

6 d

at yisv r&v

Tg t/3 aitokuyifidvovGi rov

Jtobg agxrovg poious wyrov A Kara xoovcpyv 6y[iiov poiQag A^, e'Grai Kal

r\15

[ilv AZ rtQicpQi,cc jiLoiQ&v t/3 vy', fjdf ZB r&v

KQLTI&V fig rb reragrrîoQiov uoiQCbv oj f. rovr&v

do&tvrav ywsrai itaîv dta xr\v KarayQa(pi\v [p. 76, 3]

6 rtfc; vTtb rqv dnt^v rijs ZB nobs rqv vnb xr\v

diit^v rijs BA Aoyog b 6vvr][iiivos x rs rov rijg 20

vitb rrjv diTtkijv rijg Z@ nobs rr\v vjtb r^vrr

ts H Kal rov r^ VTCO rrjv dnt^v rrjs HErr^v vjtb rrjv oiit^v rf}s EA. a/U'

i\ îlv ri}S ZBitinv gvd id Kal ^ wô avrqv evfata

25

1. 6r\iLLov] GTJ Gr}[i iov C. 2. |u,otipag(alt.)] om. D. 6.

v D. AHEF] A- renouat. C 2.

{J. i]\ supra scr. C 2.

7) jitfV] in ras. 3 litt. B 3. 11. ILQIQ&V] om. B, (JLOLQ&V

scnv D. 13. &7tokct[ipcivov6iv D. 15. As] mut. in te o B 3,

corr. ex U D 3 euan. 17. fioi^&v'] om. D. 24. ^<^] corr.

ex ~Qd B 3. p? IJTj D. vno] vn' D. 25. EA] EA SiTt/ifj D.

V7l6] V7t' D.

v v&icc xali] [ilv Trjg Z

V KttlYI

VTC

vrj) r\d Tr\g H noiQ&v QV id xccl

r\VTC

V&itt TîrjîaTCOV Qit, ifi.KV KQtt CiTCO TOV TG)V

5 V& TtQOg Td ^JC AdÔV d(pAG)[lV TOV T&V Qi& VTJ

TCC Qit, t/3, XKTCCî(p^(3Tai flplV 6 T% VTtO T^V

Trig EH agog Tr}v VTtb Tr}v diTthrjv Tr]g EA Aoyog 6

) tg eyyitiTK itgbg Ta ~QK. xcci <5Tivr\ vTtb xr\v

Tr]g EA Tîr]^,dT(ov (>x*xccl

r\ vito rr\v diTckr}v

10 CCQCC Trjg EH T&V amcbv l<5Tiv Qid I?* &6Te xalr] [iv

Trig EH jfQi(pQLccg {lOiQwv <5Tiv ppd KS h'y-

avTi] dfrjHE T&V avTcbv o/3 iy. xal

ago, r\AH TWV ksntovtifbv itinv lg TO

15 r]g dl noil Tr]v VTtb AH

KO.I Jt6Ac) T& H Xttl

rri TOV TfTQay&vov a y-20

TO RAM, o)GT, 7td o AHEnvxlog dud T T&V TOV E&MKeel did T&V TOV KAM itokcov

EM Kol KM TttaQTiiiioQiov yiV6&cu.

2. 07T

ex 8' D 3

7. rfjs (alt.)] om. D.

EJEf] HE D. 12. HE] EH D.

ovv did

H 8ml.fi D -

]corr -

corr. ex xcmdTjqp'ibfafTca A 3.

10. TT)S] -r}- corr. ex o in scrib. C.

14. (JLOIQ&V] om. D. 18.

ncc dtaatuart diccGTiiccTi, d D. 19.H] corr. ex Tr\ D 3.

nUvQa] TT D. 21. 6] supra scr. D 3. AHE] corr. ex AE D.

22. te] om. D. 23. KAM] -A- e corr. D. SKKTSQCCV]24 xat] om. D. TTor(pT7] 1uo(HOi> D.

B. ovv] d' ovv D.

D.

mut. in yiyveo&Ki A 1

,

MA0HMATIKHS 2TNTAgES B'. 171

xarayoayriv e'tirat, [p. 74; 9] 6 rrjg vTtb rqv

HE nobg rrjv vitb rqv dirthijv rijg EK Aoyogsx re rov rr\g vTtb rrjv dtjrAijjv rr\s H

tv\v vnb rriv dtjrAiJv rr}g A xal rov rr\ vitb

mKrp rijg AM agog tqv vjtb r^v di7ckr\v rijg 5

KM. AAJ

TI {ilv rrjg HE dinkr] ^LOLQCOV etinv

5T Kcd$1

V7t avxriv sv&etcc r^ftarov Qid I?, i]ds

EK VLOIQ&V Af Ad xalYI vnb Kvrv\v sv&stcc

Ag Aif, XKI Tt&Kivfj plv rijg @H dtjrAiJ

QVS id xali\

vjtb avtfjv sv&sla. r^irj^drov QI i($, ^ 10

LOIQ&V xd fig xal % vnb avrr\v v&Zcc

% [id* K>GT, iav anb rov koyov rov r&v

ptd Ig TtQbg ra Ag A^ acpeh&iiw rbv rcbv QI t/3 nobg

ra x ftd, Karakei<p%"Yi<5era,t, fjptv 6 rqg vnb rqv diTt^v

rqg AM itobg rr\v vTtb rqv dtjrAijv rrjg MK hoyog 6 15

jr/3la eyyiGra itQog ra ^.qg MK rfirjiidr&v Q% xal

aoa rtfg AM r&v avr&v itixiv it{I

la. &(5r nalij

[ilv diTthi] rqg AM 7tQi(pQiag yioig&v i<5xiv ytz x^,

avrq $r\AM r&v avr&v ^y id. xal komi] aga i\ 20

AK JtOi(f>Qia avrr] rs xalr\

vjtb AHK y&vCa<3rlv JLtg jiZg* afire xal r\

vitb AH ywvia

ig rag dvo oo&ag Ztirat, ^LOIQ&V ^Ay id" oitQ

6. KM] MK D. &Ud A. HE] corr. ex NE C 2,

corr. ex @ D 3. dady] seq. ras. 1 litt. A. 7. xg] x D.

vn'] vno B. 8. W] ly D; vno] vn D. 9. H]HO I). dtnlfje D. tGtiv] om. D.lO.jj^ (pr.)] ins. A 4

.

vno] vn' D. 11. VTCO] vn' D. 12. xi] -f e corr. D.

rov (alt.)] om. D. 13.iJ3]

ins. D 4. 16.

7TJ3]ar- in ras. B.

TJ]om. D. 17. 7J] om. D. 18. TWV 19. ytM] rC. D. 21.

AK] KA D. AHK] -HK e corr. A 1. 23. rap] ra C.

6 [lV OVV TOOTtOS Tijs TG)V

xal sill T&V koiit&v 6 avTbs GvvdyzTai, r^ifis fc', i'va

xal tag aMag ycovias TS xal itQi<peQiac;, o6ov ys.

ftxbs %Qiav v rats Kara ftf'pos ixt&dtysGitV 66&ai,5 7tQO%iQCOS %G3UV l^Tfd'fi^VCCS, 7t%0'yi<jdlL&K XCtl

TCivtccs yQa^Lxcos ttQ^a^voi, [iv djtb rov dia Mfgoys

,KK& 0V ^ pGyfavq ^(l^QU CdQ&V <5TLV

iy, (p&dGccvTfs $ ^%Q^ tov yQctcpoutvov

rbv Tlovtov dia t&v xf$ohcbv BoQv6&vov$) OTCOV

10 17 lUyfavq rjiifycc aQcbv i6nv farnLSQiv&v 7?.

7tl[

xal

XG)V TOV did ^L(J(DV TG)V t,G)diG)V

T[ir][idTcov Ty dC vbs d&dexaTriiioQiov, 7il ds

15 Tcov Ttgbs dvciTohds fyxctl rtgbs dvGpds TOV

V &<5G)V Tfj did [LICCS COQttS far][lQl,V7JS.

XCtl TrjV TOVTG3V eK&B

6TOV xht[lCC T Xttl d&dfXCCTyilOOlOV 3tCCQCCTld'VTS V

[lV TOiS ItQ&TOtS H>O6l,V TYJV TtOGOTTjTCC TK)V Trjs ty20 xdTQCC TOV ^0^^l^Ql,VOV diK^TK0BG)S ^LBTK ir\V XCiT

CCVTOV &4tiiv farftiSQW&v tb^wv, iv de TOIS dVTQOi,s

T&S TtrjAMOTrjTas t&v dab TOV xaTd xoovcprjv

XXl[lVOV d&dXKTr]llOQl

i 7tQt,Cp()lG)V) V $ TOIS TQLTOLS

25 TTKQTOIS Tag TtrikiKQTriTag TWV vnb Tr}s

1. r&v\ om. D. KfOXftpfrqc D. 4. pEgos] A, supra

scr. 't\ A 1. 6. did] om. D. Mf^drjg] Mtgoc A. 7. IGTI D.

11. wdcxjiv D. 13. IL860V D. 14. tfoofoxcm D. 19.

-v del. D 3. 21. avrov] corr. ex avr&v C 2

. 23. <5eo-

D.

MA0HMATIKH2 ETNTASESS B'. 173

vo[irg Kara TOV Lcooi6êvov lv TOOTCOV

ymviCbv, iv plv Toig Tofaoig rag t&v nobg

TOV pstfqp/fytyot? &6(OV) v de rots tTUQtoi$ rag

rcov JtQOs dv6^dg. &g xal iv &(>%% pivxvi disGrsM-

ft^, psiivriad-ai, dft, on, r&v dvo r&v -6^6 TOV sito- 5

pevov r^îccros fov dta [isti&v rGbv

v yavi&v rv\v ait' KQXTCOV TOV CCVTOV

asi 7taQEiA,rj<pa[Jiv TOÔVTWV iy xdc6Tr]s

7trjA.ix6Tr]Tcc xagKTi&lvTSiS) O'LCOV Itirlv f] [iicc

Xttl 0TiV'Y]

TGJV KKVOVl&V X#<?tS TOLCCVTr]. 10

1. TOfifjs] -o- corr. ex Q in scrib. C. 2. r&v] suprascr. D. 3. 3] post d ras. A. 4. fisvroi] corr. ex (isvroig C 2

.

6. Tftryfiocroff] corr. ex Tju.rjfiaTcov D. 8. toaovrav] mut. in

Toiovroov D. 10. Y.avovCa>v] ~vo- add. A 3. In extr. pag.

(fol. 48Y) add. ty.&EGig r&v v,axcc nugc&'krikov y&vi&v v.cd TCSQI-

(jLQor]g OJQ&V ly fioiQuv i$ t D, mg.


r&v xara

Tov dice

jtegtcps-

Qet&v

ycoWaiava-

toJlutai

vcuWori

ovtixai toôiqeiia

ytaviathva-

toJ.iy.ai

ywviatovtiy.ai

KctQKlVOV Z vy o v

qoyvy

y.y ft?

of 1Ad

Ay

g o f xd /"* "2

A s o v t o s Q n i ov

15

20

id re

ttj fia

xp xi,

r?r~ S,

'-,

i

IT;a p jua t9

c xey.n

id A? *a

To 6 T o v

26

"t

30 ff

id

iy

17

AC

o*

Ad

A* ,18

Ay xarf A

QXS

pi 4go Mod va

o9

1. iy '] om. AB C D. Ordinatio est codicum AB C, in D tres columnae sunt

cum quaternis signis. 6. /^ (pr.)] AB, N C, om. D./? (alt.)] om. D. (pr.)]

om.D. r(alt.)] IV in ras.A, om.D. 8. (o] seq. ras.A. rd]>dD. 9. r(pr.)]

post a B, suo loco B2. Ai/] vt D. r] post ^>o/

B (qui omnino numeros huius

columnae uno loco altius collocat), corr. B 1; om.D. or (alt.)] AD. 10. d (sec.)]

ABC. Ad] -d e corr. D. 11. e (pr.)] e corr. C. p] y.a D. 12. Tty] Ttg1 A.

i^-] corr. ex iy D. 15. /S(utr.)]om. D. y(utr.)j om.D. 16. xg] corr. ex

QZ B2.

Qorj] g- in ras. D. VL] v^D. 17. v] om. D. 18. e] corr. ex i D.

_ 19. vc] ft? B C. 20. *p] corr. ex xf C./9]

om. D. 21. r] om. D. o (tert.)]

AD. 22. xe] om. C. 24. Qia] DB, Qtd A, piB C. v] om.D, mut. in p B 3

.

oô] om.D. Ac] As D. T (tert. et quart.)] om. D. 25. p] om. D. o (sec.)]

corr. ex. y D. 26." o (pr.)] corr. ex y D. 27. ,uj is D. ^;J â D. 28. if]tn BC. 29. Ac] xc B. c] A? D. ooa] ood D. 30. As] corr. ex ^s C. A]

om. C. 31. d] ABC.

MA0HMATIKHS 175

ycovi&v nal

OJQ&V ij [lOLQ&V

toQ&V JttQKfS-

qeitbv

yiaviatava-

tolixat

ywvovtixai co^cov

QSIWbva- yoiviat

ovtixai

Aly ox s QOO V

s I

fittr

oa. 8

iiy Ha

9? o

gva xs

QVtJ fll]

/Lrj

xrjxa

9 o

AS

va 10

QOfi A?

Ta v Q o v

of

eQtrj

I9

'I % & V 00 V d l8v p, CQV

la, f.ig

fj. Vfi

ir\

/ua

/ua o

x/? a

y o

/S] om. D. 14. ,*#] -5 1

e corr. D. /uz] corr. ex ^C C.

7] ê C. 16. w] oc A, i& D. 18. f] in ras. A. 19.

5. v] ter om. D. 7.riy] A, fttj BCD. 8. x] v D.

â D. 10. e (pr.)] in ras. B. îj] A, vt] B C, ^^ D. 13.

om. D. ,uc] jud D.

p] seq. ras. A.,1177] ê C. 16. w] oc A,

QP&] QC,& B C. 20. id] D, in ras. A, S B C. 22. v] bis om. D. f] bia

om.D. 23. x] xa D. a (tert.)] in ras. A, a*BC. v] corr. ex t^ B 3, tf C.

24. î] tcB. v&] D, r^ ABC. r] om. BCD. 25. ^s] ^|a BC. 26. y]

y$ A. 27. f] om. AD.Jlij] rq D. 28. v] om. D.

Tov $10,

yamat&ra-

toi.iy.aiSvtixai

KctQuivov

? I

o o

ty (yxy

o o

y ^c

(UQ& JtfQKpS-ytoWoridrva-

roAtxatyuovaiovtizai

Z v y o v

xy va

la|i/e HP.

10

*<S H* 9 Qvy

9

A V X S

15

ft

y xa ^ i^0?Q7t

/In xe

A*? /

Jtt] [IS

oa u

re id

Sn wre

/la

20 S1

ff

ita vfi

|

9 o9 o oo

r/? re

iUe <^

25

30

i ftpA. v qoy ry

QOIJ yQ7t O0^" if

oy xTie xy

re ^e

Htf.1 10

pa9

5. o (quart, et quint.)] om. D. 6.

*rf] * D. 17. po#] ^oa BC. i] ^7-e corr. D. 25. ry] r? D. 28. oo^]^d] D, ?f ABC. SO. /ia] o BC.

juS] o/ua A, o/ua D. ay] rt^ D. 9.

A (/lw?). 18. o|^] |^ A. 24. /uffj

ooe B C. ufi] post w raa. 1 litt. A.


iy [_' xy vcc.

(UQ&V


Tov SLO, vf)$ nemo tfjs Atyvnrov

&Q&V

MAOHMATIKHS STNTAEE&2 B'. 179

x|3.

'uonui,

bva- /I

tolixai OVtMycaviatava-

toliixalyuiviaiovtixai

la x/?

017 r#9 o

9 o

(6 UI& xy

06/u.eoi]fi

a

of

xs /ua

te v

t ty

10

QXC

Ta v p o v

SI

vy

Ttlf

9yra /tf

xa u

* /*/

xy tij

iy I

vtj xaoa ts

15

It

t xgf r

c vC,

o17

re 20

t s

'I i <9"u co j> d 18 v (ico v

xff rtf

? y ly

QX VS

QX6 V$

xi;

Aa

Sf tf

of A

>*>? y

ft_X^Md xg

ty 25

t Ad

*r/f?

9 firj ;

o|

/uff

x ta 30

1. A x] ^ x D. 5. ty] te D. A x/S]in ras. C. 10. e (pr.)] e A.

11. fffcnr-)] ff 5 A. g- Aa] om. D. 13.c

l"d()o/dov] IX&VMV D. 14. |^]e D. 15. l&] sciipsi, Ae ABCD. xa] -a e corr. C, x D. 16. /tf] -C e

corr. D. 18. rq] corr. ex /uq D. v] x D. 26. |] f C. 27. oa] od D.

28.Qf*(i] qvp D. 29. t] e corr. D.

12*


Tov 8i& *P68ov

coot&r

MAGHMATIKHS STNTASE&S B'. 181

id /_' (IQIQCQV /I? O.

&Q&V


Tov

wnwv

MA0HMATIKHS STNTA3E3S B'. 183

UJOUV


Tov dice [isoov TLovxov

&Q&V


GDQOOV IS {_' (JiOLQCOV [l U.

tupwr

Tov

TtSQKpE-

Qsiiav

ytoWat&va-

tolixaiycjvlaiSvtixai OJQ&V

I ytavLnwe- *.,kva- vtovat

ovtixai

Z v y o v

10

oft xdita It]

9 o

vy vy

w nft

fj,y vd

Hy vg

po fian

rj

9 o

qiyoxg

xy

QVf

ga tft

9 ft

rta vg

og xd

oy i&

op xy

A s o v r o s 2KOQ7C tO V

15 fieoy/u,

a

20

*ff re

ltd t

9 o

**

Qflf

JtftVCt,

i

fia

Irj

O/9 8

ft y

9 o

Qta o

qxft e

<>va ft

oe I?V1J

xft

To | 6 r o v

25

30

ffrcf

v/ xe

la 4e

oa xJ

ta tC

9 o

Qe

od vao xd

Ydd X

vi?

qva /.//

X

odft

9 o

9ft

Q/L& X

*?'06

in1. tov di&] to dice tov B, tov dia tov C. 7. /J(pr.)] 3 B. nras. D. 9. o^] ox; D. o] 5 A. 15. i/J] ft

C. 18. A] J D. 20. o]6 A. 21. o] A. 26. o] 5 A. 27. //d] fia D. 28. o#j oe D. 29.

o] 5 A. 30. xy] f* y D. d] e corr. D. 32. o] 3 AB.

MA0HMATIKHS 2TNTAEE&S B'. 187

fl/TJ

vaqmv

y xa rr^g rcbv ycovi&v

de rotg vnor^s^voig fov rag ito%a,g r&v

xara [ii}%og xal xccra nAdrog xobg rovg

5 r&v v ccvralg <pcuvo[ievG)v litikoyiGiiovg rr\v {iv roiav-

trjv k'K&e6w âi^rov nod yfajypagptjdjg fyofievyv

xa& avrqv vn' otyiv itoiri66iL&a axo-

rats r&v rt%i,Q'ya6[iVG)v cog EVL

rovro rb idog faroQwis xcci

10 [toiQccg K7t%i rov fariiLSQivov T&V

nark tor di avrfjg yQcc(p6[ivov [i6rjiif}Qiv6v ,xal

ovxog rov di' ÂêâvdQsCag yQcccpojiEvov

JtQog avccroAcig v} dv6ig iit\ rov l^rj

dt,a rb ngbg rovrov rîlv GvvfaraG&cii rovg rwv 7to-

15 %&v %Qovovg. vvv $ rb rotfovrov cog V3toxt,[iVG)v

rcbv &6G)v jii7tlv axoAovd'ov rj'y^d^d'K^ dtdrt,

av rtQOcuQGoiif&a r^v k'v nvi rcbv v7toxi,[iVG)v

QiGiidvYiv CDQKV 6xojtiv, tfrig i]v xara rbv

ccvrbv XQOVOV l<p sregov rwbg r&v

20 orccv diacpQG)6iv 01 di avrcbv ti6rj[i/}Qi,voi,

o^ftAoficv, odccg aitfyovtiiv aMtfhcov ovroi [loigag lid

rov tGruLEQivov, xal Ttorfoog avroov

2. df] mut. in rs B 3,rf D. 3. S7tiar)[La6ici$] pr. i supra

ras. D. 4. 7r<rx'qp<9m] -at e corr. A. xara (pr.)] ttard

D. -nurd (alt.)] om. CD. 5. avratg] av- in ras. A.

v] -cc- corr. ex (iin scr. C. 1'. 7tQ<xy[icctLKs] -s

corr. ex v D 3. noir\6Qv D. 8. ins&QyuGpiv&v D. 9. TO]

ins. C 8. 10. fioLQccs] p ovtog B, corr. ex fiov C 3

. 15. TO]om. D, del. A 3

. 17. av] edv ABCD. xty] mg. D*; }f D,

sed eras. 18. cbptaa^fVrjv C, corr. C 2. ijg] ^'TTJS C,

IJTJ]S C 2. xaTa TOV~\ corr. ex xaT

J

CCVTOV D. 20. fif(7rjju.f-

givoi D. 21. an^%ovGiv~\ corr. ex enfyovaiv C 2. OVTOI]

renouat. B 3. 22. avr&v] corr. ex savr&v D 3

. ienv] om. D.

MA0HMATIKHS STNTAgESiS B'. 189

regog r vTM&TSQOs, rotiovrois t

X^V KKXCC TOV V1tOXSl[l8VOV XOTtOV

tW Ttoi&iLEv rriv iv rrQog\ xat D. 2. tonmv C. 3. xara] corr.

ex -na D 3. 6. (isimGBcos] corr. ex (islcsws D. 6

D. In fine: Kfavdiov

ABC, KJiccv$iov nroHspctiov paftiruLa. $ D.

r.

Tads V6Tiv iv T& y' Tys JZtoAf^ca'ov

a'. jrfpl TOV [leyed'ovs trot) viav0Cov %o6vov.

5 j3'. K%"6i<S XCCVOV&V T&V TOV fjMoV [l6G)V X

y'. 3tQl r&v natf dtia&jjv xal eyxvxfaov xfoyGw vno-

d'. 3t$l tils rov

sr. 7t$l rijg agog ra xara pfyos r^îara r&v ava-

10 iiccfacbv xccvovoitouag.

g'. xav6viov 1% Âiaxijg av&paMas.

rvjs Kara, xr\v tifaqv TOV v\Uov xdgodov

Tijg TOV yMov

TVJS T&V

15 'E(fG)dVllVG)V fjlllV V TOig 7COO TOVTOV

T&V T 0^00%QG)S OCpMvTG)V 7tQl T OVOCCVOV

1. P'] om. ABC, xecpdJiccia TOV rgirov D. 2. y'] AD,OJ B, om. C. t?Js] T&V D. [iad"r][jiccT;iKfi$ GVVTCC^SOOS]

D. 4. a'] om. D. Iviavafov] corr. ex ivi-

ccvGiag C. Post ^^dvov add. rf ^ (ft^ D 2) ^ D. 5. |3']

om. D. xavdvos D. 6. et 8. permutauit D. 6. y'j om. D.

8. #'] om. D. 9. ']om. D. 11. g'j om. D. 12. ']

om. D. 7ra(>odov] om. D. 13. TJ'] om. D. tfjs] t?\ C.

TOV j]liov\ f]hcM7is D. 14. -9-'] om. D.^

15. IlTotepcciov

[icc&rKLctTmcov y ABC, wfpi TOV fieyfôvg TOV EVIKVGIOV %QOVOV D.

scpodtvpEvcov C, corr. C 2. TTÔ] corr. ex Tt^6<s C. 16.

Tt (alt.)] supra scr. D.

KAATA. IITOAEM. MA0HMATIKHS 2TNTAEE&S P'. 191

xal yr^g na&rjuarix&g itQohricp&fivai, Kal In 7tol ri]g

fyxhfafcog rov dice pBticov r&v tydi&v rjfaaxov KVK&OV

Kal r&v xara p,Qog jffol avrbv Gviiflawovr&v iiti re

rr^g oo&ijg Gcpaioag Kal snl rr^g xcc&' Ka6rrjv ot'xrjGiv

S'yxexA.ilievrjg axohovfrov rjyov^s&a xal (pîjg rovrov 5

rbv 7tQ\ rov fjMov xal r^ra r 3tQtl rag xiwtJ6is avr&v

k&lv prjdfvbs v&v KQi> wvg atirtQag

avv rfjg rovrcov JtQodiaA.rii{ja)g Kara rb

dvvapevov. Kal rovr&v d avr&v itQorjyov- 10

i6xopv rr\v rij$ fjhaxfis xivrj6G

g avev itcchv ovds roc rtfgl ri\v

olov r av ydvoiro di,%odiXG)g

a'. Ilfl rov if^frov rov VLav6iov

Ilacbrov drj itdvr&v rcov 7tQl rbv rj/Uov aitodLKvv- 15

rov rbv viav6i,ov %g6vov VQtvrag plv rcov TtakaiGbv itQl rr\v aTtotpavtiiv rov roiov-

rov diacp&vLag r Kal djtootag [icc&oiiifv av IK r&v

avrolg Kal \aaKi6ra r&f

lTtitaQi& avdylr bpov Kal cpiAaAtjd'Et,. ayi ya$ pdhGra 20

Kal rovrov tg rfjv roiavrrjv aitooiav rb dia plv r&v

rag rgoitag Kal rag i(3^gCag (paivo^dvov avto-

rbv viav6iov %o6vov V

1. (icc&7]jLtarotcoj] corr. ex iLaQ"r]^KrLY,&v D 3. 2.

TOV yhccKov CD. 3. CCVT&V C. 5. tovrcav] corr. ex ro D 2.

9. ncivxtaUg C. 11. VQLGY.O^V] oQ&psv D, mg. g. 14. a']

mg. BC 3,om. AD. TISQL %QOVOV] om. D. 15. Sri] corr.

ex Si A 1. 16. eviavGictlov CB 3

,eviavGLeov B. 17. ano-

cpaGw CD, supra -a- ras. D. 18. unoQiKs] ante p ras. 1 litt. D,anoQfias C. av] D, om. ABC. 19. Post trw ras. 1 litt. D,item post Îmtdqâ). 21. ccnogiav] ante 9 ras. 1 litt. D. 23.

C.

jtl rcclg r% fi[iQai$ rov rrdorov

r&v 7tol rovs a

. 0&V ittlfittktel r<p

Iirdfia6iv xiva, 7toA.v%QOViov TtOisZG&ai, Kal avrtfv,

5 (o6rtQ Kal rag r&v rthav&iiwcoVj fig ra 7c6^va rvjs

rrjv rtQG)tr]v itîKy^y^v JtoiovGrjg (pOQccg Kara rbv

dici r&v jtoA&v a[i(porQG)v rov rs faq^Qivov xal rov

Ao|oi) yQa(p6iivov xvxhov. fiptfs ^, rovro plv on

ovr&s t fyM xal rCva yivercu, rgoitov, v rotg 7tQi10 r&v ankav&v aGrfy&v 7tidioiiV' ovd yap ra 7tgi

Xivovs civv ri}s v\kiawri xal Gfkrjviccxijs nQodiaMityecos

olov r av yzvoiro di? o'Aoi> fts&Qri&rivai' Kara df ri\v

TtaQovGav BTCiGKStyiv TfQOs ovdw AAo qyovfi

<x7to(lA.7tovrccs rbv BviavGiov rov i]Uov %QOVOV15 $ rfjv avrov rov Âtov nQog favrov, rovr^nv rov

vn? avrov Ao|6v xvxA,ov, aTCOKaraGratiiv

r rbv iviuvGiov %oovoV) xa& ov aito nvog

axivtjrov 6r][jitov rovrov rov xvxhov Kara rb $;^S

7tl rb avrb itagayCverai,, [tovas aQ%ag olKia$ rv\

20 roiavrrjs <x7ioKara6rd6G)s r^yov^vovs ra vjtb r&v roo-

TtlKCbv KOI l6r]ll

rov 7tQOiorjîvov KVKkov. edv r yaoc5 AO^GJ, ovr oiKi,oroav

rijs till rbv avrov

1. r)[LSQcci C. dial - - Sid B. 2. nsQi] corr. ex ngos D 2.

3. TOT] corr. ex TO D* (TO! fr\v\ supra scr. D 2. 6. ir\v\

-$- in ras. 2 litt. A 1. 9. yvr\tai C. 13. Gntyiv D. ~] mg. D.

. 14. anofittnovrs-s D, corr. D 2. 15. rovrscti D, comp. B.

xj\v ywoptvri'v D. 16. vn' UVTOV~] (-it av- renouat. D 2)

vn' ccvrov TCQOS TOV AD, ugh? TOV del. A 3. 18. 6f\piov] -ov

renouat. D 2. TOV] om. A. 21. <yrjju-ficov] corr. ex Grîslov C 2

.

22. sav] D, av BC et post spatium 1 litt. initialis A. 23.

Aoyco] evloya) ex renouat. D 2. 24. TOV] r&v A.

MA0HMATIKHS STNTASE&S r'. 193

rbv ijkiov Toitix&g TE xccl %QoviK&g tftot, agog Tovg

doiôvTccg i)rbv [is6rni(lQivbv i)

ra [leyed"*] T&V vv^^-[IEQC3V TOV TOLOVTOV &G)Qov[ievov OVTE aMccg da%dgEV T& duo, pEG&v T&V Jcodtcov nvxhcp, povag ds rag

XKTK TO GviiftEpyxbg acpOQi&fievac; vjto rs t&v TQO- 5

ItMCbV KO.I tov$kSQW&V 6r]HlO)V' KV TS

Tig 7tl6X07tfi TO OLXIOV, OVT

TQCCV VQ1J6l, Trjg KTtO TOV OÎOLOV TtSQi TOV (XQCC

xccTaGTtjpaTOS nl TO opoiov not Tys avTils COQKS iitl

rriv avTrjv (pfgovGrjc; TOV ijfaov OVT aMag d$%ag -J)10

liovccg, KK& ccg aC(bgcci, [iccfotiTcc diaKQivovTcci,

TOV Trjv agog Tovg attA.avZg a6Toccg

aTOTtov (pttiVEG&ai did TS ahka xal

,OTi Xal

fjCCVTCOV GCpttiQU 7tQlQV\LivY\ TWO,

flaGiv ig TK 7t6[iva TOV ovoavov 15

&G)atToci,' ovdfv yag TOVT&V ovT&g e%6vTcav

Kiysiv, ToGovTov ivcu, TOV viccv6iov TOV riMo

EV 06O) TOV TOV Ko6vOV CC0TEOK AoyOV EVEKEVi)

KCtC

TLVCC TCbV CCA.A,G)V 7lA,CCVCO[lEVG)V 6 fjAfcOg JfEOLXCCTCi^tt^KVEl,^

jro/Uot T av ovTtog xal ditttpoooi ytvowTO OL EViuvdioi 20

%QOVOI,. did [iv dij TCCVTCC itQo^KEiv OIOIIE&K TOV

EVOiGXOllEVOV did TG)V TrjQIJGE&V TKtV &g EVi lldfaGTCX,

dytb Ttfoiovog diadTdtiEcog ^.K^KVOÊVOV dno Tivog

1. r/TOt] 7} TOV BC, corr. B 3. 2. yy^-thj/x^jcov] post 9

ras. 2 litt. A. 3. Q-fcoQri^vov D, TE- ins. D 2. 4. povas

d] f) IIOVKS D. 6. idv ri\ she D. 7. rig] corr. ex TS D 2.

STTtffHOTm ABCD. 8. SVQ^GEL] corr. ex ZVQSWSI, D. 9.

^?] i- in ras. A. 12. roi>] om. D, TOV nai supra scr. D 2.

13. Ante &TOTCOV ras. C. 14. fu&Uffjtf-iK D, sed corr. 17.

ro-u] -v in ras. A. 18. K$6vov~\ comp. B, corr. ex %$6vov C.

21. odcc A. '22. IVt] corr. ex fa D 2. 23. onto (pr.)]

i D. nteivos C.


v} totftteQfas irii ryv avtrjv xal (p%ijs %()6vov

rovrov fiyBiG&ai rbv Iviav6iov rov îov.litsl de ftogyfisl nag rbv

f

'IiutaQ%ov i\xal nsql

avrqv rqv roiavryv aitoxardGraGw VTtoitrsvo^v^ dia

5 r&v KCCTK rb e%ijs yivopiv&v 6vve%a)v rrigriGs&v KVL-

dice PQCC%SCOV [irjds rovro

fisv Ettrjyorsg nsgl rov

/LM) avfaovg sivcci TOV %$6vovg TOVTOVS, f| (bv ual

avrol dice tcbv dgydvov xata rb |ijg vwy%dvo[iev

10 reTr}QV]x6Ts rgoitcbv re xcci foqptyttfp* ovdsvl yag

aitoAdycj dicccpSQOvrag avrovg SVQI^KO^LSV rrjg Kara rb

reragrov ejtovGiaS) aAA' sviors 6%sdbv o0G) jtagd rs

rr\v xccrcc6xvrjv xal rrjv ftzGiv rcov QQyKV&v vds%rcu

diapttQrdvsw 6ro%a6iivoi, $ xccl f'| avrcbv, (bv 6

15f

'Ijt3tccQ%os eitikoyi&rcu, [laAAov r&v rrjQtj<5G)v fivat, rrjv

yt()l rag avitiorrjrag Kpagriav. x&[ivog yag rb

itQ&rov v r<p Il()l rijg iisranr^sog r&v

xal fotftUQUf&it 0rjiiiG)v rag doxovGag avr&

xal p^rlg rsri^Qriâi frfQivdg r xai

20 Ttdg bôôyel xal avrbg ^ roGovrov iv avratg

rb didqxDvov, &6re di avrag dviGoryra xarayv&vat,

rov viav6iov %QOVOV imMysi yag avrcclg ovr&g'

X plv ovv rovr&v rcbv rriQ^sov dijAov, onitavrdnaGiv yeyovatiw ai r&v svuavrCbv di

3. 7 mg- D. de] corr. ex dr) C. i] *ai] mut. in xal

f)B 3

. 5. r&v} renouat. D 8. 7. nL6[ia] BD 2

, niGâ ACD(corr. uoluit C 3

).8. pri] supra scr. D. 11. avrovs~] -ov-

in ras. A. 12. TSTKQOTOV C, sed corr. 14. dnx(jicxQTfiv D.18. a-uTo5] seq. ras. 2 litt. A, corr. ex CCVT&V D. 20. flvcct,

sv avrccls D. 23 sq. > mg. ABCD. ZOVTCOV] supra scr. D 2.

corr. ex luvd. A 1. 24. nccvrdiiKGLv -v eras D.

MA0HMATIKHS 2TNTASE&2 T'. 195

7tl [iV rojv rooTt&v ovx ait^TtCtfQ xal f}[iag xccl

rov ô^^trldr] xccl v r rrjQrjdfi, xccl iv red 6vkkoyi<5iLK>

V XCcI & rErdorOV [lEQOVS fl[lEQag. KXQl-

dvvarai xccravoEtGd'cct,fj av&naMcc rcov smccv-

6icov XQOV&V EX rcov tExriQvi^vov sjtl rov v AK&tttv- 5

av SK rov

xgcbtov iiroitc*Qiv5)v farjfifQi&v 10

cTa rfirî^fVrov, iv \L\V r& 1%

xccrcc Kakmitov itQi6dov rov

rov ^jUov, percc d y rrj v

rsi rri TtQ&rr] r&v 7tKyoiiV(ov ^(xotag, ddov

ag, &6r dia7i<pcwr]Xvcc(, rerdgrGt âg fjfiEQas. 15

sviccvrbv iv r& xa' k'rsv &ga$ gr

, ojtQ xal

TJV ax6kovftov rri xgb avrrjs rrjQtJGfi. psra de Ice rrj

r& A/3' b'rEi rr^ tQfafl t&v ErtccyoiiEvov fig rrjv rEra

rov yiEGovvxriov, dov TtQcoLCcg, &6r ro3 d' it

cpcwrjxdvcci,. pErcc $ viavrbv W roo hy' Victvr& rr\ 20

1. ct7tli7t%co~] B 3D, ayf-lnfta) ABC. 2. 'Agî^Sji] mut. in

B 3. 4. ta>v] e corr. D 8

. SVLKVGLCOV] -co- in ras. D.

6. Kcdovpsvr) rtTQciywvG) B. 7. Grace] cro&i C, t eras. 8.

a^Tjrat] corr. ex c^rjrca D 2. 10. [IETOTCOJQLV&V] -&- e corr. D 2

.

iGruLEQi&v] corr. ex IGJ]^SQIV B 2, tGr]^SQiv(ov D, IGJIUSQW&V D 2

.

11. Ante v ras. 1 litt. D. i'] corr. ex ^ D 2. 12.

KctiLnnov] ABC, Kcttiimtov D. MSGOQL B. 13. T]ABC, T^ Tqiu-AOGTy B 3D. 14. xfj\ corr. ex xr\ A 3

. Tr^coTiy]

B 8D, vsoprivCa ABCD a

. 15. wffw] AD, &s BCD 2. 16.

d'] 5 D. sv Tea] Bvarm D, supra a ras. %a'] nQmrca V.CLI

siv-oGrw D. ^v xat C.'

17. KVTTIS] corr. ex ravrrj? D 2.

'

18.

T$] TO* T^ B. 19. rov] eras. B. 20. *'] <T BC. iy']

seq.- - in ras. B, >Ty C (similiter saepe), /I rîTo) D. tvt-

avrco] 8TFt D.

13*

196 .' KAATAIOT nTOAEMAIOT

d' r&v STtayonsvcov Jtpotag, oiteo xccl fjv dxoAov&ov r%

nob avrijg rriQêi. psrd ds y sty ra> kg' BXBI rr\ rs-

rdorrj r&v iitttyQpiv&v sGTCeoccg, deov rov HSGOVVKTIOV,

cbg v<p $'!*<6v<p

Ttdhiv diKTtsycovqxsvcci,.

5 psrd ds ravrcc exri&srai, xdl rag opoi&g dxoifl&g

CCQIVCCS fatjiisQiccs' iv [iev ro5 A/3'

Kara KaknntQV xsQiodov, Ms%iQ x'

xccl 6 XQLXOS ^5 <pri<5iv, 6 iv 'AteâvdQSia i'6ov

exarsQOv [legovg jtaQrjvydG&r] TISQI s' &QKV &6re

10 xal ri]v avryv l6rm,8gi(x,v diaydQCOs rsrrjQ'rj

lyyiGxa dieveyxstv. xccl r&<s sepsis de

rov % srovg GviiTtsycovyKsvai, rfj itgbs to

psta de Id trj real y xal p' srei, rov Meylg rr\

[isrd rb [istiovvxriov rb sis ify ^ ysvBG&ai cpytilv

15 eaoivfjv farjiiSQiKv, OXSQ xal dx6Aov6&ov ^v rri iv rat

A/3' srei, rrjQtJGfi, xal (jvufp&vst, qyqffiV) ndkiv xai nobs

rag sv rots fyppfroig &cetii rrjoijtisis f^JCpi tov v'

srovg' yvto ydo rov 0a[iVG)& rrj Ttocbrr] Ttsol 8v6iv

Âfc'ov perd \i,ia.v tyiqwv xccl ijfiHfv xal rsraorov sy-

20 yiGta ri}s iv x& \iyr

erst, OTtso xal eitifidkkEi rotg

&t6w. ovd' iv ravrcug ccoct rcclg

1. luiayopivayv] -o- in ras. A 1. 2. de] -e' in ras. B 2

. y

I'TTJ] corr. ex y rr\v B, TQLTOV hog (corr. ex eret m. 2) D. InD numeri plerumque omnibus litteris scripti sunt. 4. ndkiv}supra scr. D 2

. 5. iv.riQ'sxai\ corr. ex fatt&atifcu D 2. CCKQI-

|3w?] corr. ex &.%Qi$fotcna D 2. 6. IG^SQLVKS D. l$'~\

I $' AC. 7. Kdhnnov] BCD et corr. ex Umtov A 1.

MB%LQ\ MB%COQ D, MS%SIQ D 2. 9. naQvyaGftji C, corr. C 8

.

. iesqf] supra scr. D 2. 11. cpqoi, D. 12. Z'] corr. ex Zy D 2

.

13. TOJ] corr. ex t&v A. y' xat ft'] jly D. MB%S{Q A. tjf]

om. D. 14. <pr)0v] -v del. D 2. 15. ^v] corr. ex ehv D 2

.

16. avfjicpwvei] del. B 8, mg. yp. cvvscpwvet,; Gvverp&vsi D.

qpTjat D. %ca (alt.)] om. D. 18. sytvsro] -sv- suprascr. C 2

. TtQanrj] AD 2,a BC, vovwvfy D. 21. ] fjrra BC.

MA0HMATIKHZ! STNTASE&S T'. 197

yfyovs rig d^Moyog diacpoya xairoi dvvarov ovrog

ov povov iteQi rag roonixdg rrjo^6ig^ aAAo: xal 7iol

rag for]pQtva$) yiyvtG&ai ri xao' avrdg

xal p%Qi> d' [iiag f}[ioag' xav ydo rcj

xcil sâxoGiodtG) [love) [ISQSI, rov dice t&v Ttok&v rov 5

farj[iQi,vov KVX&OV 7taQccAA.d%r] rrjs aKQi^sCa^ ^ ftsdig

tyxal duU$6is i&v ogydvov, rfy totiavTrjv xarcc

TtAdros 7tKQK%a)Qri6iv 6 r/Ato^ dioQ&ovrai, XQOS rots

6r][iQi,vots rprujLKdiv rerccQTOV îtag [IOIQCCS xara pijxos

STtl rov Ao|oi) xvxhov xivri&Ms, co&rs nccl r^v diet- 10

tp&viccv y>%Qi' d' pi&S f][iQccs syyidTK disvsyxsiv. sri

& civ diaîKQrdvoi nheov iitl r&v[irj xa&cc7tK%

xai itccQ avrag rag TrjQtJGsis dxQipovf

vv6rr]Qi'yii8VG)v daydvov CCTCO tivog (XQ%ijg rotg

V7toxi{ivoig ddcp6iv ytobg TO novijiyv iit\ TtoAv rrjv 15

&6iv %iv } yiyvojifvrjg nvbg itsql ccvra vnb rov

%oovov foAyftviag 7taoccxivitJ6G)g) &g iti ye ribv

v ry rtccAcciGroa %akx&v xoixcov v roo rov

av rotiavrri yaa v\\nlv rrjoovGi xarayaivfrai diaGrooyr} 20

rijg &6G)g ccvr&v xal [idhiGra rov [iit,ovog xal

aQ%ot,ioreQov , fog vior xal dig iv rccig ccvralg lorj-

[iQiaig iLfrcicp&ri&G&ai rag xoiAccg avr&v 7ticpciViccg.

1. ys'yovf] seq. ras. 1 litt. D. 3. ylveG&ai, D. 4.

ins. D 2. 6. farjfteQivov] in ras. D 2

. 7.r[\ postea ins. D.

xcct] xai r) D, i] add. B 2. 9. T(irj[i(x6i,v~]

-v del. D 2, TJLITJ-

B. 12. 8iaybKQxa.vi, AC, ^taâ^TTj^st'?] D. nlsfov D.

/LIT]]del. B, supra scr. D 2

. 13. %ca] comp. B, v.cd ^ B 3.

ccKQifiovusvcav] &%Qi,fiov[ivcov ogydvcov D. 14. Gvve6Tr}Qiy(i-

va>v~\ corr. ex GvvfGrrjQiG^vcuv D 3. ogyavcov] om. D. 15.

sSdysGi D. 16. yivopiv7\g D. 17. tog inl] corr. ex mcitl C 2,

renouat. D. ys x&v\ renouat. D. 18. TtukaiGxa. D, corr. D 3.

20. duxGTQOCpri] r\ diaGTQOcpri D.


r&v \iv roiovr&v ovdfv ovd' avrbg 6

Iji7tccQ%og ofercci, rvy%ttViv a&oitiGrov ngbg rr\v VTCO-

tyiav iijg aviGorrjrog r&v eviccvGicav ^pox/ov, cbro $

riv&v rr}g GfArjvqg ^xtefyfov eitikoyi^oyL

5 gpT/tftV,

fon f\ av&iiaMa t&v iviavtiicw IQOVGOV

rbv [istiov ftsaQOvpEvr] ov [isi&va 7tQi%si,

i' xal d' psgovs IM&S fftiSQas' QTCSQ av r^v tfdr] TWOS

ofeiov, si'neQ ovrog d%e Kal ^ Q avr&v,

evGyidvov s&scoQelro.

10 psv yccQ did nvov 6vvs /

yyvs catkavcbv ad

xfafys&V) 7t60ov xcc& eKK&ri

Y]v 6

ayvs icgo^BltKi rov {LSTOJCCOQWOV 6rniiov,

xccl did rovrcov evQiGxew oferai, itorl JAW rb

avtbv a7ts%ovra rolg xa-01

'

eavrbv XQOVO

15 note de to &d%i,6TOv [loiQccg xccl d\ Gwctyst,

VrV&V) Oil, 1tl7tQ OV fivVCCTOV TOV Std^VV V

ovr&g oMycp XQOVG) rotiovtov nftaxwqd'rivai, ,rov

) cccp' ov rovg roitovg t&v dTt&ctv&v 6 "Iit-

20 KitoKaxK&Ta&iv. AcA^'d'f d avrov, on rov

dvvapsvov 7too%G)Qlv avv rov rov xara

iv rov f\kiov r6itov vitoxtfG&ctt, avtbg ig

rovro xa& xd0rrjv Tta^cc^cc^dvov rag

rolgr

r(ji,v Xivoi,g cp ccvrov

6. piaov] corr. ex (istov D 8,

-ea- supra scr. D 3. 7.

']

ovs D. 8. d%\ corr. ex d%tv D 2. 9. sitdoyigercu] corr.

ex iniloyi&to D s. 15. [loiQas H xatl f D. Gvvdysi] post

ras. C, -ye- in ras. A. de (alt.)] d' D. 16. dvvccrov] -rov

ins. B 3. 17. peconivriiQ'fjvKi A. 18. "inagios D. 20. 8\

8" D. 21. ngo%coQiv~] -co- in ras. A. TOV rov] corr. exrovroov D 2

. 23. nctqccla^oiVfov ]AB 3C 2D 2

, TttXQodafifidBCD. 24. Ig;'] ABC; dtp' D supra scr. s, quod del. D a

.

xal fariiiEQCa avro&ev dijlov noiel pr)de[iiav TCEQI

GvyXQlGlV TG3V EVlCCVr&V V7tKQ%OV6ttV JtCCQCi t$\V tOV

rsrdgrov EitovGcav dicccpoodv.

G)S y&Q <p' &>6 foodsiypato$ ex plv rijg EV rep

A/3' EtEi rr}s rofays xccra K&Knt'KQV Ttsgiodov TtaQare&si- 5

ex&eiTtTixijs rrjQijfa&s evQiGxew oi'srcci tbv

rov psroitOQivov Gqudice ds rri<s iv TG) p' xal rgCtG) eteu ri}s civrijs

7fQoy'yov[ievov poiQccs d'. xal dpoi&s

fg rovs

rovrotg

[isv tovT&v

rag iv rolg sredi 10

sccgwas farjiiSQicts, LVCC

rovg iv rots [ie6ois %QOVOL<S r&v

rdjrovg, djtb ds xovrcov rovg

S) ciitb ds r&v ri\<s tffAî^g rovs t&v a6re-

r^v p,ev sv r& A/3

r

S'TSI (pytil ysyovevai rov 15

M%LQ K% -jtQGjia^ rqv d' iv rat py' srsi rrj

rb inetiovvxriov rb sl<s rrjv k' peta, j$i' d'

rfjs EV to* A/3' h'reu yfyEvrjpEvrjS) otfag xccl Ttoiei rb

rsraorov \LQVQV 7tiA.a[ipav6[ivov ExaGrc) r&v {ira%vTec rcbv. i'7to ovv îtjr iv nfaCovi, p^rs iv &u66QVi 20

%QOVG) rtfs xara rb d' ETtovtitas 6 tffoog rrjv nobs ras

rv

5. KccliTtnov] ABC, KuMinnov D. nectars&ei(Jivr}s] corr. ex

itccQKTi&siJLEvris D 2. 6. >dr]7mxi?g C, corr. C 2

. 7.{_'] /_' j' D,

corr. D 2; j" ins. B 3

. 8. /u/ xal tQirco] ]iy D.^

9. f] ?/_ D,^8 D 2

. opoLfos] o/Ltcos D. 10. sis tov? 7tQov,sîsvovs] mg. D.

ioyTjitovg] BC, mg. A 1; STtdoyiGiiovs D, sed sm- renouat.

15. (fj]GivD. 16. MS%IQ] p%i>Q ^ D. K'] supra scr. C.

S' sv ro5] corr. ex $s r&v D 8. 17. ^'] TQLKKdda D. ^']

mut. in TerccQtov B3

. 20. SITIEQ ovv] corr. ex snsl ovv D 2(y^.).

21. y.atu ro] xard A. litiovaias D.

xal reragrov xsxwrjG&cci, , nag ovx aroitov ra

did rcbv vxo%i[iVG)v &Q%G*V fitifaAoyiGiifva Jtaoaâp-

fidvsiv ftobg tv\v avrcbv rCbv 6v6rr]6anVG)v avrd dta-

poAijv xal rrp> cclrCav rov iteol r^v ro^Kvrrjv

5 rov 2xK%vo<s advvdrov iiydevl [isv

*ys fivr&v t&v e^7toii]6ca TJJV

iav dwccpevcov, porous ds rats v

a)g apa aKQiflcbs Kal pi} ax

dvvarbv yap av do&iE pccMov rjtot, rag iv ccvrcctg

10 rcclg SKfofystii diaGrd^sig ri}s âA^v^g Jt^bg rovg

rovg lytLôy^povs ijroi r&v

rrjv t&v g)cuvoiiVG)v rojtcov iTtfaxetyiv y rijg rov

fjMov xtvrfGscog rijg ccnb rcbv ItirjiufQiav sxl rovg

15 [is'tfovg r&v sxfofyscov %a6vovg ^ prj dhrjd'&g r} pij

xal rbvr

'l3t7tccQ%ov Gvvfyvcoxsvcci, psv xal

ccvroV) on [irjdsv iv rolg roiovroig V0rt,v

itobg rb dvrQccv rwa r& Âtw ngotiKiirei

20 fisfiovkriG&ai d [i6vov vito (piA.aA.y&ffag prj

n r&v vtovg fig vitofyiav bjt&Gdvjnor

Vyxlv. xtyorjrat, yovv xai ccvrbg rcctg V7to&66iv

fjMov xal 6^jjvrjg <bg piug xal rijg avri\g V7tao%ov6rig

7tol rbv r^kiov Kv&pccMccg rijg 6vvattoxad't,6ra[Lvr]g

25 rc5 nobg rag roonag xccl rag farjiifotag IviavGiG) %o6vG).

1. rlrccQTOv] j' B, j D. WKivfiGftai] post %- ras. 1

litt. A. 5. iij}Sevi (iev~\ corr. ex psv (iriSsvi D 2. 6. roi-

avtr]v D. 7. dwafif'vooi/] des. fol. 68 UA, ,,deest folium" mg.

m. rec. (desunt reuera 4 folia). [lovccis] sqq. om. A. 8. PostBC.del. v.al D 2

.

9.^6|fif] D, do&i BC. 10. luJLef^satv C.

11. iyyvs D. 13. 7) rrjs] om. B. 14. Ic^fqiv&v D. 15.

cclr]Q"rivo<s D, Cr supra add. D 2, cdrj&iv&g D 2

.

MA0HMATIKH2 STNTASE&S T'. 201

xccl ovdapfi dice to l(5o%QovCovg vitoTL&sGd'ai Tag ex-

KEiîEvag TOV r\Uov TtEQiodovg ra itE^l rag sxfafysis

<pcuv6[iEvcc dscaQOVpsv aJtoAdyco tivl diacpegovra T&V

XKTK rag EXXEipEvag vito&EGEig EitiôyôÊvov^ OTCEQ

av afa&rjrbv it&vv GwEficcivEV py 6v^7taQcc^ciii^civo^vrjg 5

tils 3tegl rriv avt,6oTqrcc tov eviavdfov %QQVOV diOQ&G)-

êi xal [nag [tovov i]v poL^ccs^ dvo ds cog&v sy-

s'x TE dq TOVT&V ccitdvrcov, nod i% (bv rîEls ai)roi

8ia t&v g)^rls ^tv tErrjQyiiEvcw rov v\Uov Jtagod&v 10

xccTaA,cc(i@Kv6[id'cc rovg rcov artoxccrccGTCcGEcov ^^dvovg,

OVVE aVlGOV VQl6XO[lV TO EVLCCV0LOV [lEysft'OS) EO.V

OS fV XL KCil(li)

TtOTE [lEV ttQOS ta tQOTtlXa Xttl 16^-

rjiiEia, jtors d itgbs rov$ aithavEis KGTEQCIS

,OVTE aM.rjv olxEiorEQciv K3toxartt6ra6iv rijs 15

Kit6 twos tQOftMOv rjxccl far][iiQivov r}

xccl

6r}{iEiov rov dice HEGCOV r&v ^codCov

Jtl TO avTO cpQOv<5rjg TOV f/Aiov.

lV di K7tA,OV6TEQC()V G)g EVl

V3tO&E6EG)V TCC (pCCiVOÊVCC UTtodElKVVELV, <Jp'

00OV CCV 20

X T&V TrjQIJGECOV aVTlTtiTCTOV TTj TOl-

(pccivrjTcci,. OTL {LEV roivvv b ngbg TCCQ

ag xal JfQog Tccg l6r][iEQicts &ECDQOV[IEVO$ EviavGiog

E6TLV Tijg Eitl Tatg TÊ r\ÊQai<s TOV d'

1. fyxft/^vas D, corr. D 2. 3. rpaivoiisvcc] C J

D, qpatvo-

^svag BC. fteooQOVfiEv] corr. ex Q'tfOQOv^sva. D. rcov] corr.

ex root D 2. 5. av aUfhftfo] corr. ex ccvai6Q"r]Tov B 2

,corr.

ex KV aic^Tcog D 2. ovvsfiaivfv] -v del. D 8

. 7. fiovov r]v\

corr. ex povris D 2. 15. -9-fcop^rat.] E, jtanpeiTcu BCD. 19.

dt'] 8 B (h. e. did). 20. &Tiodiv.vvtiv] corr. ex ano-dsMVvsi B 3

,dfwvvew D. 21. avrntCnrmv C. 22. TOLVVV]

ovv D. 7 mg. D. 23. n^dg] om. D. 24. iat D, comp. B.

v yeyovev not 6Y

ds ehd66K>v <5TiV)

[iv oi)% olov T av yevoito kafielv rrjg re rov d'

av%tJ6G)g rtl Ttkeiova eiri jroog afo&rjtiiv

5 (isvovGrjg di ro kd%i6tov tr\$ dt,a<po$ag nal di,a rovro

Kara trjv dia IIKXQOTSQOV IQOVOV Gvyxgidiv dvvansvrjg

rijg svQiGxoiiewqg T&V rjîSQ&v snov^Lag^ ijv fist rotg

xal v ekurroGiv sviccvrolg rijg avtfig &GJQZ6d'tti'

10 Aaft/fcrnuro d' av syyiGra axQifiag r\ roiccvrrj aito-

, oticp civ 6 îrcc^v r&v GvyxQivouwcov rrjQ^j-

xal ov povov 7tl

ravrrjg TO xoiovrov Gvêftrjxfv^ dMa xal STCL ytaG&v

r&v TtfQiodix&v d7toxara6rd0cov' ro yag naga rrjv

15 avr&v r&v TYjQr}6G)v ati&dvsiav, xav dxQificbg

voiisvov didil>v6(ia Pga%v xal rb avtb

(bg xgbg rf}v nag avrd al'G&rjtiiv ini re rcov

dia fiaxoov xal iitl r&v Si okiyov %g6vov <pat,voiis-

vav fig ttdrrova [isv 7tL^QL^6îvov ivy iiiov itoiei

20 ro sviavGiov dîdQrrjâ xal ro ex rovrov xard tbv

^ stg

'Aa66ov.

o&v avragxfg 7tgo6r^xEi voptfav, edv, otiov 6

fira|v %QQvog JUL&V re xal (bv ye e'ôîev nakaicbv

1. yiyovs D. 2. ccnidei^s post. ras. 1 litt. D.

&O.GG03V D. 3. TS] BC, ye B 2 D. 8. iv TtlEiQGi\ corr. exnldoGiv D 2

. 10. JiCCfLpttvoLVTo D, corr. D 2. 12. z0oi>os]

cvty BC,corr ex %QOVOI$ C 2;bis D, corr. D 2

. 13. ravrTjg] tccvt

avTijs corr. ex ccvrog in scr. D, ravrr^s D 2. 15. rcov] bis D,

corr. D 2. iisdodevovTUL CD, corr. C 8D 2

. 16. yiyvoiisvov D.

didtyevGiid] corr. ex Si&tysviia D 2. 18. XQOVOJV D. 20.

%ca] del. C 2D 2. 21. 8e] corr. ex $i' C 2D 2

. 24.

corr. ex %%a>iisv in scr. D, %a)(jiv BC.

apcc xccl axoificov rrjoijtifov dvvarai jtooGxoirjGat, rfi

r&v TtsQiodix&v vito&E<3G)v S'yyvrrjrt^ rotiovrov xal

lQK&G>llV GVVEKSeVSyKSlV Kal [IYJ SKOVreg <X[IS-

ri]g JtooGTrjxovG'qg s^srccGscog, rag ds neqil o&ov

rov at&vog TJ Kal rov (iaxQ(d tivi xokkcatkadCov rov 5

Kara rag rrigriGEig %g6vov diK^âiG36ig KMorgfag

<pt,honKd'iag t xal yihaA.rjd'Mag riyto^d-cc. WEXEV pwovv TtccAcciotytog ai re vitb r&v 7t$l Mdr&vu XKL

Evurrftiova. rrr}Qr][iV(u &Qival rgonal xal aC [ira

rovrovg f)itb r&v 7C^l '^QiGrccQftov Q(pikoiv av stg 10

rrjv GvyxQiGiv r&v xa& fftnag yÊvrj^vov TtccQcdaii-

Pccv6&ai,. VKV dl rov Ka&oAov r rag rcbv rgoitfav

dv<5diaKQirovg eivai xal JtQog rovroig rag VTC

taQaddo^Lvag Qho<5%Q<5rQOv EikYimuBvag, cog

KOI rip

(

Innate:) doxt cpaiv6&cci) ravrag {iv 7taQrjrr]6d- 15

rcclg rcbv faqiiSQi&v r^^î xal rovrcw KXQL-

EVEKEV ratg r vxb rov *Iit7iaQ%ov ina

ccvrov xal raig vcp fftifiv avr&v dia r&v Eig ra rot- 20

avrcc Kara rr\v aQ%rjv ri\g Gvvrd&cog V7toddt, i

y[iVG)v

[idAiGra rrr]Qr][ivai,g' f| (bv

rotg r Eyyitira r6iv \iia f}[iQtt itgo-

rQov yivopdvag rag rooTtag nal fayiiEQiccg rj\g Kara

1. dvvccrai] mut. in 8vvi)tai B 1. 7. cpi3.o[iad'icc$ D. 8.

vnb rmv TISQI] supra scr. D, in textu/. ite^l TOO. 9.

om. D, yp. *ai fttQivai supra scr. D 2. at] om. D.

TOVTOVS] JU.ET' ccvrovg D, deinde ins. at D 2. 17. TOILS]

Tf D, corr. D 2. rriQijGstGi. C, rrjpTjfffcov D. 19.

O'rjoatg C, corr. C 3,

sed euan. tog] add. mg. B 3. &ocpa-

AfVrara] corr. ex a.GyalEGTG.'tag D 2,ac- corr. ex comp. axj B 3

.

22. a<f7rcbiTcog] corr. ex <xdt,GTKKT(p D3

;hie calamum mutauit C.

23. iv\ om. C. htGi D. 24. rag] ins. D 2. %ca] v.a.1 rug D.

TO d' 7tl tats t% rjfioai,s sxovtitccg. ev ply yao

A/3' k'ti rijs y' xatd Kdhiititov 7tQi6dov

tyv [isroTt&Qivrjv farjiifotccv 6"

o^^vrjv xal

5 avtrjv ysyovsvai, tr^ y' r&v ejtccyoîsvcsv rov

rov sis rfv d' (pSQOvtog' KVLI Btinv to srog goy' aito

fAfvrijg. ftfra df tine rrj rw yf

k'rsi

6 iGuv v%y' aytb r^

10 farinQiKv yeysvYipBvriv tr[ & rov 'A&vQ peta

cooav syyiGta ti\$ tov Âtov &vatoti]s' in&vifav aaa

i] drtoxatdijtaGis f'gp' oAotg Afyvrttiaxots 6?t

tovt6tt,v tolg ava t, fi[iQas, tag ytddccg o xal

xctl ffaocitbv h'yyiGta yuas f)iiQag dvtl t&v xata

15 tOV

oa .

to 7tov6ias Y*> *>i> iitovtir to

d)6avtG)s $ ndUv 6 plv "ImtaQios (pûv t^v iv

20 rc5 7tQoxi,[jiVG) k$' ti tijs y' xccta Kd^LTtitov 7tQt,6dov

tri ttf tov M%IQ TCQ&ICCS' KUL i<5tiv to i'tog to

dttb tijs 'Afa^dvdQov tA,vtriS' ^tg d tqv [ita td

1. rj^QK? D. 2. Kdhmtov] BC, Kdllimtov D. Ini-

ro D, corr. D 2.

~J mg. D. 10. ^crj^fpmv] far}- in

ras. C. 11. K>QUV] rj^Qccv B. 12. Iqp'] renouat. (ex vy'} D 2.

13. rovr^GTL C, comp. B. rots'] supra scr. D 2. o] 17^5-

QCC$ o D. 15. sTtifiu'kovG&v C. 16. oa d'] corr. ex o OA D 2.

17. jLua] corr. ex TtQwrr] D 2. 19.

r/

/?rapôg D. cprjGiv] -v

del. D 2.

'

20. KdUnnov] BC, KdUimcov D. 21. aî^Gra-rrjgri&eicav C. 22.

t;y~\corr. ex TTJS D 2

. M%SIQ D. SGTIV]-v del. D 2

,SGTL C, comp. B. TO (alt.)] nccxa. TOV EKKTOGTOV D,

xata rov del. D 2. 23. TO. 'GTts] Tag its D.

MA0HMATIKHS STNTASESS P'. 205

Ores dfiot&g rr] red vty' cbro rijs '.^/UjaVdpov Tf/Uurijs

mgiv^v farnisoiav VQfaxo{iv/

y/

yevr}[ievr]v rfj % rov

IIcc%G)v [ista yiCav (DQuv syyiGtct rijg ^^^/3(>iag, cog

Kttl rCCVrrjV TV\V 7CQl'odoV 7tlA.rjCpV(Xl, T&S faag fi[lQaS

o ual d' nal K k'yyiGra avrl r&v agog rb d' sjupak- 5

AOVG&V T0t$ 6718 T6lV i^LQG)V OK d'. TCQOTfQOV KQCi

xal wrccv&cc yiyQVBV fj rijs CCQIW?JS i6rj[iQias ccitoxccTa-

6tcc<5tS rijs ttaQcc rb d' itov6Ca r\[idQK yua foiTtovGrj

rb K' [lQO$. G>6T 7fi TOV CCVTOV %l, AoyOV TCC T T

bs t& 6X xcclfj pia rjpfya ngbs vqv piav 10

rb K [iQOS) GwdyErai, dioti xal iv rots r

7tQ6rQov i6tiv rrjg xccra rb d' 7tov6iccs

Jtgbs rcc farj{iQi,vcc 6r][ila yuvoiievri rov ri^Cov ano-

xav TCQOS rfjv vjfb r&v itoi Msrcava r xctl Evxrij- 15

pova rrr]Qr]iivr]v ^Qivi\v rooTcfjv cog

rijg i)(p fj

,rb ccvrb rovro VQtj

ci,f

yyvri^vri iitl '^4^vdovs CCOVTOS 20

xccr

2.SCCQWIJV^

corr. ex sctQivrji, D. yyevvr\\Li-vi]v C, yD. ^'] t^ B, corr. mg. B 3

. 3. WQUV] rjfi^Qav B.

ayytara wquv D. 4. xr\v\ om. C. sm]\Bi<pivai D. 6.

oa 61

'] o a A D. 10. T?]] supra scr. C. TO] D, rds BC.11. TO] D, agog TO BC. 12. SGTLV] comp. B, tcrcci D. 14.

5] BC, piK D. 15. 7 mg. D. xav] B, xcu CD, y.al el

C 2D 2. Supra ryv scr. o D, del. D 2

. re] om. D. 17. ava-

C. 18. noirGme&a corr. ex TCOLGOied'a C-cc in ras. B, Ttoirjadiievot, D, noLrjaofie&a corr. ex

[ie&cc D 2. tr^g] corr. ex ryv D 2

. 19. eni'ke'koyiGiiiv'riv D,corr. D 2

. 20. yeyevvr][ievr] C. 21. KQCOIKS] ne^l xr\vD.

ds rrjv iv rc5 7tQoxi[ievG) vt,y' ri anb rijs

yiddiisfta ysyovdvai rr] la rov

[ira /3 coaas fyyvg rov sis fr^v rf' [isGovvxrtovKai fotiv ra iilv djtb ri}g snl rov 'A^vdovs dvayfyoaî-

5 psvrjs &Qivfig tQOTtijs [itJCQi' t^S vô r&v TtSQi Agi-i& v' k'rsi rs

gvfi, tec d% dyfb rov ytQOXsiîsvov v' s'rovg^ o i\v

a rb [id' eros ano rrjg 'Afo^dvdQOv r^vrr]s^ pt%Qt>

10 rov v^y' rov Kara rrjv rnirQav rrfgriGw fry vt,&. iv

rots [ifra^v aga rys ohrjs dia6ra6G)s ^poa r6iv, iav

% vnb r&v 7tQl EvKrôi rov

15 opi.' y' yyi6ra avrl QpfiL' $' r&v rots <poa r<5iv

Kara rrjv rov d' 7tov6iav 7tif$aA,A,ov6(bv, &6rs noorfoov

yeyovv ^ x%i,[ivr] KitoxaraGraGis rijs Kara rb d'

7tov6ias Y\H>Qai<3 dvtil faiitovGais t& ifi [lias r}[iQas-

tpavfobv aaa xal ovrcos yyovv^ on iv oAois rots %20 k'rEGiv ras dvo itAijoMS fyyiGra fidgets o viav6io$

%o6vos 7tQokainfidvi rrjs Kara rb d' iitovtiCag. KOI dt'

7tki6vG)v rrjQrjdf&v rîfls ts rb avrb rovro

VQl6KOîV Kttl tQV "Iltlta

avr& 6vyxarari&Hvov b'v rs ydo r<p25 lviav0Cov [i

iy&ovs Gvyxoivas rr^v VTCQ

1. ^TTO] twv KTto D. 2. sTtsJioyiGdfiEQ'd] D 2,

BC, inikoyiGK^sQ'u D.~J mg. D. r^ ta'] corr. ex

ir\i a D a. rov] t- e corr. C. 3. MSGOQL BD. WQCCS

dvo D. fyyurtcc D. 4. icti D, comp. B. sW] suprascr. BD*. rov] supra scr. D 8

. 5. TQOTtrjg &Qivf]$ B.

&Qivf]g] e corr. D 2. p%Qt] -t renouat. D 2

. 7. Ka.\mnov\BC, KdlUmtov D. 9. v.ara to] om. D. 10. <u|y'] v|y'

D. 13. t^s] rfjs xu D. xa'jom. D. 15. y']sv B.

^

rgfaov e corr. D 2. ^TSGL D. 17.

17 EKKSifiswi] ysyovsv18. ro5] corr. ex to C, ex xai<$ r&v D 2

. 19. rotg] om. D.20. TE0w] B, exeat, CD. nlri^j] C. 24. yao] corr. ex

T B 3C 3.

MA0HMATIKHS STNTAgESiS r'. 207

rc5 v' rt, A.rjyovTi, rr\g

Kara Kdlinitov jcspiodov r -69?' eavrov rtdfav

stA.r][i[iV'fl rc5 py' s'tsi ^tjyovn rr^g rgCrrigKara KaKntitov 7tQiodov <pr}0lv ovrcog' ^dôv roCvvv,on iv rolg @ii ersîv raîov yyovv r\ rgonri rijg 5

Kara rb d' InovtiCag fa fj[ifaet, rov 6vvap<porQov &,

Kal vvxrbg IQOVQV"' jtdfav re Kal iv rti IIs^l

[iqvcbv re Kal fi^Q&v TtQOMTt&v, on, Karaftl Mdrova Kal EvKrrLova 6

ttQi%i ii^Qag rt,e d' Kal og' piag ^(ISQCCS^ 10

xara de Kdhititov i^LQag r% d' ILOVOV, iTtiktyti Kara

v rolg i& r6W) otiovg KaKlvot,, rov

miavrbv n Kal rov d' ghaGGov rQiaxoGioGra iiti-

p,dki6ra USQSI, {Mag fux,Qag, a)g iv rolg r 15

rGiv ^L7Civ Ttaga pv rov Mdrova f)tiQag i, nagadf rov KdkntTtov fj[iQav piav"' KOI GvymcpaAaiov-

pwog $ rag yvcoâg avrov 6%dov dia rv\g avayqa-<prj r&v idicov (Svvrayîdrov cprjGlv ovr&g* ^vvrdraâd Kal 7tQi rov viav6iov %QOVOV iv fiifiMcp vi^ iv 20

co a7todiKvvG),on 6 Ka& ijfaov iviavrog' rovro $

yivrau b %Qovog, iv & 6 TJAtog ditb rôii^g iitl rr^v

7taQayivrai rjaito i6riiLQiag iitl rrjv

25

2. Kdlimtov] BC, K&klutnov D. rj) 4. OVTO>S] mg. D 2.

4. K(&(,mtov~\ BCD 2. <pj]6iv OVTCOS] etiam in textu D.

5. on] ins. D 2. 9ft^] corr. ex pft B. i-reaiv] -v del. D 2

.

ra^tov] corr. ex rdêiov CD 2. 6. Jjro'Ufftag] post n ras. 1

litt., -g e corr. D 2.

'

<mg. D. |] Ix re D. 7. Ante

XQOVOV del. wi D 2. re] om. D. 9. Mirtov C. 10. d'} %al

%xi (-1 corr. exTj) 4' D. 05'] D, o s B, o g B 3,

o s C. 11.

Ka,limtov\ BC, KdMimtov D. d'] v,al TETCCQ-COV D. 12. ft?V]

om. C. 13. > mg. D. 15. j&iag] corr. ex ccs D 2. 17. Kdl-

ntTtQv\ BC, KdUiTtnov D. xca] om. D. 21. 6] D, om. BC.mg. D. 23. nuQuyiyvtTccL D. 24. slaecov D.

xcil VVXTOS-, xccl ov% cos of

TO d' ETtdyEG&ca ETCL TOO EL^ÊVG) Tthrfoti T&V fj[iEQG)v".

QXI [iv ovv ra n>%Qi TOV dsvQO (paivoîEVK TCEQIto [ifysd'os TOV EVIKVGLOV %QOVOV rf/

5 TJJV T&V TQOTtlXGOV XKi i0r^LEQLV6)V 6V\\JilG)V CC

GTCtGlV TtyhlXOTrjTl, 6VVT()S%Si KKTCC tV\V TG)V VVVT& TtQOTSQOV 6[LOhoyLCCV , (pKVSQQV OL[lttl,

TOVTCW $' OVTG)S %6vTG)V, IciV 7fL^l8Qi6(O^

YllieQav ELS t& * f^? 7rt/3aAAft EKK^TG) srsi,

10 fj[i8Qas s^rjxoGra devrsgcc i$, KJtSQ sav a(pE^co^

t&v Tys Kara TO d' itov6ias t& ^5 $OIIEV TOV iiti-

TO00VTOV {LEV d^ TC^ÔS TCDV r][lQG)V sty (XV

qiltV G)S EVi [idhlGTCC K TCOV TIKQOVTOV15 EVEKEV E TqS ETtC T TOV i\MoV XCcl TWV

TKS 7tKQ EXCKJTK 'yiVO^lEVKS CCVT&V XCCQo

1JV JtQOftELQOV XKi &67tQ EXXl,[lEVr]V TtECpVXE 7tO,Q%lV Y]

GVVTtt&S tilS XttTa [LEQOS XaVOVOTCOLLCCg., 7tQO&6l,V [IEV KCcl

GxoTtbv T]yoviL&K dslv vnaQftEiv TOO â^rj^ccTixoo dslâi,

20 TCC (pcav6^va EV T& ovoavco TtdvTa dt' oîa^&v ual Eyxvx-EG)V KTtOTEhoVllEVa, 7tQ06ljXOV6CCV d XCCi

Tfi TOlttVTTl TtQQ&EtiEl [idhlGTCC XCCVOVOTtOitaV

Tf}s dia Tag T&V xvxhcov VTto&EGEis doxovtirjs25 fictivEw avGoiiaMccSi ndkiv df EX T^Q [ILÊCOS xal T^S 6vv-

a'yco'yils TOVTWV ajifpOTEQCDV TCCS (pccivoiiEvas UVTCOV TCCCQ-

odovs ccTtodEixvvovGccv. LV' ovv r\\iiv xal TO TOIOVTOV

sidog EvxQrjGTOTEQOv xccl itao' KVTCCS tecs ccrtodsi&is VTtb

%EIQK kapfiavriTai, TCOIÔÊ^K EVTEV&EV T^V X&E<Siv T&V30 xciTa PEQOS b[iahG)v TOV ^LOV XLVÊ&V TQOTIG)

1. avto] corr. ex ccvtqt D 2. 4. TtQocsiQrj^vrj D, -G- eras.

5. aTtoHccTaGTKGiv] pr. T e corr. C, -iv corr. ex -ft D 2. 11.

corr. ex STCLOVGLCZS D 2. Deinde add. r^Lsgrnv D et

supra scr. B 3. ts] corr. ex id ftrj D 2

. 13. Ante TOGOVTOV

del. TO D 2. 14.

e&Tjpf^MMt D, corr. D 2. 25. Gvvaycoyfis D,

av del. D 2. 27. fva D. 29. TronjacbfAfO-a D.

MA0HMATIKHS STNTASE&S I". 209

rijg yaQ (lifts ccTtoxaTccGTaGfcog <xitodedi,'y[ievr]$

r|f id jZ^, sav iti,[iQfaci)iiv fg TccvTccg Tag TOV

xvxkov noigag T|, |oî> TOfi

TOV fyiov [noigcbv o v&rj t? Ty i$ Aa

yap pfyQi' TOGOVTCOV %r}X06TO)v Tovgtovrcw itoielG&KL. Jtctfav xov fjiiQr)6iov

^K^KVovrsQ TO xd' eôiisv TO coQiatov ÔIQ&V o

v Ip/y y a syyiGru. oîoicog TO f}[iQiJ6i,ov

&S tov vbg [irjvbs rjufyccg A

nqviatov pOLQibv x& Ad q Ag Ag i A, 10

id ds Tag TOV a AlyvTCTianov TOVS

xarj

A. TCakiv TO viccv6i,ov 3toA,A,a7tA,a6t,a6avTs itl

Trj M? dia TO (pavr]66iivov 6v^Toov Tijg xavovo-

XCCi tt(phoVT$ oAot> XVX&OVS Ô^lV IrJTrj- 15

7tOV6taV [IOIQG)V TVS A^ X Aff X Ad A.

ovv xccvovicc Tr

vO' TtfQlS&t, d TO [lV TtQ&TOV XKVOVLOV TCC TCOV

STriQidov iisGa xivnjîaTa^ TO df ft' TCQ&TCC TCC iviuvGia 20

xal V7t avTa TCC cDQtata^ TO $ y' TCQ&TCC [iv Ta

VyfOXKTO $ TCC r\^,QTq6lK^ TCOV [lV TOV %QOVOV TOlg 7CQG)TOtg llQ6t, TCC060^lV(DV^ T^S $ T

iv Totg /3' XCCTK Tag olxstag fxccGTcov iiti-

Kg. xaC sfaw 01 xavovsg TOLOVTOL' 25

2. r|f] ante ras. 1 litt. D. ravrcc D. 3. T|J] seq. ras. 1

litt. D. TO] totvvv TO D. 4. o v-fr] corr. ex ov& D. 6. 17^-

QIGLOV C. 7. lufiovTes D. o f] corr. ex op D. 8. O/LMHOOS]6- corr. ex D. TJIISQIGIOV C. 9. Post sôfisv del. i\ D 8

. 10.

(jiGov Kivrifia D. ^,g(alt.)] supra scr. B. 11. a] svos D.

- e corr. D 2. 12. $ mg. D. 15. oxtooHcafoxccfrTî'-

17. vdt-ofisv D. 19. TrifTegLdtov C, dxrcoxcadfttaer?;-D. 20. KivrKiatK] in -vrj/Ltem* rursus incipit A fol. 69.

] Is" A. 21. tap to;tec] opta m C. 22. r][i()iGi,cc AC. 23. rj)s

D.'j

TWV df TT)S D. 24. Traâ-O'fVfos] corr. ex

|3'] SswsQoig BD.

t

I

s

i-iIS

ssi-Srf

-< o -

TS^rst"

*

"J

CQ_ p-X

g

CO.~j ?k toto to

H

^gO

O I

6

S i. ,

o

i 1O

^ o

QOPQ

1 ft ^ ^ *M

- g

1IP-J* _

|.g

S 8

^ co

i -92

.9

'

g

d d

'I

OS e-. Oto ca ?

4;S|sIP - gV .

** f

-fd, i

.9 2

MAOHMATIKHS 2TNTAEE&S r'. 211

O -4 O

IP S. *

I 8?-

IP QQ. PT^ s a.

Hioa. s. -

i 1 rjP .V" o

P t-*

pq

^fi

.3 t

H P^?PI i

a

CO

'o

'0*1?!<->

00510 T^ I 1

03.XM

I

<*0

a

fi^ 5-

a. fci' oa-

* ft a-

t

0.^<UO CT- O

O^P

14*

S|8

3-j

Qa.sr

*est

t.f.e^ ^ g

o ?=

o o o

. o> < S j!

" 9 P-* *4^|1^ i i . . _ . O g*

<t aa ^00 OQ

*-H ^. ^2 M

'-

1 fl *:

MA0HMATIKHS STNTAHE&S r'.

l

5-<fe

213

git

2?

o o o o o o ooo

3 'g

f 4

tl-

-0fcw 3

w

= co QM ^ ICU

'

Q? 14'**

Q QH o ^-u^8 d

in? i

"8 1 I

O

'

o 5

cT %,oa

o <^ <* o <

s ^Or Q/

to vu *o

111o a a.

8 00. ?

* ci *[i*!"

1

i O *

ffl I $. f J:

MA0HMATIKHS STNTASE3S T' 215

's. X*4 ft"

to -y~n o-a.

<*$ I:8 2"

a. a. a.

S U ^

i 111o o

*T-i co ^

IH o co ^

y'. Ilsal r&v Ka&' bpakriv nal

VJCO&S6S&V.

d' ovros xal r^v (pawoiisvrjv dv&iiccMttv rov

det%cci TtgoAynrtov xalhUou, diort, xccl al rcbv

5 3tAav&iiVG)v sis ra jtoîva rov ovaavov

ci)67tQ Kal sis t& riyovpsva yoga r&v

f*fV elctiv nation, xccl syxvxAioi, ify cpvGst,., TOVTSGTLV aC

voovpsvai rtSQidysw sv&stcci, rovg aGTsgas vjxal xovg

uvxAovg avTKtv 7ti TtdvT&v catAcbs zv tolg

10 l6K<s yoviccg aTto^K^dvovîv agog rots KVTQOISX&V 3tQiCpOQ(bV, CCi $ (pKiVOêVKi 7tQl CC

ytccga ras &fasts xul rd&is t&v w tats 6<pttigKi$ ccvr&v

xvxAcov, di' <bv xoiovvrat, rds XLvt]6iS') ccitoxskovvrat,,

xal ovdlv dMoTQiov CCVT&V ri}s didiotrjTos rtQi rr\v

15 V7tovoov[ivr]v rcbv cpccivoiiva)v drcc&av rc5 ovn

Gviifiawsiv. rb d' cd'nov r^g dvcoîdôv

xccra dvo [idAiGTCc rds ttQcaras xal ccitAas V7tod'0i,s

v6ftui. rrjs ?&$ KLV^SCOS ccvrcbv

rbv 6[i6xVTQ6v T T& x66[iG) xal iv

20 eTtmtdcp rov did pfaov r&v fydtov voovpevov

cos ddia<pootv nabs rb xwraov avrov rv\v

otyiv, ccvrovs nrou xara[irj dpoxwrQcov r&

xvxh&v ofiftAwg V7tohr}7trov noiBiG&ai rds xi

xccrd 6[ioKvrQG)v /u-fV, ov% ccnh&s & iit

1. y'j rag. BC 3,om. AD. 3. (T] ds D. OVTOJS C. 4.

D, corr. D 2. 7. sfoi CD, comp. B. 10. fvtaffrrjs]

f cp' sndcTris D, corr. D 2. 11. itEQicpoq&v] corr. ex nsQicpegsiatv D a

.

12. ra|fig] -eis e corr. D a. t&v av-~] in lacuna minore

ins. D 2. 13. wot-] in lac. maiore ins. D 2

. dbr-] in lac. D 2.

14. oijfoV] -8v in lac. mai. D 2. KÔTQIOV] -ov in ras. 5 litt. D 2

.

16. <?'] 84 D. 17. -AUTO] wia. rd B. 20. ptGov] ptccov D.

24. KUTCC] KUXO. to C. cbr/USg] a- e corr. D 2. 8s~\ S' D.

'

itl

eitlXVXA&V. KU& XKTQCCV ya.Q TOVTCOV TG)V V

vd%6[ivov (pav^STcci TO v foots ccvrovg

avfoovs (pccivsG&cu rats otyeGiv i\^&v 8iQô^vovg TOV

dia n<5G)v rcov ^cpdicov xvxAov dpoxevTQov TK> notice) 5

10

lav T yap iitl rijg XCCT

TOV plv XXVTQOV XVXA.OV, Cp

j CtGTYlQ XlVfiTCCt. TOV ABF4B

XEVTQOV TO E xccl did^Tgov

/,TO ds Z 6r][itov ?t

r}[lTQCCV OtylV, O)6T Hal TO

A TO KJtOyfiOTCCTOV

TO

T L6CCS yfOL(fîCCS

T AB xccl rfv 4FTCCS BE Kol BZ xal FE xccl TZ,6Tai,, dioTi Tag AB xal Td 7tQi(pQias wa-

TOV icegl TO Z XWTQOV /

yQccg)oîvov xvxhov dtfAÂv- 20

7tQi(f>BQiccs dice TO farjs oviSrjs Tils vrtb BEATfj VTCO FE^J A.a66ovcc [iv yCvsG&cu T^V V7tb

BZA xciToas avTobv, piova ds Tqv vjtb FZ4[Eucl. I, 16].

KV T' Bill Tils XCCT 7tMVX&OV VJtO&6G)S VOWGWVLSV 25

1. al'kd D. vn' SHSLVCOV] vnoHeifjitvcav D. 3. %Qovoigccvrovg D. 4. CCVIGOVS] &.- supra ras. 2 litt. D. 8i,Q%6Q'cci D,corr. D 2

. 5. v.vv.'kov] nvnlov KCCL D. 7. sdv\ civ D. f'x-

KEVTQOTriTa] gx- in ras. 1 litt. D 2. vnofttosoov C. 8. bpul&s\

6- supra scr. A 4. 14. J] J -to D. 18. IGTLV D. 816x1]

supra scr. D 2. 19. do|ft] dti&i B, SO^SL supra scr. B 2

. 20.

TO] corr. ex rov D. 22. rj[\ seq. ras. 1 litt. D. 25. T'] re D.


rbv per 6[ioKvroov rc5 did (U-titov r&v Z&di&v KVK&OV

rbv ABP4 Ttfol Kvroov rb E xcci did{irQov rf)v

AET, rbv d' lye9

avrov (po6[iEvov eitfavxAov, Ecp ov

xwsfacu, 6 dtirtfo, rbv ZHK5 TtEal Kvroov rb A, cpavfobv

Kttl ovr&s avro&sv h'^roa.,

rov sjuxvxhov d^icc^&

(isvov rbv ABT4 xvxhov (bg

anb rov A Aoyov svsxa sal rb

10 B KOI rov aGreoos rbv iiti-

xvuhov, orav [lev xccra r&v Zxal yavrjrat, 6 a6rr^Q^ ddiatpo-

QWS tpuvriGErai, ra> A uevroc)

rov STiiKVKkov,

orav ds Kara

15 Kara psv rov H (psos SLTCSLV

riG&ai, KivviGiv rrjg b[iaA,ijg ry AHds rov K shaGdova O^IOLCDS rr] AKtl [isv ovv rijg roiavrrjg xar' XKvroorrjra vno-

dfl o^v^^rjK tv\v [iv A.a%far7]v KIVYIGLV Kara

20 ro aitQyeiorarov jtaQaKokov&eiv, rrjv d [lE'yLG'rrjv Kara

rb TtEQi'yfioraroV) srtsl Kal ndvrore ^ vitb AZB6rlv rijs vjtb z/ZF, jil $ rijg Kar

dvvarai tivpfkdvBW. rov

rd 7t6[iva rov ovoavov

ovxsrt,

nteiova

1. /u^v] ^ D, ftD 2

. 3. #'] seq. ras. parua A. 9. ccno]in ras. B 3

. A Aoyo-u] cdoyov C. Wxi> D. 10. B] corr.

ex a D 2. 11. Ante ptv ras. 1 litt. B. xara] &u' D. 12.

ysVrjTca] corr. ex yftvTjrat A, ytV^rat D. adiaqpd^cog] A, corr.

ex diacpoQtos B 3C 3D 3. 13. tov A KSVTQOV D. 14. xorr' D.

15. Ttliova. D, corr. D 2. 17. ^X] ^4- renouat. B 3

. 7tQi-corr. ex 7iQi(pQtia.i D. 18. o^v] om. B. yy,VTQa>-

D, corr. D 2. 19. alsl D. Gv^r]v.v D. 22. fffti D,

comp. B. 24. pttdBaai C.

MA0HMATIKHS 2TNTABE&S r'. 219

cog Aoyov svXv dab TOV A inl TO 5, eav plv 6

ovT&g v tip 7ti,xvxA.G) itQirpai r^v

rqv aito rov ajcoysiov jietccflaGiv ig ra

a7toTtei6&ai,, rovre^riv aitb rov Z cog sitl rb

H, xara rb aitoysiov TJJV ^s'y^rrjv ndgodov yivBG&ui 5

6v[ipri6Tai dia rb 7tl ra avra rov re srtixvx&ov r6rs

xal rov a6rQa xwsM&ai, sav ds r\onto rov aitoyeCov

rov adregos [isrdfladig slg ra TtQorjyov^sva rov iiti-

xvxAov yivY\rui, rovrtGnv cato rov Z &s eitl rb K^xara rb cutoysiov avKitakiv

rj skaftfarr] jtdoodog aito- 10

dia rb st<s ra svavria r^ rov

rov dtiTSQa Tors psTaxivEiG&at,.

rovrov d' ovr&g %6vrcov (p%rl$ xdxiva

,on r 7tl [iv Tcbv di66a Ttoiovêvcs

d[Kpors'()ag Tag vjtod'6tg ravrag svdeêrai 6v[i7t- 15

&g v rolg rtfgl avr&v anodô^v^ iiti d

Kal rfl avrr^ x%Qy[iVG)v dvG)[iaMa xal ptaTK)V XXl[lVG)V V7tO&6G)V d()X6l, Xal OTi Ttdvra tk

xaTQav avrCbv ditaQaMdxT&g dno-

T&V avrCbv koyov v d[KporQaig TtQis%o- 20

TovT<5ri,v orav, ovs-yjti koyov rj ftta|v T&V

XVTQO)v sjtl rijg xar' fxxwTQOTrjTa v7to&6G)g r^g re

ofa&g xal rov MXWTQOV xvxhov agog rr\v x rov

XVTQOV TOV XXVTQOV) TOVTOV #7? TOV koyOV Ttl T^g

Xar' 7tlXVxA,OV V7tO&6G)g i\X TOV XVTQOV TOV BTCi- 25

XVX&OV JtQOg T^V X TOV XVTQOV TOV CpQOVTOg aVTOV

Tl V 00G) %QOVG3 TOV XXVTQOV

2. noiziTcci B. 3. &7toyiov~] e corr. D 2. tig

\fd corr.

exel\GTcc.

A 1. 5. KKTO] -rd supra scr. D 2

. 8. efe] sni D.10. s\aG%i6Tri A- 18. aex&jfi] -ft renouat. inter duas ras. D 2

.

21.i-'zy

D. ^] mg. D 2. 23. Supra rov add. HSVTQOV

rov D 2. 24.

s'xj]] A, tî BCD. 27. ?Tt lv\ corr. ex tort, D 2.

6 aGrriQ cbg sis v

d[iTd7tTG)Tov ovra dia7CQQVrai, v roôvrcp xal 6

TOV 6[i6%VTQOv rfi otysi xvxAov

cog ig rd 7t6^va [iTaxi,vov[ivo$, 6

5 rov 7tiKvxkov t6oTa%G)$, cbg îevroi rrjs XKTCC rb KTCO-

yeiov {iTafld6G)s sis ra TtQorj'yov^vcc yiyvoiiwys.

On $ TOVr&V OVT&S V7COX^VG)V TK CCVTK TtSQl

Mccrfyav r&v vnoftfafcov (paivo^sva 6v^ri6srai^ dice,

l$Qa%G)v (podv6oîv did t Tcbv hoy&v avrcbv xai

10 [ira ravTK xccl dia r&v ^cpodvoîVG)v iv ccvroig eitl

TOV fikiov ava)[iaMcis agid'ii&v.

j TtQ&xov, on xcc& xatQav avrcbv1} ft-

diaqiOQa yCvxcci tys oâA^g KIVÔ<S TCKQCC rqv

15 t&v a6TQ(ov voeirai, orav % qpcavo^V?? didtiraGis ano

rov aitoy iov TsragrrjuoQiov dnoAappdvr], xal on 6

anb rov artoyuordrov p>%Qi rrjs Eiorjpwrig ft<?^g

nagodov %QOVO<$ psi'Cfav 0x1 TOV dnb T^S [ifaris 7tl

TO 7tQif

yLorarov. o&v 6vâCvi Kara [iv rv\v r&v

20 XXVT()G)V V7t6&6l,V t, Xal XaTCC rV\V T&V

de, orav ai aito TCOV dnoyficov avrcbv

ra 3tQor]i

yov[iVtt yivovrai^ rbv dnb ri\

TOV anb

TT

3. $LeQxsTcei, D. 4. 8'] 8t D. 5. Ante cog del. piv D 2.

g] rrjs rfj$ B. 6. yivofisvrjs D. 7. > mg. D. 8.

alt. v corr. ex Q C. 9.rs~\

corr. ex dH D 2. 10.

did] seq. ras. 1 litt. D, om. B. kpofovoi&rov] AD, -svtov

euan. B, ecpodevpevav C, scpoodsviisvav D 2. 11. rov ^Mov}

fjUctKfis D. 12. uvr&v] -co- in ras. A. 13. ofta/lffc] -?)-

e corr. A. 14. &vd>iLcdov~\ corr. ex avâliav D 2. 15.

diaGTucis] -G- del. D 2. 16. 6] ins. D 2

. 19. o^cv] corr. ex

ontQ D 2, supra scr. yg. oitfQ. GVV^KIVEL A. 22. ytWi>Tca] B,

yivovxai AC, ylyvwvTui D. 23. ytVfdât] -I- e corr. D 2.

MA0HMATIKHS STNTAEE&S r'. 221

H,s6r]g snl rrjv \Lsyi6w\v dta rb Kara rb aitoysiov

iv SKarsQa rrjv i\ct,%{&syp xdoodov

8s ryv sis ra sitopsva r&v sitixvxkcov rag aitb rov

aitoysiov Jtot,ov6av nsoLaywyag rcov atirsQwv avdnakiv

rbv ajtb rijg fieyfatrig XLV^SCSS snl rr\v iistfqv %QOVOV 5

a yivsG&ai rov anb T^g ft(?^g iitl Tqv

a rb xal svrKv&a Kara rb anoysiov rr\v

drj jto&rov 6 sKKSvrQog rov dtirsgog

o ABF4 Ttsol Ksvroov rb E Kal did^isroov rqv

^ stp* rjg si^fp^G) rb KsvrQOv rov

^(pdiaKov, rovrsGnv rb Kara rrjv

ofyiv, Kal stirK) rb Z, Kal dua

rov Z rtobg oo&ag ycoviag rift

AEF dia%&i6r]g rrjg 5Zz/ vjto- 15

%^ ra/lrfi&m 6 dtfrfiQ STcl r&v B Kal

>,Iva drjhovon reraorrj-

tyri rov A anoysiov. dsinrsov, on nobg

rotg B nal z/ Gruisioig 17 psyfarrj yivsrai diayooK ryg 20

yag ijrs EB xccl

r]E4. on

ov avsj^t] koyov i\

vitb EBZ, y&vCa TtQog rag

d oQ&dg, rovrov s%st, rbv koyov f]rov ytaoa rr^v avco-

1. TO (pr.)] supra scr. D. 2. tr\v\ r B, T* B 3. 6.

ovci\ ABC, ttdcoovcc B 3D (renouat. D 2, supra est ras.). 7.

did] corr. ex S$ B 3. &x6ysiov] -siov renouat. B 3

. 9.

nag. D. 6] punctis del. D, sed puncta eras. 12. ^codianovD. TO] om. C, ins. B 3

. 19. A] renouat. A 4.

-i- ins. A 1

,corr. ex dsiKTociov D 2

. 20. yCvErai r]

Df 22. 17] ins. D 2. 23. av\ supra scr. D 2

.

corr. ex fyei D 2. rd$~] om. D. 24. rov] supra scr. D 2

.

[ICiMcCV dittCpOOOV 7tQl<pQl,a 7tQO$ rOV 0&OV

Civr6d'v yivetcti (puvsgov, 7tidi]7tQ % p,v vytb AEBycovia rriv rv\s b^a^g xivijciscas vnotzivei

fjd vrtb AZB %v\v rr\g <jDan/o^Vt?

5 o%ri d CCVT&V fanv % vnb EBZ ycwicc [Eucl. 1,32].

j^ on, rovtov ixarfyccs &My y&via H%(QVcci, xgbg rg TOV ART4 xvxAov 7tgi-

ia 7tl rijg EZ v&iccs.

6vv6rccTG)6av yag ycoviat, ytQog rots xal K10 6y[itoi,s i]

vnb E0Z xal % vitb EKZ, KOI

&G)6(X,V fyt 4 XCcl

f]K4. 7t\ OVV

y&vov jj [i%G)r ntevQtt vnb tqv [i%ovct y&viav vito-

relvi [Eucl. I, 19], pstfav $ farw y Z rijs Zz/

[Eucl. Ill, 7,3], peftcov forai xcci % vnb 4Z yewfa

15 1% -INTO z/@Z. fay $ 6nv % vnb EJ@ vy vnb

[Eucl. 1, 5], 7tiitQ xccl % E rr] EzJ i<$nv

V\vjtb EZ.

6rlvf]z/Z rrls KZ, yLit,G)v itfxlv Keel

r\ vjtb

20 ZK4 rrls vitb Z4K' fay ds faxiv r\vnb EK

Tfj V7CO E4K, 7tl7tQ Xtti fjEK TtdklV 1% E4

fay xal XoLTCr] O.QK % VTCO E4Z, rovrfanv y vitb

EBZ, rijs VTtb EKZ 0nv

2. rpccvtQov} -o- in ras. A 1. 4. AZB~] A- in ras. 2 litt.,

-B ins. D 2, supra scr. a. Post avfo^dlov add. xii/i^coo?

in ras. 1 litt. B 3. -fijrepo^] v- add. B 3

. 6. dij] corr. ex84 D a

. 7. TtQOs] TtQos I itQOs B. 10.i] (pr.)] ij

re D. 12.

VTtb rrjv iLtcgovcc ntevQav 17 [iia)v ycovicc D. fift^cov] [tei-

cav<x C. 14. JZ~\ mut. in JZ A 4. 15. ^@Z] mut.

in &JZ A 4. tan D, scri D 2

. *%] %r\ C (ut saepe), xf\i C 3.

16. EJ TTJ E D. 18. Supra nfi&v scr. Harrow A 4. larlv]

comp. B, -v del. D 2. 19. [itigcov SGTLV (pr.)] om. D. 20.

ZKzf] ZK4 yaviu peifrv D. ZJK] ZKJ C, corr. mg. C 2.

!(mD, eGTlV*. 21.E4K~\EJKolyI). 23. JerrtD, comp.B.

MA0HMATIKHS 223

OVK ccQtt dvvatbv a.'k'ka^

via<s, need' ov

6v6rtJ6cc6d'aL yco-

^T&V 7tgbs rots B xal

(f,

on, xal17AB

TOV <X7tb rife kK%i<5rriQ KivriGs&g Ijtl xr\v 5

[isifav <5tlv T^ B FI ^t'S rtQi'Xi> tbv

O

dvtil rats to didyogov rv\q dv&iiaMas 7tQi,%ov6ai,s

7tQirpQlKl^ 7tl,dlJ7tQ V] {llv VTfO AEB yCOVlK [1%O)V

6rlv op-iHfe, tovrfativ vrjs VTtb EZB, rr\ vnb EBZ 10

BET ticcttcov t$ avrf) [Eucl. I? 29].

VXV tOV KCtl 7tl Ti}s

t^Kl TO

<3TG) 6 [JiV

r& notifies xvxkos b ABP rtfgl 15

XVtQOV TO 4 XCX.I dl(X[JiCT()OV Tr]V

A4B, b d' V T(p KVTG) 7ClJtda)

(pQOllVOS 7l' CiVTOV 7ttXVXAoS

6 E Z H 7tQl KWTQOV TO A^ Ktti

V7tOXi<5&G) K6TVIQ HUTU TO H, OTCCV 20

TttUQTrHLOQlOV CC7tt%G)V

TOV XCCTCC TO dsCO /yLOVKOI 7t&V%&G)(3ClV i]

T AH HOI 4HF. Afyco ,OTL %

(pCC7CTTCU TOV 7tlXVxA.OV' TOT yCCQ TO ItkslGTOV

didcpogov TJ\Q b{iaA,rjs Kivtfdf&s TCKQCC rr^v dvG)- 25

1. (lei^covccg C. ycoviccs avariJGaGd'ai D. 2. xat] ins. D 2.

3. ar](ji8Lois 4. TtfQicpSQSia] ~mg. D 2(nfifievov}. 4. TIEQI-

etiam in textu D. 6. sorL D, comp. B. 10. tovr-

comp. B, -v del. D 2. Post EZB del. yavtcc [leigcov

eariv dQftfjs D 2. 11. <T] ds D. -cfjs avT^e D, corr. D 2

.

17.8'~\ ds D. 21. T\TfT(XQTTl^6QLOV C. 23. fTtl^V^fOGCCV C,

corr. C 2. Y.a.1 (alt.)] %ul f) D. 25. dpalfig] corr. ex b^aUg A 4

.

pcdov. itd yao % plv opccM} ccTtb TOV unoyeiov

itQi,%Tai, vitb rfjg VTCQ EAH ycoviccg' i6oTa%8>$

o re atirriQ rov IrtfavxAov xal 6 7fiKvxA.og TOV

ART xvx&ov dia%ovTai' TO ds didyoQOv rr\g opaArig

5 xivr]6G)g TtaQK rr)v <pcavo[ivriv vxb Tr\g vnb A4Hy&vias 7tQis%Tcci,j (pccvsQov^ on xal

r\ vitQO%ri tys

VTtb EAH y&viccs ftgbg ri]v vjtb A4H, rovrfanv ^VTtb AHz/ y&vitt) rfjv (paivo^vrjv TOV a6rQo$ aitb

rov anoyeiov SwGraGiv 7tSQiB%et,. &cir aitsl vit6xi,Tcci,

10 avrrj TttaQTrjiiogfov, OQ&r} ply forcci, uai ^ vxb AH4ycovia, g)anto[ivr] de dice rovro [Eucl. Ill, 16 cor.] xal

f\AHT v&tcc rov EZH miKVKkov. % AT

^tt|v TOV A KSVTQOV XCtl

6Tiv dicicpoQcc TOV naga rriv av(x)[iaA,iciv.

15 xal xaTK TCC CCVTCCr]EH JtQi,(pQi,cc^ iJTig rtQi%t,

KCiTCC TYJV fVTCCVd'CC V7tOKi^lVrjV 7tl TOV 7tlXVxA,OV

TOV KTcb Trig A,cc%i6Tr]g Kivr]<5G)g iil xv\v

ov, [ifiZ&v i<5r\v Tr\g HZ.,

TOV anb Trig [i6r]g mvr\<5(ag Tcl rr\v

20 dvfil Tccig AT ytQig)Q^cag., 7CiJtQ) av

2. KivriGig] -r]- e corr. D 2; supra est ras. Supra EAH

ras. 1 litt. D. 5. vno (pr.)] post ras. 3 litt. D. Tfjs vno\ins. D 2

. A4H] AHzJ C, corr. mg. C 2. 7. tovreGTiv] TOV-

in ras. D 2.

TJ] om. C. 8. AHA\ corr. ex AAH B 8. 9.

MOTS fTtft] corr. ex &GTISQ D 2. 10. >rca] sari D. 12. EZH]

corr. ex EZ B. AT ago] ydq seq. ras. 2 litt. D,ayct.Q

tt D 8.

13. TttQLClp^QSLK] COri*. 6X TtCpSQSlU D 2. ^SXK^V SCpCCTCTO-

pivr\s\ supra scr. D 2. 14. iortv'] comp. B, -v del. D 2

. TOV]seq. ras. 1 litt. D. Kvcopuh'av] a -ICav inc. fol. 66 m. rec. B.

15. EH] -H in ras. D 2. tjtig] ij- corr. ex v in scrib. A.

16. KMTCC] v.a.1 ynxrd C, nut ins. D 2. 18. u&arp] peGrjv

KLVTIGIV B. %QOVOV] -v e corr. D, deinde eras. son. scrLv]

comp. ins. D a. TT)S HZ] -s H- e corr. D 2

. 19. \Ltyt6tr\v\

-yi- e corr. D 2. 20. ^cc^iaj^v BD, corr. D 2

.

MA0HMATIKHS STHTASE&2 T'. 225

AH xal dydycoîsv rr\ EZ TCQOS

rrjv AK, feat, ftcv ywovrui ijr VTtb KAH ycwicc

rfj vnb AAT [Eucl. VI, 8] xcclf}KH 7tSQi<pQia ry

AT 6ôta, rccvrrj ds rov svbg rsraarr][ioQiov [isftcov

l<5tivi\ EKH, eAK06G)v ds % ZH' OTCSQ edei, 5

on, ds xal 7tl rcov Decree [lEgog xivrfdEcov Icp KK-

rcov vjto&6EG)v v rotg I'Goig %QQVOI<S r& ccvra

yiv&iui rtdvrcc itQi rs rag 6[iccA.&g

xccl rag (pKivoybtvag xwtJGsig xal 10

sn rccg v7tQo%ag ccvr&v^ rovr-

rb Tcaoa rr\v

Evrsv&w av

156

r&vdice

ASTi'Gog ds rc5 ABT opoxsvroco, 6 EZH

rcov A xal xEvrocov xal rov E aitoyfiov f\ EAA, 20

xccl cc7to2,r](pd'Ei6r]g jtl rov 6ôxvroov rv%ov6r]g itQi-

tpQiccg T^g AB xsvroG) rc5 5, dia(3rrjîan ds r& A6 KZ 7tlXVxA.Og) XCCi 7tt

> V%&CQ f}KB A.

Eyoa(pd'\.Al

âi\ H.G- (

1. AH\ JHB.i'o- e corr. D 2

,o

2.-d- corr. ex o in scrib. C.

B 3. rf? (pr.)] se(l- ras - 1 ^*- ^xat] ware xat B. xal

<fj4. opoia] supra scr. D 8

. 4.

6[ioict xy AP D 2. 5. EKH~\ E- e corr. D, EK B. ajrep

BD, corr. D 2. 9. ytyvttui D. 11. Toure'crt?] -v del. D 2

,

TovrfffTt B. 14. KccTU[id&oL] seq. ras. 1 litt. B. 15. TOO]corr. ex rtbv D. 17. 8s] 8' BD. 18. ro5] corr. ex ro CD 2

.

20. T&V] corr. ex TOV C 3. E] E^4 C.

'

22.

Ê] %ai diacTrifiari, BD. TW (alt.)] TOO I'ffoo TOO B. 23.

D, corr. D 2.

on 6 ftev atirriQ vq? mareyas r&v

jtl rqv Z ro^v rov SXXSVTQOV xai rov 7tixvxA.ov

ndvr&s Kara rov faov %QOVOV ivejflrftetai, rovrstirw

at y iteQUpfyftai oôiai h'tiovrai, JMijfais

5 rOV XXVrQOV Xai'Y]AB TOV 6[lOXEVtQOV K

TOV sitixvxAov, 1}

de diacpOQK rijs 6ftA^^

itaga rr^v avcoîaôv noilrj (paivopwr] rov

ua& exarsgav r&v vtto&sGe&v bôia xal

10 7t&v%&GM)av *yaQ ijre Z@ xal

v\BZ nal h'n

% z/Z. iti rsrâjt^vgov rov B4&Z ai aitevavrCov

ittevQal faai eltilv uarQa xaroa, ^ i&v Z rr^

rj$ BZ rr\ z/@, rtccQaAArjA.6

/

yQa[iiiov h'tirai rb

rroa7tA,VQov. faai ccocc falv ai y y&viaL ijre vitb

15 E0Z xal ^ vitb A4B xaifjvnb ZBK [Eucl. I

; 29]'

totfr' insl itobg rots xwrooig ti<5i, xal rag vitorewo-

[ivas vn' avr&v 7COiCpOias bôiag aMrjAais yivstiftai

rr^v rs EZ rov ZKKtvrgov xal rv\v AE rov dpoxwroovnal rfy KZ rov zitiKVKkov. xar' a[i(poroas aoa rag

20 M,vtJ6i,s v r<p fa(p %g6vG) lid TO avro drmeZov rb ZV%fi'tfo'rai, 6 a6rr}Q xal rr\v avrrjv rov dia [i6G)v

r&v ^G)diG)v uvxhov 7tQi(pQiav ccTtb rov aitoyuov rr^v

AA <pavri6rat, dtfAÂvthos, k'tirai, rs aKokovftoQ xal rb

1. vcp'l B, y^. scps supra scr. B 3. 8.

rj] postea ins. D. 10.

. C.om. C. JBZ] ZB B. hi\ r)hi C. 11.

BJZ& C. 12. stciv i'occL D. SKKXEQCC] mut. in succrsQcti? D 2.

xar%] supra scr. D. 13. BZ] ZB B. A&\ A C.

i'cTccL] 'iGri corr. ex scnv D 2. Bz/Z@]ABC, Bz/@ZD.

14. ca] fTTft >tai j/aHc<;| at D. y] om. B.-fj]

fTtfl %at

Jyanal at rpftg ycovicci ij B. 15. xat (alt.)] ins. C. ZBK}-BK e corr. D 2

,ZB^T facu B. 17. yiyvsadui, D. 19. v.ara C.

20. rd (alt.)] seq. ras. 1 litt. D. 23. HGXUI p. 227, 1. nagd]supra scr. D 2

(yp.). 23. %Gtcti re] I'arat C, cocrf D 2 et suprascr. C 2

. v.a.1 TO waâ] etiam in textu D (-& renouat. D 2).

MA0HMATIKHS 2TNTABE&S T'. 221

Ttaoa TY[v avG)[iaMav didcpooov TO avrb xa& exarsgav

r&v v7Co&6G)v, itidr] t^v roiavrrjv

till \i\V Tife XCCT

VTtb rrjg vitb 4Z y&VLag, iitl de rijg

xar 7ttxvxAov VTCO rijs into 5z/Z, KOI a^rca de

TS nod vaM.a% yCvovtai dia to jtccQK

rriv Z Tfj B4.

dtfAov d\ oti xai litl TtccGcov rcbv diaGrccGewv

avra TtccQccxoAovd'tfGei, 7taQccA,A,r}A.o/

yQcc[i[iov itdvrots

[isvov tov 4ZB TstQccrttevQov xai yQacpopevov rov 10

SXX8VTQOV xvxhov vit ccvr^ rye; XCLTCC rbv

rov ddrsgos psTccflccdGa)^ orccv oC Adyot xcctf

rcjv VTto&etis&v opoioi re xal faou GvpflKivcod

on, de, xccv opoioi povov G>6iV) avidoi ds tip

ra avra ita'kiv cpaivopeva 6v^yj6sra^ tpavsgbv xal ovr&s 15

faro yaQ aGavt&s 6 plv o^ioxsvrQog r&

o ART nsgl XSVTQOV rb z/ xal did-

)xa&' r^v ajtoysioraros re xal itSQiysioraros 6

^ rr^v AAT^ 6 ds Ttsgl rb B sitixvxhos

a3t%a)v djtb rov A aitoyeiov r^v AB rv%ovtiav itsgi- 20

xal xsxwiJGd'G) b atirriQ rrjv EZ TiSQicpEQeiccv

tiav yivQ\LivY\v drj&ovon ry AB dice, rb l6o%Qoviovg

1. TO] seq. ras. D. 2. tr\v\ rr\v plv BD. 4. JZ] J-

in ras. A 4, z/ZED, z/ZD 2

. 5. vno (alt.)] addidi, om.ABCD. Ez/Z] corr. ex EZ D 2

. I'GUL] I'G- renouat. A 4.

6. yivovTUL] fLvoix av B. 8. 8'] 8s D. 10. 6>z/ZE]AC, Ez/Z BD, @z/EZ Halma. 11. vnb tccvrrjg D. 13.

Gvpficcivovoiv C. 14. fiovov] post -6- eras, i A, -6- in ras. 2

litt. B. 15. TK KVTO] TK ccv- in ras. C. 16. ysvriGsxai] GV(I-

fiiJGopev B (supra -do- ras.), noiriGo^sv D. 17. nsgi 19.

AdF~\ nag. D 2(Ksfysvov). 18. TS v.cci Trf^tyfidra-rog] om. CD.

21. xca] 6 EZ %at BD. wf\G%v> C, corr. C 2. 22. cffl

seq. ras. 1 litt. D.

15*

sivat, rag r&v xvxh&v ajtoxaraGrdGsig, xal

<3av ijrs 4BE xul r\

BZ xal $ z/Z.

on ftv ovv facet, rs sltiiv Ttdvrors rj rs vnb AAE,

ycovict notr]

vrtb ZBE, xccl on sjtl rijg z/Z sv&stccg

5 6 &6t$ig <pavri6srai) Kara

ravrrjv rqv vxo&sGw avr6- H

ds

Kiyw $', on, xal $LK

ri\<3 xccr' sxxsvrQorrjrcc, sdv

10 rs [isi,G)v sdv rs shdrr&v

YI6 sxxsvrQog rov ABP

diLOxsvrQov, rrjg rs r&v k6-

yov 6{ioi,6rr)ros povrjs vito-

xsiiisvrjg uccl rfjg r&v cato-

15 xarcc6rd<jSG)v fao%Qoviorr)ros

sitl xr\$ avrijs jtdkiv sv&siag

rijg z/Z (pccvtJGsrat, 6 atiriJQ.

ysyQacpftG) <yaQ psftcov piv, &g scpaiisv,

o H Ttsgl XSVTQOV STtl rijg AT rb X,20 6 AM Ttsol ndvrQov d^ioicsg rb N, xal

rijg rs z/MZ@ XKL rijg z/AAH sit^v&K xai

r\MN. inti <5nv, dig <%

4B agog B Z, ov-

rog ijrs K itpbg K4 xccl % MNxqbs N4 [p 219,21],

xal ycwia fji)7tb 5Zz/ ycovia rf] vnb M4N fay dia

2. TE] re BZ -AOL r) BD, corr. D 2. z/BE xca r]

BZ v.ct.1

i]\ om. B, JBE nccir] D, corr. D 2

. 3. TS] om. B. etai

BD. 13. &7COKi(jivris C, sed corr. 19. Y.KVTQQV] KSVT(O D,

vivify D 2. llaxTcov BD. 20. AM] corr. ex z/M B.

ofioicos TO] -ff TO e corr. D. IxjUq&etrifoj in -&SIG&V rursus

inc. m. 1 B fol. 68. 21. TTJS (pr.)] corr. ex tr\ A 1. Post

dAAH lac. paruam ob naturam pergameni C, ULTIEL svravza

mg. D 3. 22. sTtEi 23. MN] xng. D. 22. ineC] s 3tt D.

BZ 23. MN itQos] postea add. A 1.

rs

rb itccodUrjAov flvai, iv\v z/A rf/ BZ [Eucl. I7 29],

faoyaovid itiuv TK y rofyoovcc [Eucl. VI, 7] xal at vitb

rag avdkoyov jtAsvyas ywvivu facet,fj

re vitb B4Zxal

fjvjtb 4K xal

i]vitb AMN' jrapaAA^Aot ago,

ffalv at B4 xal K xal MN sv&elai, [Eucl. I? 28]. 5

co6rs nal ycovi'at, T]VTtb A4B xccl ^ vjtb AK xal

ilvjtb ANM teen sfaC [Eucl. I, 29]. xccl sxel itgbs

rots xwrgois efal r&v xvxA&V) onoicci, etiovrai xccl cci

iii ccvrcbv JtSQKpSQSicci, rjre AJS xal H xccl AM'

iv roj faa agcc %QOVG) ov povov 6 rs B7tCxvxko rqv 10

AB rtSQUpfysiccv xccl 6 atirriQ ryv EZ dis^^v^cc6iv^

AA xccl jtl r&v xx8vrQWV 6 aGrrjg %v\v rs H xccl

rqv AM dLshyAvftcos h'tirca,, xal iitl rijs ccvrrjs sv&sias

itdvrors r?i$ 4MZ dice rovro ^scoQ^tj^srai xccl

xccra [lev rbv STtixvxkov enl rov Z tiyiietov yiv6\ntvQS, 15

xccra ds rbv [ist&vcc fxxsvrgov iitl rov,

xarcc de

rbv B^drrova sitl rov M, xccl sjcl nccG&v r&v

d'?

ort XML, orccv fayv ytQicpQiccv 6

dtti,A.r}<pG)s cpaCvrirui dno r rov dnoyftov xccl 20

rov 3tQiyiQV) i'Gov 6rcci, xa& xccroccv &<5iv rb

itaoa rfv CCVCJ^CC^LCCV didyoQOv. iiti r ydo rfi$ xar

fxxfvrQorrjra^ ccv 'yodipcj^iEv rbv ARTA xxvroov

xvxhov 7t$l Xvrgov rb E xccl did(irQOv rr^v AEF

2. GTIV] comp. B, mut. in Ictl &QK D 3. y] A, om.

BCD. TQiywvcc] -Ly- e corr. D 2. 6. i] (pr.)] scrips!, at

ABCD. i] (alt.)] om. D. AK@] AK B, corr. ex AJK D.

7. TJ] om. D. ^(7t] comp. B, corr. ex SLGLV D 2. 8. at]

ins. D*. 9. 7J H v.ali] AM D. 11. dwJL$U;#e D, corr. D 2

.

13. a-uT?)?] supra scr. D 2. 14. Sid] 8iav C. 19. faces

itQicpQias D. 22. Int re] corr. ex sneiTtsg D 2. 24. AEF]

AETJ C.

230 KAATAIOT HTOAEMATOT

did rov A dnoysiou rr\g OIJJE&S vitoxeiiisvris id ccvrijs

xcctd to Z Gypstov xal did rov Z r^v BZ4 rv%ov<5a.v

diayayovtss rtisv%G)[iEv tds EB xal E4^ ai rs yccwo-

[isvcci, ttdgodoi i'cfcci*r xdl Kitsvawtiov 6ovtcci) rovr-

5 i^riv ijr vito AZB y&vCa rijg aitb rov

xalr\

vnb .TZz/ rn$ UTtb ro#

TO r itagd rqv dvco-

didcpogov to avtb b'tirai,

did to fayv eivai rr\v JJLEV BE10 tfl E4, rfy df VTtb EB Z y&vCav

rr] vjtb E4Z [Eucl. I; 5]* &<5rs

t<j}avr& diayoQG) rijg (pcavo^Lvr]g

-,tovtEGtiv rrjg v(p

r&v^vTtb AZBxalrZJ15 y&VlCOV 7tQl%OlLVri$ , [lEi&Vtt [lEV

rov A Kitoysiov rr^g

6ova df rr\v ditb rov F3tQicpQiaV) did rb xal ri\v /

,ova Eivcci rr\g vitb AZB, rit

20 rijg vnb FZ4 [Eucl. I, 32].

xal litl rr\g xar

rov iilv 6[i6xEvrQov

XEvroov rb ^ xccl didpErgov rrp> A4F, rov d'

ETtixvxhov rov EZH XEol xEvrgov rb A, xccl diaya-

25 yovrEg rfiv 4HBZ rwYovGav ETti&v^&uEv rdg AZ

trjv coco

rrls o^a^ijg

v vrtb AEB ycovCav

$ vjtb TE/1

av ya-xvxhov rov ABP

2. Y.uf] v.ca SiuyuyovTsg D. BZJ] corr. ex Bz/Z D. 3.

SiccyccyovTsg] om. D. 4. re\ ins. D 2. 6. VTTO] v- renouat.

B 3(propter fig.). 7. Post nccQci lac. ob naturam pergameni C.

Item ante fcrjv lin. 9. 13. TT)S 14. AZB] mg. D 2, r^g

V7tb ABZ in textu D, AZB supra scr. D 2. 16. ^KGGOV BC,

corr. C 2. 18. 7i8QL<psQiav] om. D. 19. AZB] corr. ex

ABZ D 2. 23. d'] 84 D. 25. JHBZ] corr. ex JBHZ D 2

.

MA0HMATIKHS STNTAgEfiS T'.

xal AH, 17 p&v TOV Ttaod T^V

7tQiq)Ql,a fjAB

fj

231

0Tai V7tOX[,[lVr]

TOVTStiTLV av T XaTK TO

HTI

6 dtiTriQ, xal i'Gov d dite%G)v

(pavrj6Tai, aito T TOV xaTa TO dito- 5

TOV did [l6G)V TG)V

,OTav

r\xaTa TO Z, xal dab

TOV xaTa TO TtSQiysiov, OTavft

XaTO, TO H, Ttid^7tQ 'Y] {lV dltb

TOV dnoyMov yaivoyizvri 7tQi(pOia 10

3tQid%Tai vitb Tfjg V7CO 4ZA y&-

Trjg T oftaAij^ xivrJ6G)s xal TOV

jcaod TV\V dvo)[iaA,iav diayoQOV r\

dab TOV itQifyiov (paivo^vri 7t$i%Tai, vitb Tijs 15

ZHA y&vtas' l'6rj ydo i<5tiv xal avTrj Tfj T drtb

TOV TCSQiytCov 6ftaA?J xivr^6i, xal TK> jtaod T^V dva)-

yiakCav diaq)6oG)' l'6r]d i6xiv xal

j]VTtb

ytnvia TTJ vitb ZHA [Eucl. I7 5] did TO xal Tqv

r AH i6r\v ivai. co6T xal VTv&v Ttu'kiv 6vv- 20

dyBG&au, OTL TO* avTKt diacpooc)) TOVTB&TIV TTJ vjtb A4Hy&via, [iM&v piv fanv

fj nobs T& ditoyuG)

Tijs cpai,vo[ivr]S) TOVTBGTW ^ V7fo EAZ ycovia

v D, 2. TtSQicpEQfia i]}corr. ex

C 2D. 7] (alt.)] ins. D 2. 6. tf^tmW] corr. ex Grjusiov C 2

.

15. <^] d' D. 16. VTCO] om. C. SGTIV] comp. B, -v del. D 2.

17. TOJ] corr. ex to C 2. 19. TO] om. B. 21. TOVT&TTH;]

comp. B, -v del. D 2. AJH] AJB D. 23.

p. 232, 1. ovoris] supra scr. D 2.

AZzI] AZIZ23. rovTEGTLv] r D 2

. 24.

rijs avrr^q ovGyg, rovrfanvrj

vitb HA z/

rijs vjtb AHZ [Eucl. I; 32]' 07Co

ft'. lisp! rqs rov Ât'ov (pccivo[ivrjs

5 Tovrcov drj ovros itQoexrd'i[iVG)v

xccl rijv jteol rov ijfaov (paivo^svr]v avopaMav svsxev

rov [iiKV re swat uccl rbv aito rijjg Aa%i6rr]s M,vij0G)$

7tl xr\v [i6r]v %$6vov îôvcc TCOISLV 7tKvroT rov aitb

rrjg [i6r]S && f^v p&ffavtp' xccl rovro yao10 ov vofaxonv rotg <pai,vo{jivois' dvva,6&ca [ilv xal

Sia ri}s xar7

3tixvxAov [iwroi,, orav Kara r^v aitoy

ccvrov HQi(pQiav ^ rov Âtov [ird(lcc<3i,s lg ra

rtaoyyoviifvcc ytvyrai,, vô-ycoroov (f av

15 cc(p&rlvca rr} xccr xxvraorr]ra V7to&6

over] xal vjtb [nag) ovyl d vnb dvo KLVijtifcoV) 6vv-

roivvv rov rbv koyov rfjs 3tol rbv

xxvra6rr]ros VQiv, rovrstfnv rCva.

20 Aoyov k'%i r\ iira%v rCbv uwrocov rov rs xxvroov

xccl rov Kara, rr^v oifriv xzvraov rov dia p^cw r&v

tfpdi&v xvuAov nobs vnv &K rov Ktvrgov rov Mxevraov,xccl hi, xara notov [Jidhidra r^r^La. rov dia [i8<5a)v r&v

xvxhov rb cc7to'yi,6rar6v itinv rov XKvraov

1. TTJS uvrfis ovorjs] etiam in textu D. tovxicxi D. 2.

D, corr. D 2. 4. *'] C, om. ABD. 5. ^^vno^nrôv D.

9. cvfupcovov 6V] corr. ex cvfirpatvov D 2. 12. xara] f)

a. D, rj add. B 3. vr\v\ corr. ex TO B 3

. 13. 17] om. D.14. 8' KV fVj] corr. ex av D 2

. 19. tovtEGTiv] comp. B, -v

del. D 2. 20. T(] om. C. 21. TOV (alt.)] -o- corr. ex co in

scrib. D. 22. KVV.I.OV] -v e corr. D 2. TOV (pr.)] supra scr. D.

MA0HMATIKHS ZTNTASE&2 T'. 233

,dsdeiurcti pw ravrcc xccl rc5 'l7tTtdQ%(p

, rbv lv cutb

rv

9/3/.

/

,diCC [IOVG)V tOVTCOV tiibv Cp(Xl,VO[lVG)V CCTCQ- 5

ri]v {lev îsrcc^v TK>V ttQoeiQrjiiev&v XSVTQCOV

sv&siccv ixo<3toT8TccQTov fyyiGTci ftfôg ovGccv ri\g ex

iov XSVTQOV rov sxKSvrQov, TO d' aitoysuov ccvrov

rrjg &Qivij$ rooitijg rpâtftv xd/.' $y-

oi&v 6rlv 6 dice [L6cov tcbv fcaditov KVKko$ r%. 10

xal rovg

tovg avrovs iyyittu uai vvv ovrccg VQfoxo[iv,

dia rovro xai, QTI Tqv avrriv ad ftztiiv b

rov v\Uov Kvukos GvvrriQti ytQog ra rgoitiKa xal far}- 15

vtQov t\\Liv yCvzG&ai. VXv d rov

3tccQccA,A.i[i[ivov ii>oa tov roiovrov roitoV)

rb &O)Qr]iicC) 3toirj6o[id'tt xal avrol rr^v rcbv

lizv&v del&v &s fal MXWTQOV xvxhov %Qrj6d[ivoi, 20

rots ccvrots (pcavo^voi^ rovr6riv, a$ scpa^sv^ ro3 rbv

lv dnb Kivf farfQiac; pfyQi &QLviis Tôjr^g %oovov'

jrbv d' djtb &Qivi\g rQOTt^g

Qiccs 9j3^. xccl yag diet rcbv

vq? rjii&v xara rb v%y' frog 25

1. (TTjftftcov C. i7t<x()%(p A. [ista] (Jifccc na.GT}<s D, na.Gj]g

add. B 3. 3. rov 5.

/_'] mg. D 2. 5. tinodeinvvet, B, ccno-

dsiv/if-i C. 11. SB] seq. ras. 2 litt. A. 16. yevso&ca D.

18. ^nersQcov A. icptodsvofisvov B; sfpoSevîvaiv C, co corr.

in o; scpoSfviisvov D, corr. D 2. 23. ^SQKS] -i- eras. C. 24.

ditb ris 'Afa%dvdov T&VTig iGiSi&v rs xal

GV[l<pG)VOV TO T&V dl,a(3TCC0G)V Jthijd'Og T&V

VQi<5XQILV, 7tidlJ7tQ, Ci)$ (pCC[lV [p. 204, 10;

2057 2; 206,2], ^ plv iisToitoQiv^ faqpfQia yzyovsv rr\ #'

5 TOV 'A&i>Q [iTd Trjv J]Mov dvccTohrjv,

5' TOV Tlaytov psTa Tr\v peffrjiiflQfaV) cog

de

ia TOV GOQI {iTa TO

XCCi TCCVTrjV [lV Tr^V dlCC6TCC(Jl,V, TOVTEtiTlV TrjV KTtO

10 ccQi,vijs faypfQias 7tl TJJV

v (id/_\ tufc&fafat&f&Ki d9

is TJJV CCTCO Tijg &Qivijg7tl Trjv Qijg ^TOTtcoQivr^v far][iQiav Tag koi-

sig TOV viav6Lov %QOVOV ypfyag fyyuGTa gftL'

etiTG) drj 6 did [i6cw T&V t,(pdiG)v xvxhog 6 ABF415 nsgl xwTQOv TO E, xccl ditfx&coGccv Iv ai>T& dvo 8id-

ttgbg oo&dg d^iq^Kig did TMV TQOTtM&v uccl

r][ita)v ij TS AT xali\B^J

',vitOKSiG&o

de TO [iV A IdQLvbv <5r][itov TO df B frfQwoVj xccl

id ^ilg dxohov&cng.

20 OTl {lV OVV TO %VTQOV TOV XXVTQOVTG)V EA KCil EB

TOV TO ply ABFTOV ftfLtdovs TOV IviavtiCov XQOVOV Keel did

TOVTO [li&V dltolc(,^dvLV TOV XXVTQOV25 KVXliOV, TO dl AB TTCCQTrjUOQiOV XCCi KVTO

1. i6r}[iQL(bv] D 2, l6Jip,SQL&v D, iGrniSQivfjq ABC. 4. yi-

yovs ry D, -f T- renouat. D 2. 7. r$] rf) AD, rf]i B et C

(77

e corr.). 8. ia'] i- e corr. D 2. iiBGogi B. 11.

/_']corr.

ex s D 2. &EQwfjs] &- corr. ex a in scrib. C. 16. a/UUj-

lcu<S~] ycoviag tiiltfiais V.KI D. 18. or](iiov~] -ov e corr. D 2.

'

20. yitvrQov} v.- in ras. A. 21. EA] -A renouat. D 2. 23.

om. D. 24. zptfpti] nvukov rpfjiiu D. 25. 7ilelovci\rs D.

MA0HMATIKHS 2TNTAEE&S 235

xal

rov xxevroov XKoa TO BF rEraarypoQiov. rovrov ds

ovr&s %ovros vjtoxffa&G) TO Z Grjpetov xwrgov rov

XXVTQOV) XCCi $1-

[iv fjdi 5

rcbv

rov

f) EZH,KsvroG) ds r& Z 10

9-co 6

rov r\Uov xv-

xlos 6 KAM, 15

xal dta rov Z

AT $ N&O, rfj ds B4 % 77P27,

xai Ti riffi&Gccv xd&sroi, ccjtb pey rov & iitl xr\v

N80 Ji TT, fab $ rov K 7tl r^v IIPZfjK&X. 20

roCvvv 6 ijfao$ rov @KAM nvxhov dficck&s disg-

{18V &K 7tQKpQl,CCV diCC7fOOVrCCi V

dl KArcclg 9d'/.

oicov 6rlv 6 xvxhog r, iv d rats ^$Ll poioas 25

?r ccv rb ilv &KA

3. TO] corr. ex rrj D 2. 18. N&O] corr. ex N8 6 C 2

,

~O e corr. D 2. 20. NSO] corr. ex TVS? 6 C 2

. K] e corr.

D 2seq. ras. 1 litt. K$X] K- e corr. D 2

. 21. &KAM]-A- supra scr. A, &- e corr. D 2

. 22. K\ corr. ex K& D 2.

23. xr\v /_'] mg. A 1. 25. Iv] -v e corr. D 2

. /_'] renouat.D 2

. 26. Supra Tec scr. F D.

&vvayL(p6tEQd ds to re N xccl TO AO tcbv

psta to NTIO fywfafaw noia&v d jc, ^ ds di7tA.fi

[Eucl. Ill, 3] XSQUpSQSlCC 7% NT]

NT tC)V aVt&V

d x. &6t teal ^ {ilv vn' avt^v sv&siccfj

T toiovt&v

5 6tai d A/3 lyyiGta, otcov stitiv ^ tov sxxsvtoov did-

f]ds iîi^sici ccvti]S i] T, tovttGtw 17

7g. ndhv snsl to 0NIIKokov iioiQ&v e&tiv yy #

?etitiv ds xal to N

fi ~i,to ds Nil tstccQtrjiioQiov [IOLQ&V 9, xal

10 ply stitai UK itSQiysQeia poiQ&v o v#, ^ ds

avtijs ^ KTIX xsQiysQsicc poiQ&v cc ~vy. &6te xccl 17

fti/ vjt avtr^v sv&sta ^ K<&X toiovt&v sGtai, ^ dy

OiCOV Ititlvr\

tOV SXXSVtQOV dlK[ltQOS 103C 9 ^ ^' l}ft^-

îoj avtijs f} jRC0, tovtstitiv % Z&, t^îdtov aft.

15 t&v d* avt&v sdzfyd-rj xalfj E& sv&sta ft 7g. xal

sjtsl tK an' avt&v Gvvts&s'vtcc Jtoist to <XTtb ti]S EZ,

[Eucl. I? 47], fatal, xal avtri [irjxsi, toiovt&v ft K&L'

syyiGta, ot&v stitlv ^ sx tov xsvtaov tov sxxsvtoov %.

i]aoK ex tov xevtoov tov sxxsvtQov xvxAov tstQccxcusi-

20 xo6aitha6iG)v Ititlv syy^ta tri$ [ista^v t&v xsvtacov

avtov ts xal tov

1. cvnyorsQcc ^C^corr.C 2

. N~] @N D. AO] in

ras. A 4. 2. ftf-ra ro] BC et post ras. 2 litt. D, mut. in r&v

stg TO A 4. NIIO] seq. ras. 2 litt. D. x] A, x ncti WKTE-

QOV (isv ago, avrav f'crcci, poiQ&v $ T BCD. 3. 7tQi<pSQi,ci]corr. ex nsQicptQiu A 1

. 4. x] ins. C 2. T] TT D. _7.

Ante ^ ras. 1 litt. D.&NUK D. 8. olov] om. B. 9y]

-y in ras. A. tGxiv~\ comp. B, /j supra scr. D 2,om. D. tro]

TO ptv D. 9. z] corr. ex y A. jito^wv] om. D. 10.

&TCU] ^rtv C. JT.S:] XH D. o] 6 BD. i] --9- euan. D.11. 7CQicpQiu 12. #$JT) mg. D. 12. fi^v] om. D.

K$X] K&X TCfQKptQSLa (comp.) D. tf] jitf AC, ut sae-

pius. 13. *'] ds D. 14. Z#] SZ D."

17. Post ufaydel. tpfiiLu D 2

. 18. TOV (pr.)] supra scr. D 2. 20. KSVTQCOV]

comp. supra scr. D 2, HSVTQCOV i] B.

MA0HMATIKHS ZTNTASE3S r'. 237

itu, O'L&V f}EZ zdeiffiri /3 x&l_\ roiovrov

xal $ Z& vd"la a /3, xal olcov aga 6rlvfjEZ

neCvovGa px, roiovrov k'tirai xal

ftg k'yyuSra) r\d

3 fV avriis 7tQi(pQi,a rov

xvxhov itsgl rb EZS oa&oycbviov roiovrov 5

oi&v <5rlv 6 KVX&OS r%' xalfj

vitb ZE&CCQCC y&vtcc., oi&v H,BV sltiw ai dvo dg&al rj, roiovr&v

6raL/Lt-9

1

,o'i&v ds ai d doftal T|, roiovrcov xd A.

BH itQi(peQELa, tyv TtQoriytfrai rb Kara rb H ait6yi,ov 10

rov B &QLVOV rooTCixov 6r][Liov, poiQGbv i^nv xd A.

Aotjrov df, itidfj rb [iv O2 rsragrrHioQiov xal rb

21N xdroov [loioav i<5xiv 9,

[iv OA 7tQi(pOi,cc avrtf r xccl

[loio&v /3 I, r\d MS ILOIQ&V o v^1

,xccl ^ [iv 15

AM 7tQt(pOi,ci 6rai ILQIQGOV ytg ^vcc, 07$ M lioi-

o&v nrj {ifr. AAa rag [iv ytg 'vu poiQas 6[iaA,&s 6

^iSQ%srai, v fifisQCUrS nri xal17 ', rag $ ^ ^

iv Yi\Ligtti 9 xal 77' syyitira' &6r xal rr\v [ivT/l 3toi,(psai,aV) ijns 6rlv CCTCO [ifron&Qivijs farj- 20

2. T]v\ corr. ex rj C 2. 3. TOVOVTOOV D. Post BGtca add.

%l f ri>L' C, del. C 2. *uC] supra scr. C\_ Z8] ZZ D.

5. EZE] ZEE corr. ex ZS D. 6. rf] r- e corr. C.

ZES] ZE- in ras. D 2. 7.

6g&a A. 8. <?] post ras. 1

litt. D. 9. TO -Aivrgov D, corr. D 2. fab] -v del. D 2

,

comp. B. 10. 7iEQi(pf

Qici A. yv] corr. ex j\ C 2. 11. SGXIV}

-v del. D 2, comp. B. 13. SHKTSQOV] -o- mut. in co C 2

,sed

rursus corr. t<?ni/] icn D, comp. B. 14. rs\ in ras. D 2.

0N] corr. ex ON D 3. 15. o] ovSsv D. 16. [IOIQ&V (alt.)] ^

supra scr. A 1. 18. tftt'^STca] corr. ex SQ%STKI D 2

. 19.j\'~\

ob D, oydoaj D 3.

xal yf

, TYJV ds 4A, iJTig

TO, 7COO-

10

6 r^hog v

aitb

fjHSQCUS 9 Kttf\ ytfttt* *w SVQrjTKl,

xi[iva 6v[i(pG)va)S tots vitb TOVf

l7titda%ov

5 KKTCC ravras ovv rag

TQOV, itoaov 6rlv rb

itaga rr\v

xfai 6r][iioi,$

OVTOV 6V[l/5lJ6Tai,.

StiVCD dfj MCVTQOgABT rtQi ndvrQOv TO

dia rov A fatoystov

(p fy 6T& TO XV-

TQOV TOV fydiaxov TO Ej xal

15 agog OQ&ac; y&vtag xr\ ATf) EB, xal

X TOV XVTQOV ,TOiOVTCOV 6rlv

xwTQ&v /3A xaTa TOP TTQaxaiixo6a7tA.a6tova

xal OICDV aga i6t\vr\B^d vrtOTtvov6a ^x^ TOLOVTWV

k'tiTcci, xalr\ pkv z/E v&la

, YJd' ji avTijs rtQi,(pQi,a

TOIOVT&V d jiZg syyiffta^ oi&v 6rlv 6 7tQl TO B/1E OQ&O-

ycbviov xvxhos T%. cc)6T xal % vno z/BE ycovia, iJTig

TO 7ikl<5TOv didyoQOV Tijs avco^iaUa^ ofay pivai dvo og&al T%, TOIOVTCOV 6Tau d

jilg,QIK>V d'

1. 7j'] 7j A, rj D. ^rig lettv\ -s Iff- et -tv in ras. A 1.

2. ano ^90-] cc- in ras., cetera in mg. A 1. rr\v\ om. D.

3. TJ'] r\' AC. 4. lyo[i8voi$] 7iL^^oyi6^VOisD, 5. KQO-

TQOV~] ngoTSQcov A, TtQmToov D. 6. Ivtt D, comp. B. 8. xLai\

seq. ras. 1 litt. A. rotovtrov] corr. ex roiovro D 2. 13.

6Tca] fart D. 14. xat] &nb rov E xat D, %ai ccnb rov ED 2.

_ 16. sni&vx&co BC, corr. B 2C 2. BJ~\ corr. ex BA C 2

. 18.

f] post ras. 1 litt. B. 19. BJ] corr. ex BA A. 20. d']ds D. 24. <T] 8e D.

T8)V

20

MA0HMATIKHZ S r'. 239

at d oo&al T|, roiovrov/3 xy. r&v & avrcbv

xal i\ yLV VTCQ BE4 oo&r} y&via 9, r\ds far]

dvtilv vjtb B4A drjAovon 9/3 l&y. xal Tt\ nobg rolg

xvrooig sfalv rj [isv vno B^dA rov xxsvroov^ f}ds

V7tb BE/I rov tydiaxov, %o[iv rb psv rtfalGrov did- 5

tpooov rov itaod ri]v dvcopaMav poiQcbv /3 scy, rcov ds

ttQi(pQiGbv, TCQOS alg rovro yivfrai,^ rqv îhv rov x-

xvrgov xal 6[iaA.r}v IJLOIQ&V 9/3 ~wy dnb rov dTtoyfiov,

rr^v ds rov tydiaxov xal dvcoîaôv (paivoyitvriv rCbv

rov rttaorriiioatov, xa&ditso xal 7tQorQov dttduâiisv, 10

lioia&v 9. (pavsQbv d' sx r&v TtQOSfpcodfv^vcov^ onxard rb dvnxsC^svov rîijîa ij {ihv (pawo[ivr]

ndoodog xal rb Ttfaitirov didcpooov ri\

xard rdg 60 [totoag., f\d? bâ^ri xal xard rov

sxxsvroov xard rdg &, Af. 15

Lva ds xal did r&v

csg cpayiV) rdg avrdg it-

di,G)[iv tivvayoiisvag xal 7tl

xard rov snixvxhov

orav oi avrol Aoyoi, xafr' ov siotf- 20

Xa[lV TQOTtOV) 7CQl%G)Vrai) S0TG)

b [isv bpoxwraog re* did [ifa&v

rcbv t,G)di(Dv xvxAog b ABT Jtol

xsvrgov rb z/ xal did{iroov rr)v A^tP^ b d' iiti-

xvxôg b EZH rtol xvroov rb A^ xal ^froo ditb rov 25

1. icn D, comp. B. 3. 9|3] ^ ^9(3D. 8. p

corr. ex ILOLQO.V D. 11. cpavegbv d' fx] in ras. B 2.

[itvCOV C. OTi] OTIY.UL D. 12. T[Lfj[l<x] r)^ltlVV,^LOV D. 14. KCCtO.

n,oiQcts~] et in textu in ras. et renouat. D 2(ao /not'âg) et supra

scr. D 3. <T] ds D.

^

19. wta TOV] KKT' D. 21. nQii%ovxai CD,corr. D. 22. 6 jLttV] om. D. Sid 23. gcodicov] wdtaxcoi D.

24.T1J1/] corr. ex TOV C 2. a*] 6s D. 25. EZH] E- corr. ex N

uel H A 4.

TOV 7tixvx&ov ev&Sicc 4ZB, xal iit-

AZ. yivBtai dq aticcvTag [p. 219, 21] sv

T<p AJZ TTQKXKiLXO<5aTika<5CG)v rjAd

rr}S AZ, wGre xai, otW ItixlvTIAz/ {worsivovea ^%,

5 TOLOVT&V itttkiv xal rijv psr AZ yCve6&ai ~s, r^v ds

7t avrijs 7tSQi(pQiotv roiovrcov djitg, oi&v fGrlv 6

Ttsgl TO AdZ QQ&oy&viov ygcccponsvos xvxhos ?>' xal

i\vitb AdZ CCQCC y&vitt) oi&v psr efaw at dvo OQ&al

T%, TOLOVTC3V tGXttl d jdg, Ol&V $ CCi d OQ&CCi T%, TOl-

10 ovrov /3 ~uy. TO [isv rtfalGrov CCQK SidyoQov Tijg avco-

TOVTEGTW f AB rtSicssia xal

15 Tils

7ti7tQ fab

OlQ&V 9, ^

EAZ ya)vcc,

titto AZdCCA.'tj, 7tQV itdkiv 9/3

VTtO

20

EvXv ds TOV xai Tag XKTK {iQog avcoîdôvg

xd<5TOT

ZCp' fXCCTSQOCg TG)V V lJtO&<3G)V,

CCV [U,ttg T&V X-

XCCi T&<

1. 7t&v%a) C. 13. snfasQ A, corr. A 1. AZ/J] corr.

ex AJZ D 2. 14. 8s (alt.)] om. B. 15. vno] D, om. ABC.

EAZ] D, corr. ex EZ A, Ez/Z BC, corr. C 2. 9^" xy] in

ras. B 2. 16. f' mg. C, om. ABD. TJLKTU e corr. B 2

. . . .,

. . .,

supra scr. D 2. rr/g ccvcofLaMas] T&V CCVCO^KÎ&V nccvovoTtouag D,

corr. D 2(79.), r&v ccvoDîd^cov uavovoTtouas e corr. B 2

, y^. nsglT&V HUTU USQOS rfjs avmiLKlias B 2

. 17. STUGntyecog] ABC,T&V HUTUom. D. 19e corr. D 2

.

B 2. 17

-si- e corr. D 2. 20.

MA0HMATIKH2 STNTASEQS T'. 241

S6TG) drj 7CQC3TOV [ISV 6[lOXVTQOg T03

6 ABF TtSQl XSVTQOV TO z/, 6 d' sxxsvTQog o

EZH 1tQl XSVTQOV TO @, ^ &dl? <X[l(pOTSQG)V TG)V XSVTQOV XCCi

TOV E ccitoysiov dt,d{isTQog % 5

EA4H, xal aTtoArjcp&siGrjg Tfjg

EZ TtSQicpSQstag STCS^SV^CD^CCV ij

TtQ&TOV % EZ 7tQl,(pSQSia [IOIQOOV

ovtia Aoyov svsxsv A, xal sxfH.r]- 10

rjg Z xa&STog sit

TOV z/ ^ z/JiT.

TOIVVV f)EZ 3tQLCpQSl,CC VTtOXSiTCCt, {lOlQ&V A, XCCi

VTtb EZ CCQCC y&vitt) TOVTSGTIV y vjtb 4K^OiCDV [ISV 1<5W Oil d OQ&al T%, TOLOVTCOV 6T\V A, OiG)V 15

ds ai dvo oQ&al T%, TOIOVTCOV . xcclr\ ^LSV STtl Tr^g

CCQCC rtSQlCpEQSLCC TOiOVTOV 6T\Vjj,

OIG)V 6 7CQi TO

oQ&oy&viov xvxAog rj, ^ ds sitl Tijg K T&V

sig TO fuiixvxkiov [Eucl. Ill, 31] ^x. xccl ecu

VTt CCVTCCg CCQCC V&EtCCl, S00VTCCI,'Y] [ISV AK TOLOVTOV 20

f, oTov <5T\vi\

z/@ v7COTLvov6cc ^3c, ^ ds K T&v

CCVTG3V QV VS' 030TS XCCL ol'cOV S0Tlv Yi LiV ^

ft A, fjds Z X TOV XSVTQOV |, TOIOVT&V XCcl

fj

6Tcci K Ti, % ds K T&V CCVTOJV ft I, rj ds KZ2. ABT] ABT4 B. 6. EA4H~\ EA&J D. 7. EZ]

corr. ex ES D 2. sn^sv^coGav BC, corr. B 2 C 2

. y] at D.

8.rj]

om. D. 13. EZ] corr. ex EA D 2. 14. vno (pr.)

-7} (alt.)] mg. C 2

. EZ JK] mg. A^. r] (alt.)] ins. D 2,

supra scr./

D. 15. text D, comp. B. I] D, in ras.

A 4B 3 C 2. \1.^K\ in ras. A4

. 18. K] K B. 20. vn}V7t6 D. 21. ioxlv

j]\ corr. ex. IGTL D 2. 22. ^y vs] in ras. D.

23. I] in ras. A4. 24. K] K D. X0Z] corr. ex KZ D 2

-

oA?? /31. xctl sjcsl ra ait avr&v 6vvr&vra

rb cbro rf}s Zz/ [Eucl. I7 47], <5rat, ncti

j]Zz/ vito-

xEivovtia rotovrcov/3

la fyyitira. nal otav CXQCC 6rlv

fjZz/ ptt, roiovr&v 6rcci xal % [lev AK sv&sicc

/3 x>5

r\d' en? avrilg ttSQicpsQeicc xoiovt&v

/3 t^, oi&v 6rlv

6 itsQi rb Z4K OQ&o'ycoviov xvxhos T%' coGrs Kalfj

4ZK ycovfa) OLCOV \iiv efaiv cci dvo ogfrctl T^6tlv

/3 wy, otcov ds ai d opftal r|, roiovrcov

a ft. rotiovrav aga stirlv rb TCCCQK rfjv

10 rors didyoQOv. r&v dy

ccvr&v i\v ^ ^#6 E&Z&' xal Aowr?) [Eucl. I

7 32] CCQCC r\vnb A^JB

r\AB rov ^cpdiccxov Tt

on de, nav aMrj rig r&v yovi&v do&i], xccl ai

15 Aoirtccl do&tjtiovrcci,, cpavegbv avro&sv s'^rai xa&srov

u%ftei6ri sitl rtfs avrils xawygaipfis ^o v & 7tl

rfjv Zz/ rrls &A. Mv re yap rqv AB rov

do{ivr]V) rovr6nv rr\v V

rovro <5rai xccl 6 ir\ z/

20 A Ao>og ddopvos [Eucl. Dat. 40]. ddo[isvov de

Kul rov rrls <<4 nobs Z tofhttferat xal 6 TTJS @ZA [Eucl. Dat. 8], dia rovro 81 flo^v dfdo-

rijv r vito ZA y&viav [Eucl. Dat. 43], rovr-

rb TtaoK rr^v avco^ia^Lccv diKfpOQOV, ncd rqv vjtb

2. 4'orat vno-] supra scr. D 2(vno- etiam in textu D).

3. i'yyiGTa] i'yyiOTK ol'cov i]dK r\v a Ts D. 4. ?; (pr.)] bis B.

QK r)ZJ D. 6. 6 TfEQi] corr. ex OTCSQ C 2

. Zz/^] 4ZK D.

8. TOIOVZCOV T|] supra scr. D 2. SGTL D 2

, comp. B. at]in ras. A 4

. 9. sari'v] -v del. D 2, comp. B. 11. ?]] post

ras. 1 litt. D. vnb AJB~] corr. ex AB D. 17. 0A] -A e

corr. A 4,

<9z/ B. idv\ &v D. 18. TOVTBGTI, D, conip. B.

19. 4A\ FJA B, B4A B 3. Ante 8ia del. dtdo^vog

psv D 2. 21. z/6>] yl@ e corr. A 4

. 22. fo'] corr. ex ^' D 2.

MA0HMATIKH2 SXNTAEE&Z r'. 243

jrovr6riv rrjv EZ rov xxvroov itQiq)aiav.

av rs rb Jtaga TYJV avoîaîav didyooov vito&coiis&a

dedopsvov, rovr6nv r^v VTtb

ycoviav, ttvajtakiv ra avra

dsdoîsvov [tv dice

rovro rov rijs &Z nobs A k6-

yov [Eucl. Dat. 40],

cd rov rr

xa rvrtjg z/@ 7tobg A Adyov [Eucl. 10

Dat. 8], dfdoe&ai, d dia rovro

xal r^v vxb 4A y&vi'av [Eucl.

Dat. 43], rovr6nv rrjv AB rov ,q)diaxov 7tQicpQiaV)xal rriv vnb EZ [Eucl. I

7 32], rovrtenv rrjv EZrOV XXVrQOV 7tOl(p0iaV. 15

3tdA.iv <5rG) b [iv b[i6xvraog rc5 dia n&covb ABT 7Col xvroov rb z/ xal did^roov rrjv

b dl xara rov avrbv 2,6yov faiXvxAos b EZH& ital

Xvroov rb A, xal cbroA^gp'frffctf^g r^g EZ 7Coicp0iasr ZB/1 xal ^ ZA' vnoxsiG&G) ds 20

fjEZ 7tQicpOia r&v avr&v [ioi,Q(bv A" xal

aito rov Z xdfarog iitl xr\v AE i] KZ.7tfl

fjEZ itQicpQia {lOiowv 6nv A, ft'iy

av xal

i\ iiev vnb EAZ ycovia^ oi&v \iiv i<3iv ai d da&al

dj, roiovrcov A, otW d ai ^ oo&al T|, roiovrcov 25

xalr\ {ilv 7tl rrjg ZK rtOig)Qia roiovrov 6rlv

1. TOVT&6TI D, comp. B. 6. Z] Z D. 8. 8s] 8" D.

Z] Z D. 11. 8s Sia] -s 8- e corr. A.^

12. rtjv] x^vrs D. 13. rovrsGTi D, 'comp. B. 14. TOVTSGTL D, comp. B.

16. SLU ps'euv'] faSicwai D. 18. EZH] corr. ex ZHD 2

. 21.TJ] supra scr. dX 22. AE] A D. KZ] ZK D.

23. EZ] ZE D. sett D, comp. B.

16*

I, oicov 6 rtQi TO AZK oo&o'ycbviov xvxhos T, 17d'

7cl Trig ^K rc v hoirtcov is TO rnnxvxA,iov [Eucl.

Ill, 31] ~QK.Kcd

CCi_V7t CCVTCCS UQCC V&iCCi 60VTCCi<Y\

[lV ZK TOiOVTCOVI",

Of

lCOV

5 6TiV r\ AZ diK[lTQOS ^>%,^

j]$E KA T&v CCVTCOV ^vy

V' &6T XCCi, OiCOV <5T\Vfj

ILV AZ V7tOTiVOV(5CCft A,

07$ A4 X TOV X8VTQOV

10 5? TOIOVTCOV 6TCCi Kttlfj

jlV ZK V&EiCC CC ij ^ 6s

KA TCOV CCVTCOVft I, fj

d

TK ait avT&v 6vvT&evTa

15 7fOii TO CCTtO TY\ Z B Z/

[Eucl. I, 47], C)Tcci xal %

Zz/ {lljxi TOiOVTCOV |/3 la,

oicovTIZK i\v cc T. xccl oicov CCQOC 6Tiv ^ z/Z vno-

TiVOV0CC ^JC, TOiOVTCOV fCjTCCi KCCi7] [lV ZK V&iCt

ft

20 5^5 ^ $* 71 CCVTrlS 7tQifpQiK TOiOVTCOVft 1^, o'iCOV

6 7tOi TO 4ZK OQ&OyCOViOV XVX&OS T* CO(5T KCtl i\

vjtb Z^/K ycovicC) oicov ftfV ffaiv at dvo ooftccl T|,

TOiOVTCOV 6TiVft 1/tj,

OiCOV d' CCi d OQd'Ccl T, TOiOVTCOV

CC &. T060VTCOV CCQCC C)TiV ItttliV TO TtCCQCC TT}V KVCO-

25 {icchiccv dittcpogov T^S -AH 7tpicpOiccs> tcov d' CCVTCOV

1. d'] A, j$eBCD.

S._Ji] D, in ras. B 3,S A, corr. ex

^ C 2. 13. |p^ 1] corr. ex f seq. ras. 1 litt. D 2

. 14. <rw-

Ti&svxct D, corr. D a. 15. TO] TOV BC, corr. C 2

. ZBz/]z7Z D. 17. Z//] ^Z D. 18. -^v 5] corr. ex rj va C 2D 2

,

a in ras. A 4. ^Z] Zz/ D. 21. 6] ot

rC. ^] ins. D 2

.

23. e'crt D, comp. B. d'] ds D. 24. ZOCOVTOV D. fart D,

comp. B.

MA0HMATIKHS STNTASE&S r'.

i]v xal % vxb EAZ ycsma A*

fjvitb AZ^d y&viK, TOVTSGTLV

KOV ltQl,(p0l,CC) ILOIQ

litl Tils xxVTQOTrjTOS

ds Kal Hv&dde, xav

6ovrcci, xal cci homed

245

[Eucl. I, 32] 'dga

TOV tcodia-

do&rj

TovT6Tiv

$$0- 5

7tl TijS

ditb TOV A 7tl Trjv z/Z Tijs A A.

av T yao xdfav rrpt

TOV ^CodiCCXOV ',

vitb AZA y&vi'av, 10

dl& TOVTO &TCCi XCtl

b Tijs Zj4 nobs AA Aoyo? [Eucl.

Dat. 40], ddo[ivov d a'| aQ%ils

xal TOV Tils Z4 xgbs Ad do-

d"i]6Ttti xal b Tijs dA nobs AA 15

[Eucl. Dat. 8]. dice d TOVTO xal

[Eucl. Dat. 43], TQVTZGTIVi]AB ?toi,cpQi,a TOV

Ttccod xv\v dvcoîa^LKv dicccpooov, xalj]

vitb EAZ[Eucl. I, 32], TOVTS6TIV

?5EZ TOV 1UXVKA.OV 3tQL- 20

<pzoicc. dv T TO itctQa T^V ttvcopccMav dt,d(poQOV VTto-

+a Ssdopmov, TOVTBGTW T^V vitb A/IB ycoviav,

sv did TOVTO xal b Tijs

AA nobs AA A6yos [Eucl. Dat. 40], dfdopwov d '|

TOV Tils x//A Ttobs AZ dod"*J6Tcci, xal b Tijs 25

1. AOITTTJ] ncti \Qntj] D. 2. Tovr^cnv rf\ rovrscti D. 4.

] post -o- ras. 1 litt. A. aTtodsSfiyfievKtg] -cci-

in ras. D. jrTjAtxoTTytoff D, sed corr. 8. sav] &v D. 10.

TOVTEGTL D, comp. B. 12. TCQog] corr. ex 7tQ6 A. 13. ê]8' D. 14. Azf\ corr. ex AA B 3 C 2

,AA D. 17. AJB] corr. ex

AJ A 1. 22. ro-uTf'ffTtBD. 23. -g do-] e corr. D. 24. A/f\ in

ras. C 2,dA D. TZQOS 25. d A] supra scr. D 2

. 25. TTÔ? AZ]supra Z scr. A post ras. D 2

,eadem uerba supra scr. D 2

,sed del.

ZA XQOS AA [Eucl. Dat. 8], dia de TOVTO xalij

TS

VTtb AZd y&via dedo^vrj 6x0,1 [Eucl. Dat. 43], TOVT-

l (pcavo^svr] TOV ^cpdiaxov 7tOig)Qici^ ualfj

EAZ [Eucl. 1, 32], rovrtenv % EZ rov iiti-

5 XVX&OV 7tQt<pQlCC.

JtdhlV 7tl

XXVTQOV

LA.1j<p&(O COIQ TOV H 3lQt,fytOV

TOV XXVTQOV i\ H Z 7CQlCp-

10 QSltt V7tOXl,[lVr] T&V KVTG)V ftOt-

Q&V A, xal jtv%&(a6av ijT

xaiI] Z@, xcd

G* anb TOV z/ Inl TVJV

15 7Cir\ZH 3tQl<pQl,a [lOLQCOV 0TLV A, iY]

KV Kttl

% vitb Z&H y&via, oi&v piv i6w ai d oa&al r|,

TOLOVTCOV A, OiG)v $ ccC dvo OQ&al rj, TOLOVTCDV (j.

K)6T Kttlf} yiV 7tl TT^ Z/K V%"lO,g 7COi(pOLCC TOi-

OVTCDV <5Tlv 1, Oi&V 6 7tOi TO 4K OQ&OyWVlOV

20 xvxhos rf, rjd' 7tl Tils K T&V AoiTt&v [Eucl. Ill, 31]

ig TO fjnixvxfaov TprjiiaTCdv ~QX' xal ai vnoTivov6ai

aoa avTag v^Lca ZGOVTCU % plv /IK TQIOVT&V,

o"lG)V 6TIVfj4 dlK^LTQO? ^3f, J]

dl K T&V KVT&V

^y vl. xal oi&v aocc i<Sxlv fj {ilv z/@ vTiOTeCvovGa

25 ^ A, 17Se 0Z K TOV %VTQOV |",

TOLOVTCOV <3T\V Xttl

1. rs] om. D. 2. AZJ] AZ BC, corr. C 2. 9. HZ]

H- in ras. D. 12. Z6>] 0Z D. 13. @Z] "Z' B. 14.

T)] A, in ras. D 2, TJ dt BC, corr. C 2

,^ eras. B. 15. sari D,

cpmp. B. 16. Z0H] H C, H C 2. 17. ^vo] |3

corr. ex

t(3D. 21. T^rj^drcov] om. D. i>7roTtiVo'u<Tart] corr. ex ano-

C, corr. ex vnoTtivovca D 2. 23. iorlv ii\ corr. ex

t D 2. 25. SGTL'V] comp. B, tcrca D.

MA0HMATIKHS STNTA3E&S T'. 247

4K v&ta a I?, f)ds &K o^otog ft I, % ds

KZ Tcbv hoiitav v v. xal sitel TO, an? avT&v GVVTE-

ftevra xoist TO aito rifc z/Z [Eucl. I, 47], stirai xal

ccvTrj ptfxEi, TOLOVTCQV v va syyitira, oi&vf\4K fa

a 7s. xal clew aoa stirlv % z/Z vnoTSivovGa ^, rot- 5

ovrcw xalri per /IK s'titat, /3

Ad AST, f)d' id avrijs

TOIOVTCOV ft xj, OltOV 6 7tEQ\, TO Z/ZJf

xvxAog T%' &0TS xalfj bub 4ZK y&via,

OLCDV [lev BiGiv ai dvo OQ&al rj, toiovrcov <5tlv/3 x^

oi'ayv d* cci d OQ&al r|, TOIOVT&V a id eyyiGra. TO&OV- 10

rcov aga sari TO naga Tqv av&iiaUav didyogov. xal

7tsl T&v avT&v VTtoxsiTai xal$1

vitb Z0H ycovta A,

ztirai xal17

vnb jBz/F o/b?, TOVTS'GTW % FB TOV co-

diaxov TtSQKpsQEia, yioiQ&v ha id.

xaTa Ta avTa ds xal Iv&dde fafityb&fckis T^g B4 15

xal xa&stov Bit avTqv ax&sfarjc; Ti\g A, edv TS rv\v

JTJB TOV ^G)dt,axov xsQifpeQSLav d&^tsv^ TOVTSGTIV T^VV7tb dA ycovtaV) do&tfGSTai, [ilv dia TOVTO xal 6

A Myos [Eucl. Dat. 40],

1. &K~\ corr. ex OK D 2. ojtiotcog] -o- e corr. in scrib. C.

r] corr. ex Hi C 2. 4. Supra v va scr. v^ v pd D 2

. ^v a]

corr. ex17 va C 2D 2

. 5. xat] H^' BC, corr. C 2. 6. 1^]

fa, f in ras., D 2,

^ supra add. D 2. As] Ad in ras. D 2

,s

supra scr. D; cfr. p. 249, 20. d'] 8e D.a'uxr^s]_C

2D, afajv

ABC. 7. ^ZX] corr. ex JZ A 1. 9. dvo] A, J3_BD,

dy C.,

fifrtV] comp. B, BGxai D. 10. d'] d D. a td] corr. exA D 2

. roGovrmv} corr. ex rotfoftrov D 2. 11. iGti\ AD 2

,ct

comp. B, fWiV CD. 12. Z&H] corr. ex ZH C 2.

]

C.D, XQIKKOVTU D 2. 13. %GTUI\ corr. ex <mi>

mut. in BJH C 2. 14. g^g ^ orayfaoi| fol. 70 r

D,fig. seq. fol. 70V

. 15. TO. avra.'] corr. ex ra-ura D 2. BJ]

BA C. 16. rf] corr. ex yg D 2. 17. rwciGxiv\ comp. B,

-v del. D 2. 18. @JA] corr. ex J @A D 2

. ycoi/mv] corr.

ex yavlu C 2.

dsdopEvag rtfv re vTtb

Dat. 43], TovT6Ti,v TO ycccoa rrjv

de % uQ%ijs xcd TOV tr\$ 4 nobs Z do&rjfcTai, xal

6 T-r}sZ nobs A [Eucl. Dat. 8]. dia TOVTO 6"

[EucL

didcpoaov, xal rfjv VTtb

[Eucl. I7 32], rovrtenv

HZ rov SXXSVTQOV TCSQL-

T TO TtKQK T^V KVG3-

v dicupoQov dcbjisv, TOVT-

10 BtiTiv

Tttt'klV

KOI 6 T^s Z rtgbs A[Eucl. Dat. 40], dedo(i&ov tf %

agyfls xal TOV Tils Z XQOS 4 dofhjtierai, xal 6

15 d Ttgbs A [Eucl. Dat. 8], dice d TOVTO

TVJV T vitb 4A y&vfav [Eucl. Dat. 43], TOVT-

TriV -T-B 7tQl(pQiaV TOV Z&dlCCXOV, Kttl XV\V

V7tb ZH [Eucl. I7 32] 9

TOVT&TLV T^V HZ TOV x-

KBVTQQV 7tQt<pQlCCV.

20 Oi)6(XVTG)S fal tyS XQOXl,[JiVr]S tOV b[lOXVTQOV Xttl

TOV 7tixvxkov xaTccoacis &oHi<frfaig ajtb TOV

av-TOVTO

T AH xal

anb TOV H inl rr\v Ad r^fto r\HK. Insl ovv

25 ita.'kivi\

H 7tQiq)aia IIOIQ&V IGTIV A, efy av xal

1. Ss] S' D. J] J D. 2. Z] corr. ex ZE D. 3.~

Z BC, corr. C 2. 4. xovrtcn D, comp. B. 6. rovr-

6Ti D, comp. B. 9. TovrtoTt, D, comp. B. 16. dA~\ corr.

ex J&A C 2. TOVTOTL D, comp. B. 18. TOVTSGTI.D, comp. B.

23. Supra JHB scr. Z D. xa-O-frog] ante -g ras. 1 litt. D.

Se\ 3' D. 25. H] H B. icxiv] s- e corr. C, comp. B,lent D.

MA0HMATIKHS STNTA3E&2 T'. 249

&AH ycdvCtt) QiG3v \iiv i<5iv at d OQ&al T^TOLOVTC3V A, olcov ft at dvo dg&al ri; 9 TOLOVTCOV jj*

6Tlv,Ol&V 6

7tl Ti}g HK <

JtQl(pSQlK TOiOVTCOV

sgl TO HKA OQ&o'y&viov xvxhos T|,

3]d 7tl Tfjg AK TG)V koiTt&V 5

[Eucl. III? 31] ig TO fiiiixvxfaov

QX. xal T&V vit avTag aga v-

&EI&VYI [lV HK <5TaL TOIOVTGJV

|, OIG)V 6TWTIAH V7tOTLVOV6a

03c, fjd AK TCOV avT&v 97 v. 10

xal oi&v aga 6Tlv y pv AHv&ia

/3 A, TId Ad x TOV

XVTQOV 5 5TOiOVT&V Xal

Y} [lVHK h'GTai a T, 07 ds AK b^oC(Qg

ft I, TId KA T&V koiTt&v v v. xal frtd Ta 15

(for' avTcov 6vvT&VTa TCQIBI TO anb Ti]$ 4H [Eucl.

I? 47], (irjxi, aga <5Tcu xal avTrj TOLOVTCOV v va

fyyiGTa, otcovrjKH v&ia i\v a i. xal oiov

aoa itiTlv r\4H vnoTsCvovtia ox, TOLOVTCOV sGTai, xal

TOIOVTC3V /3 tt, otcov 6 7tol TO 4HK xvxhog T%'

xalTI

vitb H4K y&via, oicov(i

r

v ffaiv aC dvo

t rS, ToiovT&v i<5rlv 3 xt* oiwv d' at d

2. 5.Ss D. ^o] B. 4. HKA] AHK_D.9. AH] JH BC, _corr.

C 2. 12. ^17] far} A.

in ras. D 2. 13. |] post lac. 4 litt. B, post lac. 11

litt. C. 15. r] I AC. i] 8s KA\ renouat. D 2. 16. GW-

tifti-vra. D, corr. D 2. 17. ctvrj] R _ 18. f-v&eta] om. D.

riv a] corr. ex 77 va C 2. 20.

J3^ Ag] (SW? D. 9s] d' D.

21. JHK] 4HK oQ&oywviov D (co corr. ex o D 2

).23.W D, comp. B. d'] ds D.

AB itoi(pQia.


r|, roiovr&v cc id eyyiGra. ro&ovr&v KQK e<5rlv rb

didcpooov KKI wrccvd'cC) rovr6nv

xcii jti r&v avrcbv vitoxeircurj

VTtb KAH y&via A, <5ra,i uali\ vnb BHA oAr}

5 [Eucl. I, 32], tjtrtg itQis%i rrjv (pcuvoyidvYiv rov tydicc-

xov rtQig)Qiciv j iLOiQ&v Aa id 6v[ji(pG()VG)g ratg 7tl

xara ravra df xal v&dd

rrjv z/J5 r^g AA^ idv re rrjv rov

AHA y&viccv, dofi"ij6rai

dia rovro 6 ri\g HAAA ttyos [Eucl. Dat. 40],

dedoîevov d'J

| aoxrlg xal rov

15 rqg HA nobs A4 dod"iJ6erai

Keel 6 rqg z/A Ttobg AA [Eucl.

Dat. 8]. dice d rovro dedo-

Hvag %0[iv rtfv r vitb A4Byaviav [Eucl. Dat. 43], rovr-

20 6nv rrjv AB TieQicpeQeiav rov

rtaoa rr\v av&inaMciv diacpooov,

xal rrjv VTCQ @AH [Eucl. I, 32], rovretinv rrjv H rov

eitiKVKÔV 7tQi(pQiKV. KV re TtttkiV %Y\V AB 7tOl><p-

Qiccv d&nev rov itaoa ryv avoîaliav dicupogov, rovre^nv

1. a ia-cLv] supra scr. D 2. sort D 2

, comp. B. Deindedel. e'GTLV &QU D 2

. 3. r) (alt.)] ins. D 2. 4. KAH] HAK D.

5.IJTLS~\ ij- corr. ex v D 2

. 7. f'xxfVrpo-u] ifx- supra scr. D 2.

8. TKvrdi TCCVTCC A, TctvTct mut. in xa. UVTCC B 2 C 2D 2. 10.

TOVT^GTIV] comp. B, -v del. D 2. 14. V.CCL 15. A4~\ supra

scr. D 2. 15. HA] H- corr. ex N in scr. D 2

. 16. A A]renouat. D 2

. 19. TOWEGTLV] comp. B, rovricri D. 20. TIJV]in ras. 1 litt.D 2

. 22. &AH] HA0 D. TOVTSOTI, D, comp. B.24. XOVXGT;L D, comp. B.

MA0HMATIKHS 2TNTASE&S I1'. 251

TY\V VTtb AdB ycoviav, avcc7tcc2.iv coGavr&g doftijtisrai, [iv

dice rovro 6 T% AA ngbg AA Myog [Eucl. Dat. 40],

S M& v rn ^^ ngbg AH do-

xal 6 rr\s HA ngbg AA [Eucl. Dat. 8]. did

de rovro dsdopsvas eôpsv rtfv ts vnb AHA y&viav 5

[Eucl. Dat. 43], rovrdenv r^v rov %G)diaxov 7tQi,<ps-

QsiccV) xal TYJV VTtb &AH [Eucl. I7 32], rovTsGtiv xr\v

H rov ejtMvxhov itQi(pQia,v. xal dddsMrm îvra TtQorE&dvtK.

dia rovrcov rcbv &0)Qrj[idtG)v dvva- 10

xavovoTtoiiccg t&v 7tQis%6vcG)v

rag sx rijg dva)[iaMas tcbv cpatvoîsvoov

dictxQiGsic; Ttgbg rb f'J broCôv ku\i$ix.vsiv rag

rcov Kara {isgos diOQ&ooGs&v TtqhixoTrjtccs ccQsGKet, [ictMov

<YHLIV YI ralg 6ftaArg jtSQicpegsicug TtaQaxsLîsvag e%ov6a 15

rag TCKQCC rrjv avaiiaMav diacpOQag did re rb xar'

avrdg rag VTiofrBGeig Kx6kov$ov xal dia rb artAovv re

xal V7ti(loAov rijg xa&' sxatira iltrjycxpoQiag. h'v&sv

rolg rtQ&roig xal iiti rcbv dgi^îcbv

r&v faagrjiidrav xal iitl r&v xard 20

r[ir][iidrG)v itho >

yi,<)dn&a dice roov

ojtiavrcog rotg a7tod$i'y^voig rag xd<5rr] r&v

xafrohov d ra kv JtbgâTto'EiOig rfrarroia xal

1. A4$] afid D, ctdp D 2. 2. A A] corr. ex AA D 2

. 3.

om. C, ds C 2. 5. s^co^sv C. 6. TOVTSGTLV] AC, comp. B,

C 2 D. 7. rovTEcnv] ACD, coinp. B, -v del. D 2. 10.

$rj] ^TJ TT^S D. 8vvuîvTf]<i\ corr. ex dwdpscas D. 12. tag]rd C. 13. ^K^dvfcQ'ca D. 14. diajQ&djGEcov A. KQSGKSL]seq. ras. 1 litt. D. 16. KMT' avrdg\ corr. ex Y.KTO. ravrctg D 2

.

18. fvsTtifiolov] mut. in vm]fiol.ov D 2. t/>T7<piqpO(Hag C,

corr. C 2. 21. Eiti-loyrjGdiit&ct C. 23. STf^KUovoccs] pr. I

del. D.

7tl rov r]kiQv xal TCL r&v aM&v dieiô^v fig

, fog yiv6&cci, ri]v TtKQa&eGiv sri ccvr&v

^, ra dl agog rolg rtQt,ytotg ig T[nj[iara A,

cog xal rtl rovrov yiv6&ai, rr\v 7CaQd&6iv dia {LOIQCOV

5 y, 7tiSri7tQ psiôve'g i6iv aC itQog rolg ttQiysioig

toig i'Goig T[irj[ia6t,v diafpOQOV t&v

rolg ctTtoyEioig yivopwcov.

TKÔIIW ovv Kul TO Trjg Tov fjMov10 xavoviov 7tl 6Ti%ovg [ilv nukiv

jil^,6eM8ia ds y,

ra ftfv XQ&ra dvo 7tQid%i rovg KQi&iiovg T&V

ra xgbg TG> anoysiG) fi rerKQrriôQia^ r&v

fav A ra ngbg rc5 TteQiyeiG), rb ds y' rag xcc6tq>

15 r&v 64aAwv aQifr[i&v 7ti,paA.A,ov6ag (uolôg ti}g

acpaLQ6K)g rov TCCCQCC rqv uv&ii(x,kiav dicupooov.

<5ri, rb xavoviov roiovro'

6. eTtLficdovTcov D, corr. D 2. 7. TftT^tatft D. 9. rov

v] rjUccKijs D. 10. ceMdici] ju^rj D. <oi>] cog D. 11.

D. 12. If] dsnansvTS D, ut saepe. GTL%GOV] -co-

e corr. D. 13. ra\ -d in ras. D 2. 14. 1] a BC, corr. C 2

.

TO d] AD, ji BC. y'] y ABC, rgirov D.ra,<s] corr. ex

TO. D. 15. ^TtlficdovGCCS D. 7tQ06(X(pttlQGCQg D.

MA0HMATIKHS 253

1. 5-'] B, om. ACD.?/Uax??] om. D.

^ D. 2. ,orat] AC,om. BD. a'

/?' y'] om.

D;habet in lin. 4. 6.

</?] -/#e corr. D 3

. 11. tec,

tov artoysiov dvo tftaQtrj-

mg. A 4, artoysiovet mg. et

inter coll. 12 B s. 12.

ûy] corr. ex Ay B2 C2.

14. r] seq. ras. A. 15.

aqrf] -9<? in ras. A. 16.

OTtrj] corr. ex ffî? C, -7t;

in ras. A. 17. Gilp\ -itfi

in ras. A. 23. ovtj]

Ortrj D. 31. a] ftD.

32. aâ] a- e corr. A.

34. tbt. tov ftsQiyeiovia mg. A4

,

et mg. et inter coll. 1 2

B 3. /s] D, -c in ras. B 3

,

/# A C, corr. A1. axe]

-e e corr. A. 41. o] e

corr. D. 42. o] corr.

ex a D. ry] e corr. D.

43. o]5 o C, corr. ex

a D. /ug~\ e corr. D.

44. o] corr. ex a D.

A#] e corr. D. 45. o]

corr. ex a D./I/?]

e

corr. D. 46. o] corr.

ex a D. 48.;]

e corr. D.

49. (iTt"] corr. ex /) C.

xivijastuv

9

9?

.

D*

tflTJ

ait*]

aogoo

avs

ovfi

o/ug

a/uy

old

axrjay.s

ax

otyOl

o to

o x>/o mp

y.a

y.y

xy

y.a

y.

? *a rj;

a wa /<â [.id

28

10

15

25

:JO

-10

KAATAIOT IITOAEMAIOT

xccrd rqv ^6rjv rov fjA icdgodov

254

g'. Jleol

AoiTtov d' ovrog rov rfjv iitoyftv rtfs o^a^g rov

fjMov xwiJ6G)s 6v<5riJ6cc<5&ccL Ttobg rag r&v xard

5 excctfrore TtctQodcov fastfxetyeis STtonqGcciis&a xccl

roiccvrrjv lK&6iv dxoAov&ovvrss psv xa&oAov

ini re rov ^Cov nctl r&v aMcav ratg vcp'

avr&v axQL{$e6rccrcc rsrrjorjiisvais TtccQodons^

ovres ds oat ccvr&v rag rcbv STtoftav GvGrcttiEig ig

10 rr^v KO^V ri}s Na(lovcc66dQOv Patiifoias dice r&v ctito-

xivij<5G)V) acp' ov XQOVOV xal rag

rov

*x r v f / ~ jE7

(7TO) 0^ O JI1/ O{lOXVrQOS TG)

15 di: [i6cdv XVK^OS 6 ART iteQi

xevraov rb zJ, 6 d1

xxvroos rov

y]kiov xvxA.og b EZH 7Col xvroov

TQCOV xal rov E dnoyeiov

20 rgos % EAHT, vitoKeiG&G) Serb -B'

B 6Tr]u,EiOv rov Z&diKxov rb iiero-

ItCQQLVOV, Xdl 7t%VX&(n6'CCV [lV

rjre BZ^J xal ^ Z, xd&rog de dno rov litl

rr\v Zz/ txf&rj&sfaocv YIX&G* ^ K.

25 Insl rb ulv B

om. D.1. T] B, mg. A 4, %, mg. C 3

,om. D. 2. ST

3. 6'rog D. rov (pr.)] om. D. rrjg 4.

rov ii'kLov ri]$ diKxkfjs GvGTrjGac&ai, v.Lvr\6Kcog D. 5. 7toi7}6o-

ps&K D. 9. Ss an'] 8' V C, 8' D supra scr. &n '. 14 TWSiu [jiGcov~] r&v (pSiay.G>v D. 23. ndO'eros] -g add. D 2

. d\8' D. 24. &K] corr. ex K D 2

seq. ras. 2 litt.

MA0HMATIKH2 STNTASE&S r'. 255

rCbv XiqkCbv ap^V, TO ds F itSQiysiov rag rov Toôrov

lioiQctg e/_', 17

BF CCOK TtsyKpfysia [IOLQ&V itinv |f

L xalfj

VTtb BJF CCQCC ycovia, rovrfanvfj

vnb

4K, otcov {iv i<5t,v ecu d ood'cal T|, roiovr&v f A,

OLCOV ds aC/S OQ&al r|, roiovt&v ghcc. &6te xcd

jj5

lilv iitl rils K sv&stas TtSQUptysia rowvr&v fGrlv

pAa, oi&v 6 7t()l rb /J&K OQ&oycoviov xvxA.o$ r|, ^

d V7totivov6a avrriv sv&elar\&K roiovr&v Q& t/3,

OICQV 0TLVi]

/4 dlCClltQOS Q%. oldOV CCQCC 6xlvfj

filv z/@ v&ia, rj

$ Z v7toTivov6a ^3c, roiovrov 10

Kol17 pv &K 0rcci d Ay, ^ df fV aurijjg

rotovr&v d x, otW fV-rtv 6 ^^>l TO ZKT|. o5<?r xa^

17vjco ZJf yowia, olcnv

at dvo 6()0-al T|, rotovrcov fVrtv d x, otrai/ df

at d opO'at tr, rotovrov/3

i. irwv ff ctvrCbv f]v v\ 15

VJTO EAT y&via % A* Ht Aotî) [Eucl. I, 32] CCQCC r\

VTIO Z@H) rOVXBGtiV rjZH rOV XXVrQOV 7tQl<pQl,(X,

itixiv %y x. orccv agcc jtl rijg yLsroTMOQivris

y 6 r/Aios, rov pey itzQiysiov, rovrfanv r&v

rov To%6rov poiQ&v /_', jrô^y'ircu ^6cog xivovpwog 20

X) rov $ aTtoyeiov ,rovrttinv rcbv xccra

2. /.'] Z D. 3. I] in ras. A. Ez/T] corr. ex BTz/ C 3.

4. |e] s'dTtv |e D. 5. ^] f(7rlv â D. 8. ds] S' D.

?j] om. D. K] @- e corr. C. 9. ol'cov] v.ai otcov corr.

ex %ai wv D. J&] corr. ex z/E D 3. 10. f] in ras. 2

litt. D 2. 11. @K] @- corr. in scrib. C, deinde del. etifofa D.

84] d' D. 12. 8] post ras. 1 litt. D. @ZK] Z&K D.

13. TJ]ins. D 2

. @ZX] <9_Z^D. 14. 5vo] g JB. IGTI'V]

comp. B, -v del. D 2. 16. e] -f e corr. D 2

. A] seq. ras. 1

litt. D. 17. Z&H] Z- corr. ex ? C. 18. |y] -y e corr. D 2.

^19. zovreevw] comp. B, -v del. D 2. 20. /.']

Â D. 21. d<]d' D. TOVTSGTL D, comp. B.

rovg 4idv[iovs {IOLQ&V s I, aitfysi

[lVK {lOLOag (H ft.

romov dr} &coarj&vros<) sitsidrj r&v ev rats

rcus flpiv rrr]Qr]HVG)v iîq^Qi&v pCa TKtv a

5 A,rjcp&i6(bv yfyovev l(5ruLQia [isroTtcootvr} rep 1% srsi

[isra dvo syyiGrcc

a CQQCCS rijg îs6r]aftîas^ dÂov, on tear'

exstvov rbv %QOVOV 6 ijhios [isGws xivovpsvos aitstysv

rov ccitoyeCov Kara rbv swcsvrQov xvxhov slg t& sno-

10 {leva jioiQag pt? ji.AA

7

ajto [ilv rifc NafiovaGGagovrr Gvva-

ysrai xar Afyvrtrfovs vied, aitb de rrjg'

rffavrris p%Qt> rfjs AvyovGrov j$a6iteia$ rr) (J9d, aitb

d rov a hovg Avyovarov nar Alyvnriovs rijs iv

15 Tc5 co& a [i6r]n@OLas >^ytsid 1

^ rag

ILSO'vuifiQiag 6vvi<5rd[Le&a, p%Qi> tov 1% srovg'

vov 'A&vQ'

yisra dvo falftiQtv&$ COOKS

?l yivsrui o%a xal f][ioai, |sr xal cooai,

/3* nal ano rov a f'rovg ctoa NafiovaG-

20 GCCQOV Kar AlyvTiriovs rijg iv rf] rov G)& a

rr}s xxi[ivr]

xal

Jg nal COQCCI, i<5r][iQi,val /3.AA' iv rco roGovrco

6

3. ngajTcus] -TCCIS add. D 2. 4. rjfiLv] seq. ras. 2 litt. D.

fcriiiSQi&v] -i- in ras. 2 litt. D. 6. *A9"oq\ 'A- supra scr. A 1.

8. "n,8Lvov(jiEvos C. an8i%f: D. 10. aAA'] ccihd D. 12. /tar'

AtyvTt-tiovs] om. D. 13. Avyovcrov] -y- corr. ex T A. a9$]ff- eras, in extr. lin., add. init. sequentis A 1

. 14. a'] TT^W-TOV D, ut saepius. 15. a'] vovfjuiviccs D, T?)g add. D 3

; rov^r]-

mg. B 3. 16. t^'] corr. ex f C. 18. yCvovrcci D. 20.

y B. a'] VOV^TIVLK D.TM

MA0HMATIKHS 2TNTAEE&2 T'. 257

6ia x syyiGra. kav ovv rats tijs xara

[iro7tG)Qivr)v i(Sr^LQiav aito%rjs anb rov

aitoysiov rov SXXSVTQOV poiQaig jng ft 7tQO6&cbp,8v

vbg xvxhov potoas r\ xal anb rCbv yt,vo[isvG)v cupe-

rag 6ia xe ftotâg rijs nark rbv [iera%i> %QQVOV 5

rc5 a' srsi, Na(iova66ccQov xar Alyvnriovg

li6rjiipQias aytEGrcbrcc ^LSV rov cntoyeCov rbv v\kiQv slg

ra sjtopeva xad^ bpabrjv yiiv^Lv [loigas 6% t?, site-

ds psting rbv 'Ijfhfav rijs poiQccs %rjxo6rK 'jis.10

rj

f

. Jlsgl rrjs

av s&sA&iiev r^v KCI& snccGrov

QQV&V rov viUov rtKQodov

rbv OvvKyoyiSvov dnb rfjs snoxijs %Q6vovrov V7toxi[ivov TCQOS rqv v '4A.%ccvd(){a &QCCV 15

ts ra rrjs bpaArjs xwrjGEcos xavovia rag

rolg ol%ioi,g a

r&v rijg arto%fjg 6% i H,OIQ&V xal

r&v yvo[iVG)v xf$aA.6vrg oAovg xvxAovg rag

acprjGoiifv attb r&v v rolg didvpoig poiQcbv A si$ 20

ra 7toiiva r&v tydicov xaC, OTCOV av X7t6r] 6 &rov

1. ovv\ comp. ins. D, del. &qu. TKIS 7775] e corr. D 2. 2.

D.D. 3. Kitoysiov} corr. ex

-f* sv({>D 2 in loco minore. 5. xs] %' D. 7.

QOV AC, NaôvvccGaQov D. a '(alt.)] 6 a C, vfo^viK D, vov-

^TIVLK supra scr. B 3. 11. TJ'] mg. AB, om. CD. 12. occous]

o- e'corr. D 2. av] D, sdv ABC. &&a>iisv C. 16. rd]

tag D. 18. 7to%fjs D. 19. yivopsvtov BD. f'otâHovreg D.

20. ILOLQ&V 8 I] ? I' \L D. 21. ^(o8i(ov Hat] corr. exD.


d rbv avrbv apiotyioV, rovr0ri,v rbv ditb rov dno~

ysiov n>%oi> tils ftf'tf^g Jtaoodov, i6Vyx6vrg sis fb

rijg dvconaMag xav6viov rag naoaxi,^vag r<p

poiQag v r<p y' GsfodiG) Kara plv rb itgCbrov

5 rov aQiftpov jrwrrovrog, tovr&xiv

yGhovyiSv anb rv\ Kara r^v

.)Kara ds rb $' GsMdiov rv%6vros rov a

rovr0rtv vftsgyteGovros ^yt poious, Ttô^ôêv rift

lisGr) nagodcp nal ovrcog rbv <xxoi,f}rj xal cpcciv6[ivov

10 ijAlOV VQ1J6O{lV.

Ta pv ovv Jtsol rbv rjhiov povovvr iGriv ax6A.ovd'ov d

y

av sly rovroig

L dia f$Qa%O)v nal ra 7tgl rijs r&v vv%&r]-

15 [itoav dvi06rrjros oyeikovra 3tooA,r](pd"YJvcci, dia rb ra

psv xr&i,iiva iftLiv nad1

'

Zxatirov arth&s ptGu KIVV\-

para ytdvra xar faag v7tEQO%a$ r^v Jtaâ

pdviv &s xal rcbv vv%d"rj^Qcov itavrcw

ovr&v, rovro dsfti) ovrog %ov &G>Qt6d'ai,. rrjg

20 roivvv r&v oAcov (Srgofp^ dpaA&g re cbroTfAovfteV)?^

xal jtgl rovg tov farjpfQivov xoAovg nal rijs roiavrrjg

d7toxara6rd<30)s Kara rb 6rjfiicod0roov tfrot,

rbv 6otovra r) Jtobg rbv î6riîftoivbv A,a[if$avo

xotipov plv rtfOHyrgocpij dÂov on, pia ttirlv rj rov

25 avrov GyiiEiov rov far][iQi,vov dno nvog rptfparos

ijrot, rov doôvrog ^ tov ii6r][if$()ivov iiti rb avrb

1. xovrsGnv] comp. B, -v del. D 2. 4. Tcg&rov] a B. 8.

PTT] rag Qjt D. 11. #'] mg. ABC, om. : D. 16. iv.nQ's^va. D.17. itdvra] om. D. 19. f%cov C. 21. rf/?] corr. ex rots C.

26. [isofippQivov'] comp. e corr. D.

MA0HMATIKHS 2TNTASE&Z P'. 259

VV%&IJ[IQOV ds anfabs v\rov

twos rptfuaros r^roi rov bf%ovrog fyrov

rtdfav 7tl rb avrb d7toxccrcc6ra6i$. bjiaAbv [ilv

ovv vv%&ri[iaov yivtxai did rccvrcc rb itQi%ov Ttdoodov

r&v rfjg [lias TteQidroocpris rov faypsoLVOV %QOVG)V r$ 5

nccl k'n vb IQQVOV efyxotfrcbv v& syyiGrcc, oticc ev

tv r% xal k'n r&v ijroi Gvvava-

rov 10

rovro dy rb 3tQo6dia%6[ivov rov

rots r% %QOVOI avitiov dvdyxr] yiv6&u.i did r

q)aivo[ivr}v rov r\Uov dvaj^aUav xctl did rb rd fact

rov did ii6&v rcbv ^cpdicw xvxkov rprjparct ^ iv 15

%o6vois [itfrf rbv boi&vrcc {irjr rbv

xdroov [ivrot, rovr&v

rov vbs vv%d"miQOv dtacpoodv rf[

6rd(5G)S nuQd rrjv dvcopahov dvfitcciG&qrov itoil,

20

Ttaad [iv ovv rr\v ijhictxriv dv&[iccA,Lctv rb yiativTvi/

yivro:i didcpoaov 3tl r&v ditb pices rwv pfaav rov

1. 17] tv 17 D. 2. (iar)iiQivov] /t D. 3. Post avro del.

liti D. 5. r&v] TCOV TS D. tGJiiiQivov~] $, D,a add. D 2

,

lit saepius. 7. TW] om. C. 8. T^g] corr. ex rfj A. 9.

GvvavacpQa)[iEV(ov C, sed corr. 10. GvvpsGovQavovvToov AC.12. TO] om. D. 13. Tot?] -015 in ras. A 4

,-or- e corr. D 2

.

ccvdynrii A. 15. TOV] corr. ex TO C 2. y.vY.T(.ov] corr. ex

Avnlav D 2. 17. tovTcov~] r- in ras. A. rijv p. 260, 23. -&]

mg. D (W^fvov), ad lin. 21 pleraque cum mg. recisa; rv\v 18.

iv etiam in textu. 23. r&v (pr.)] ins. D 2.

17*

260 .KAATAIOT IITOAEMAIOT

sroav diaGraGEcov ra

ovrag Gwayopwa w%&tf(iSQa dioitisi r&v

%Qovoig dL' xccl d' k'yyitirK) aAAÂov ds rots

XQOvoig #/.', din rb xal r^v rov r\Mov <pccivoiLvrjv

5 TCctQoSov nccQa TJJV 6|itaAi)v Kara [lev rb agog rc5 aito-

JiiniKvxkiov $' d' [IOQCC$ skteiTCSiv, xccra ds rb

r& itQt,yiG) Jtfaovd&w rcclg ccvraig' naya ds

T&V GwavaroAcav ty GvyxccTccdvGswv ccvG)[iaMav

rb TthsiGrov ywsTcc&diccytOQOv iitl r&v vnb r&v XQO-

10 TtiKcov Gynst&v acpoQi,o[ie'vG)v fftiiKvxM&v' xal

ai sxarsQOv rovr&v rwv

r&v [isv oîa^cbs &(OQOV[IVG)V %QOVG)V

rolg SiK<poQOi<s r^g [isyiiSr'Yjs rj Aa%i6rrjs f}[iQKS

r^v i6r}iiQi,vijv, aM.tfA.cov da, olg ^ {isyfatrj r&v

15 Q&V -ijvvxrcbv rye; s^ccî^rrjg diKtpSQSi. staga ds

rcsv GvpiisGovQccvriGscov avidoTrjrcc rb

yivstui diKyoQov sitl r&v dvo [icifoGrc

rcc xarQ&&v apar&v l<5rniQiv&v (Ajpe&M^ xccl rovrov yap

20 rcc 7tgbs rots rgojuxoZs 6vva[i(p6r()a r&v [iv bpah&s

&SG)QOVIIVG)V 8ioi6i %Qovoi,s d /.' tyyiGrcC) r&v ds

agog rolg i&r^tEQLVotg 6vvan,(porQG)v Tt&kiv %oovoi,g

^, dia rb ravrcc p

1. diaoraGEcav] r&v 8iK6ra.GE(ov B, SLUGTO.G D. 2. OVTCO D.

5. TO] x D. 6. /.'] e corr. D. <T] g A D. TO] x D. 11.

&vacpoQcci D. 12. 8(,oiGovGi D. pTt XQOVCQV D. 14. de,

Oi?] dlOVG D. 15. VVKX&v] B 3, QQ B. 17. ScQdXKT7](lOQLu]

D. 21. Sioidrjoei, C. ^] TSTQCCGI vctC D./,'] B,

A CD, rjfiiGeis A 4. 22. GwcciicpOTsgoLS comp. D. 23.

^] B, ^ lyyufra B 3. 2

r exetev fol. 73V D. ^ta p. 262, 5.

fjMov] mg. sup. fol. 74r D, usque ad cvviGTa^B&K p. 261, 3

recisa.

MA0HMATIKH2 ZTNTABESS T'. 261

/to/tofV, Xiva df rep foot 6%sdbv nteovd&iv. i'v&ev

xal rag iv rats no%al a$%ag rcbv vvx&rjpSQ&v dnb

TG)V {l00VQCCVYi6G)V 6VVl<5ra\Ltfttt, XCCI OVX CC7CO TG)V

KvaTok&vYI

dv6(ov TOV r\^Cov dia TO Tqv [iV ngbs

tovg 6giovTag %'Oôv^,dvriv diacpOQav xccl [i^Qi itoh- 5

<p&dvLV KCCI ^ ivai rr^

rcbv

ds JtQos TOV ii6yii(lQivbv t^v avrriv T

vKL xara naticcv ol'xqGw xal [irjde rovg x r^js fata- 10

as (Swccyo^vovs tov diccyogov %()6vovs

rovrcov îôs vfjs r nuâ xr\v

xal rfis Maya rag 6vii[i6ovQavri6i,g TO didyogov iicl

T&V KKT ai(OTas Tag ir, f

vas diaoac; VTQI TIOG- 15

[i6ov IH%QI Xrjk&v T^âTos^ TigoGd-fTixov ds TOV

dab Z!XOOTCLOV ftf^^t p&ovf

Tdoo%6ov, dia TO xdTgovTG)V KKiêVG)V T{ir][ldTG)V TO TtfalGTOV rTOl TtOO^TL- 20

acpuiQEiv itaoa [iv Tr\v rjAiaxrj

iQccg y zyyitira xal diTQiTOV, rtaoa $ Tag

3. KTIO] ni D. 5. xat] om. D. 6. OQ&V C. 7.

"C. x%\ rriv A. 13. ^t'ov] rj- oin. C. 14.

D.D. TO] ABC, xb ntefa-tov B 3 D. 17.'

D, comp. B, v$QTr\%6ov AC. 19. fifWu] om. B. 'T

vSgrixoov AC, ^ -' (LECOV B. 21. TJ] upa ij D. 22.

TQLTOV C, Io D. 6VV[LGOVQClVri6eiS A, [L60VQCCVri<>Sl$ D. 23.

F seq. ras. AB, r A 1

D, f C. cog] tog to D. 24. ow-D.

rcbv

agog ply rd 6[iahd %$6voL$ rj xal y', rovrfanv a

L' M;', agog aMyAcc ds r&v dMhaGiov %QOVG)V 7g

rovrs'tinv WQCCV a xai &'. rb ds rotiovrov sal

5 fjMov %ccl rcbv aM&v TtaQOQ&iiEvov ovdsvl av

xccrcc^ccTcroi rrjv r&v nsgl avra

,7tl ds Tys Gehtfvrjg di,a rb rrjg

|fcdAoyov av ijdrj rr}v diatpogciv d

xai (J>%()i' y s' [nag ILOLQKQ.

10 wcc ovv Kdl ra xcc&' drtoiccvdrjitors diccGTaGiv di,-

cc vv%d"ij[iQa) heya) ds ra ccitb [isGrjiiflQias rj

sjfl îs^rj^^QiCiv rjeitl IISGOVVXTLOV, et$

rs rr)v jtyoreQccv 7to%rjv xccl rijv VGTSQCCV

15 didoiisvys t&v vv%d"y]iiQG)v dLKGrdtiscos, xara

<3rlv rov did [isG&v r&v tydiov xvxkov poiQcbv 6

?j/Uo 6[iahG)s rs Xivovîsvog xal dvo^d^cog^ sitsira r^vdnb rqg av&pdkov, rovrstirw ri}g (pcuvoiisvrjg, sni rr\v

cpccivo[isvr}v didtiraGw r&v rijg snovGiag ÔLQ&V20 sfasrsyxovrsg stg rdg sit' 60-9% rijg GyaiQcig dvcupogag

rov

2. x] om. D. ZOVTSGTI, D, comp. B. a] AC,BD. wâff] comp. AC.

_3. r3} r ABD, T seq. spat. 2

litt. C. 4. xovTSOtw atQccv a xai] xal $>QCC$ (li&s D. to

5. r\Uov\ etiam in textu D (ro postea corr. ex did}. In fine

([<>** mg. D. 5. alcov C. 6. ccvrov? D. 9. y e'j r ?'

ABC,rqiCav 7ts[i7tTcov D. 10. oinoLKvd^nore C. 11. Z^yoo] corr.

ex ttysi, in scrib. C. 12. Int (alt.)] om. D. 13. 6taorXZa C.

&vcdva>(jiv~\ post -co- ras. 1 litt. A, -co- corr. ex o CD 2. GY.S-

ipmiisQ'a C et uoluit D 2. 14. xara re] corr. ex v.aQ'KnsQ D 2

,

yg. v,a&K TB mg. D. 16. iazlv] comp. B, -v del. D 2. 18.

&vco[Lcdiccs D. TOvreGnv] comp. B, -v del. D 2. 19. rfj$

STtovGtag] -s - e corr. D 2. 21. noooi. C.

pr. ftadd. A 1

, GVVÊGOVQCCVOVGL C.

MA0HMATIKHS 2TNTASE&S T'. 263

at rye; dvcopd&ov dt,a6rd<5G)s, &sxal kafiovreg rqv vitQO%fiv r&v rs SVQE&SVTCOV

xal r&v ryg ofiaAijg diatitaGecos

C re to rtQi,%6[ivov iifys&o

r&v Tijg i)7tEQO%rjs %QOVG)V rovro Tthsiovoq 5

fJLSV SVQLdXO^lSVOV TOV TG)V %()6vG)V aQL&[lOV t

r& didojievG) rcov

ds acpEhovpsv an? avtov,rbv yevopevov %QQVOV %o{iv stg ra dpaka vv^rj-

,& xal ^Qriôêâ ^dh^za agog tag 10

rCbv iv rots xavodi r^g 0s^vrjs [ifacov

. svxaravorjrov d' avrod'sv^ QXI xal dxb rfjg

v vv%&r]iisQG)v VTtodrd^scos tvt, KaiQina xal

%QOVG)V 3tQo6&a<pai,Q'6G)g avdnakiv yivoiisvrjg. 15

rti%ev pivxQi Kara rrjv fyiTE/

Qav jto%riv 6

rovT<5nv res a k'ri NafiovaGGaQov xar

a' rfig ^s6rniîag^ bâl&ns {ilv

[p. 257, 6] aTtBdâiiev, 'I%&vcov ka o ~^s^

dl y poiQas xal q b'yyuSra QqxoGra rcbv 20

1. cog] -g ins. D 2. 3. duxcrdoEmv D, 'corr. D 2

. 6.

BC 2D, KQL JL A, &Qi&ii6$ C. 7. StSo(iEvcp'\ rnut. in

in scrib. C, -v del. C 2; dedopsva) D. 9. rov] corr. ex TO A 1

.

D. ctg] tbv sis D, rov add. B 3. 10. xal

a] corr. ex g KSXQ<r]6'oped'a D 2.

ai12. $'] 8t D. 14. Post

D,del. vTto D 2. 15. nQOGcccpsQEGecos D, corr. D 2

. 16.

-v del. C 2, 7ti% D. 17. tovtiuii D, comp. B. Ncc-

D. 18. toO1

] -ft ins. D 2. a'] vovpr]Viu D. 6fta-

Zco? C. 19. &nedetoii,ev D, corr. D 2

.

^]om. D. o] om. A.

In fine KlavSlov TlroJiSfucfov â^rjâr iv.fi? cvvrd^scos A, KKuv-diov nxotepctiov [La&r]ii(XTi'xris Gwrdt-scas $i$Uov y' B, KluvSiov

y C, Urotencciov ftaab^cmxcoi/ y D.

4'.

Tads k'vstitw V r& d' rijg ntote[iaiov

ra itQi rr\v

5

f}'. itsgl r&v TteQiodw&v %Q6v&v rr\

y' . negl rcbv xccra pegog bpal&v xivtfescov rife

rag

10f

. Qti xccl rti ri] KitkriQ vJto&6G)s T^g 6Aivrg ra

civra (pccLv6^va TtoiovGivrj

t XKT'

rrjra xalij

xccr' iitiKVKôv.

xccl catAijg av(D[ittMKg

15 5'. rtQi r^g dioQ&GHSfag t&v pfacdv TtccQod&v rvjg

pijxovg r xctl avapaMccg.

trig Jto%ijg r&v dpcd&v -r^g 6&rjvr]g xivt]-

[iijxovg T xal avG)[iccMag.

&'. 7tQi xi^g dioQ&GxSf&g rcctv xccra nhdrog

itKQod&v rilg^6Xr]vrjg xal ri^g eTto^g avrcbv.

1. ^d'] om. ABC, Utotepa.LO'v (jLtt&rmccrw&v A D. 2. xijs]

r&v D. jâ-9'T]ftaTtx7)s 0tott<$|ea>9j (iafi"r}[JiccTiyi(bv D. Deindeadd. ~j C. 4. a'] et ceteros numeros om. D. dti] dri C.

TrjQrjGsajv] -G- corr. ex p in scrib. C. 13. anodsiîs] corr.

ex anoSs&s A. Tfjs (pr.)] t- corr. ex s in scrib. C.

KAATA. IITOA. MA0HMATIKHS STNTAEEaS A'. 265

'. ifjycpotpoQia xai xavoviov rr^g TtQ&ryg xal o

ia'. on ov "JtKQK rag diacpooag r&v v

Ttaoa rovg 7tt,A.oi

yi,6(iovg ditjve'yxsv xara rov

rijg GeAqviawfig &v&- 5

a'. 'Ano noCov del trjQiJGs&v ta Jtegl

'Ev r<p TtQO rovrov ^vvrd^ccvrsg^ o6cc av %i i'doi

ovta 3tQl t$\v rov r^Mov xivyGiV) aQ%6[ivoi 10

TS xatcc i$\v sepsis aKokov&Cav xccl rov tteoi rijg 6s-

Aoyov itQ&rov fj'yov[i&cc Ttoo'

cag etv%v TtgoGitvai rcctg r&v fig tovvo rrjorf

%Qtj66iVi aMa agog ply rag xa&ohov

vaig pdfaGra 7tQO<5%LV r&v ajtodt|fG3v, oticct, py 15

[iovov IK rov Tifaiovog %QQVOV, aMa xal an' avr&v

r&v Kara rag 6&r]viaxag Kfohl}ig rrjQtJ6ov kayipa-

vovrai' dia [lovcav yaQ rovr&v axQificog av 01 ronoi

ri\s 6^tjvr^g VQi6xoivro r&v aAAcov, oVeu ijroi, dia

r&v 7tgbg rovg anhavflg adrsoag jtaQod&v vj dia r&v 20

ogydvcov T)dia r&v rov r\Mov fxfafyf&v

itokv 8iafyv<5&i]vat, dwapfacov di,a rag

ryg 6^tjvrjg' Jtobg ds ra xara [ioog

xal artb r&v akkov ydr] rri^6C3v TtoiziGftai rr\v iiti-

1. -Adi (pr.)] lac. 12 litt. C. 3. ia'] cci B.

e corr. C. vno&EGscov] om. D. 5. iris crtriviKyifis &vco-

s] om. C. 7. a'] om. ABCD. 11. <p^ff] corr. exD 2

. 12.[ii]']

corr. ex ps in scrib. A. 13. nrjdt D.D. 14. %QIJGGLV] corr. ex XQTJGIV C 2D 2

. xarar-

i/>ig] post -r\- ras. AC (^ eras.?). 19. 6'aca] corr. ex OGU D 2.

22. nQccMd&is A.

6xit>iv. TOV yap ajrotfrtârog, 6 vcydtitiptsv v\

T^g Gshtfvrjs djtb TOV XVTOOV Tijg yifc, pr\ ovTog

xal TOV xaTa rbv ^cpdiaxbv xvxhov TrjfaxovTov ,

6lf][llOV JtQOg ttVTO MyOV %LV TO T?jg

5 dvdyxrj Tqv ebro TOV KSVTQOV TY\$

ev&slav 7tl TO, TOV dia ê(5ov T&V fcodt'aw xvxkov

, agog r}v ai axQi^flg Tt&Qodoi, rtdvrcov VOOVVTKI,

OS afadyGiv Tr\v ccvTyv yivetiftui ndv-

TOT Tl] CCTtO TiVOQ falCpCCVffas T^S Y^S) TOVT&TLV T^S

10 Oll>G)S t&V OQ(DVTG)V) 7tl TO XVTQOV

paA,ho[ivr), ngbs r}v ri (paivo^v

QBlTKi, dhh<X OTCiV [lV XCCTtt XOQVCpriV TjTOV

)TOT [lovov [iiav xal tv\v a,i)xr

T^V dno T TOV XVToov Trjg yijg xai Tijg

15 ofa&s TOV &&QOvvTog 7tl TO xwTQOv T^g 02,tjvr]g xal

TOV ^cpdiKKOV xf}aM.o[ivr]v ,OTCCV $ anovsvsvKvia %

07C(D&dlJ7fOT TOV XCiTCC XOQV(pr}V T07COV, dltttpOQOVg T

Tag %M6ig T&V 3tQOXi[ivcov

xal dice TOVTO TTJV (paivo[iwr]v rtdgodov ^ TVJV

20 yivBGftui Tr] dxoifet Jtgbg aMag xal ahhag &6ig Tijg

aoiivr]g T&V did TOV XWTQOV Tqg

avdhoyov Talg Jtr]A.ix6Tr)6i Tcbv vnb

TK)V [JlV

1. o] ov D. 2. pri] -r\ e corr. D 2. 5. ccvdv,ri A, corr. A 4

.

^ff] TTJS yiis rovTSOTi TOV ^cpSwAov 8ia TOV V.KVTQOV r^g D,corr. D 2

. 8. yiyv0&cu D.'

9. rovrtcm D, comp. B. 10.

TOW] 6- corr. ex a> C 2. 12. aU' D. 77] om. D. 13. r}]

D, % r) D a. 15. xat] corr. ex vard D 2

.

'

20. yiyvEGdai D.

rri'v C, -v del. C 2. &Gtis v.ocl aUcc? D. 22. ccva-

D. nt\kiv.oxT\6iv B, TITÎY.QXJ\IGI D. 23. sy-nXtjosmg C.

24. Gvî^Tf]Y.sv D, -v del. D a. sntityscov A, corr. A 1

. iv.-

fatipscov yivopivaiv] om. B.

MA0HMATTKHS STNTAgE^S A'. 267

VTtb rfjs <y&r]viaxi}s vTtodQo^rjs xal

ijris E'lLTtfarovGa ELS rov dnb rijs oifjs&s

XG)VOV TtOLEtrai rrjV ^%QETUtixorrjew, [irj xavra%rj ravras [itfrE rots

rots %Q6voi<2 coGctvt&s aTtorsA.EiG&ai, pyre 5

di' as SIQIJXCCIISV ccfoiaS

rijg Gshrivrjs [irjts Kccra rcbv avt&v {ISQ&V rov

rowvrrjv dicccpogav EX t&v

Zv rov yi,vo[iE'vov Jtsol rr\v GEhtfvrjv Extent- 10

V rtd&ovs p) (3VintccQccA.appdvovros rqv rCbv do&v-

rcov ofyiv sis inv ufafav fov (tofl&Mfyiavo

yccg fj Ê^VYI ndvrors VTtb rrjs

EitEidav xccra did^LErQO

rbv {LEV ukkov %QOVOV cpccivsrcci, JHLLV ohr] 15

dice rb TC&V rb 3tQo6A,a[i7t6[ivov ccvrijs

apcc xal rîiv rorE rtccv TtooGvsvEw,orav

$E ovr&s diaiiErQrj&f] co6rs ELS rbv ri\$ 6xici$ ri\$ yr\

XCbVOV EpTtEGElV XQV CiVriltEQlCiyOÊVOV CCEL X& ÂtCO,

rors yivErai a<p&n<5rog avahoycos fccis rijs EiMtrcoGscos 20

Eiti6xorov6r]s rijg yris rats fov rjMov

xard ndvra rd

3. itKQdlivGBcos C, corr. C 2. 4. rccvrus] corr. ex rag CCVTCCS

D. 5. ^LIJT (alt.)] corr. ex ^ D 2. 7. /u-rjrt] corr.

V del. TJex (ir]d D 2. Post KVT&V del. TJ C 2

. rov rjlfov [itQobv D.

8. cpaivopsvrjg] D, cpatvo[iV(av ABC. 11. 6vvnciga'ka[i^d-VOVTOS A, Gv^nsgi.'kci^Kvovrog C. OQOVTCOV C. 12. GvîTtrm-

-eg in ras. A 1. 13. cre&ifi/q] -e- in ras. A. 14. KQO-

C, corr. C 2. %ara] fort. V.KTU rr\v xara. 15. TOV

mg. D 3(v.Eiptvov add. D 2

). i]piv] -t- in ras. D 3.

16. 7iQocluiin6pvov~] -p-jiopwov e corr. D 2. 17.

-ft,- in ras. D. 22. TO] supra scr. C 2.


xal rots pey&ftffy xal rots r&v diaGrdtiscov

ravra dfj nabs rqv xa&6A.ov sitfaKetyiv r&v

roTCov rijg tffA^V^g, AA' ov r&v yctivo-

5 [isvcov, 0(fL^,6vrc3v jtccoaA,a[Ji,(ldv6ft'at, , sitsidtfitsQ xccl

to Tsraypsvov xal rb opoiov rcbv ardxrav xccl avo-

dvccyxatov avsi'rj

jtoovjtoustGd'cci, rats (J&v &k-

jQiJGsGi cpa[iv prj dstv 6wy%Qrj6&cti, r&v iv avrcclg

dia rijs otys&s i&v ryaovvr&v10 /iaVov, [novais & ts r&v sxAefys&

v avrats ovdlv ngbs rqv r&v roncov xccrdhrjilHV 17

fiil>is 6vppdM.rai,' o yaQ av r^îcc rov dice ufacov

rcbv fydicov 6 ijfaos X%G)V fbafax'rjraL xccra rbv

li6ov %aovov rrls bctefyftogi w co rb rijg 6J.rjvrj$

15 xvroov vnb rov rov tyiov xara [lyxos dxoifltbs &$rcc dLa^roftrcct., rovrov dôv6ri rb xara

(p^t xal rb ri}s GfAtjvrjs xwraov nabg

xara rbv avrbv [i6ov %QQVOV

ft'. Jloi

20 *Ay OICQV fiv ovv rrjQtjGf&v rd 7tQi rr^v

rovrov xccrd rb rvncodfs

1. [iy8&6iv] -v del. D 2, [isys&eGi B. 3. 8i] itgog] -77 n-

in ras. A. 5. snsi-d^TiSQ] -17- in ras. A. 6. rfrctyptvov] -y-in ras. A. avo[ioicov] -co- corr. ex o C 2

. 7. ngovnoKfiod'ai]-v- in ras. 2 litt. D 2

. 8. cpaîsv fi^jj corr. ex cpKpev C 2, -fisv

(i- renouat. D 2. dstv] -e- corr. ex

r\in scrib. C. 6vy%Qf]Gd'ai]

-y- in ras. D 2, -fj- corr. ex t C 2

. 9. TT}QovvtQ>v~] seq. ras. 2

litfc. D. 11. avrccis] rccvraig D. tiardlirflpirV] corr. ex. ex ft C,AC 2

. 13. fuî'cxrjrat] -77- corr. ex ft C, ex e D. 15.

xov TOV~] A, rov BCD. 19. 0'] mg. AC, om. BD. XQOVOV C.

20. ol'aiv] ofioicov C, cup' ol'cov [i8V ovv mg. C 2. 22.

BD, sed pr. c eras.

MA0HMATIKHS ZTNTAEE&2 A'. 269

rbv ds rgoitov, xa&' ov is 01 Ttakaiol rats rcbv aito-

ov 7ti{loA.ats %gri6avro, xal xa%? ov civ

r&V TtQOS rd (paLVO[lVa

5

litsl toivvv av&iiKh&s [ivXKTK rs prjxos KOI TtAccros xal

rbv dice [ifacov r&v Jcodtov xvxAov aid dtQ-

pijr agog rqv xara rb Tcharog avrov xagodov

%G)Qls $ vi}S VQ6G)S TOV rijg avcs- 10

avrr}s djtoxccTctdratixov %QOVOV xccra rb dvccy-

XKLOV ovd rag r&v akk&v 7tQi6dovs hafetv oiov x

Jcv ywoirO) xara jtdvra [nsvroi ra [iQr] rov ^cpdiaxov

rd r y,B6a xal ra piyiGta xal ra skd%i6ra dia rcbv

xara [iQO$ rrjQiJGfcov yaiverai xivov[if

vrj xal xara 15

ndvra ra H,QYI poQiordrr] xal von&rdrr] xal xar

avrbv rov did [ifacov r&v tydtov xvxhov

01 nakaiol iiafrr][iari,xol %$

o6ov ndvrorefj 6e^vri rb foov xivrjfi-iJGErai, xara

rovrov povov rr\v dvcoâîav anoxa&i<5rdvi,v 20

dvva[ivov. 7taQarL^îVOL di]

fao[jiv airLag ^

{iiqvcbv didtiratiis t6o%Q6vi6$ r yivoixo Tcdv-

ror rats rov i'Gov TC^tjd'ovs dia6ra66i, xal i'6ovs

xvxhovs itQi%ot, xara [lyxos r^roi o&ovs ^ [ird nv&v 25

4. v%QriGT6zQov~\- corr. ex o D 3

,-ov mut. in av D 3

;

iQT}6r6TQQv B, sed u eras.; ^v%ccgi6r6rKôv C, corr. C 2

.

ftu] mut. in Ttotov^sâ D 3. 8. TOV] AB 2D 2

,r&v

BCD. KMov] corr. ex v.v-A\tov D 2. alsf] AC, foi BD.

9. TO] om. D. 14. ra. re] noi ra. D. 16. itavzcc] om. BC.Y.UI (pr.)] rs KKI D. vorLcordrrf] D, vonordrri ABC. 17.

pscov C. yivovofjLsvr] D. 20. novov] om. B. 21.77']

ds D. 22. a.trias\ supra scr. D. 23. yivoixo D, corr. D 2.

bko6%SQ<3reQOV [lV OVV 01 STt

rbv %QOVOV rovrov vns^dâvov slvcct,

V <p7te xal yr'

dice rotiovrov yag fyyitiru ecb

v d7tOTEA,ov[ivovs

[iv tfA'fr, nhdrovg ds

(Spa xal ETI,, oGccg xal 6ij

KVXhOLS SV 1& 7tQOl,Qr][lEVG) %QOVG)

tt3toxara6Ta6G)s ccvrcbv TCQOS tovs

&(QQOviiEvr]s. xdl.E6av da rbv %$6vov rovrov

10 ftSQiodixbv &s itQ&rov sis [iiccv aTtoxardGrccGiv ayovra

rds dicccpogas t&v xiviJGecov. xccl wcc

avrbv 6v6rt]Govrai^ srQiTtkttGiaGav ras

y' fj[iQas nut 6%ov fftifQcbv dgi,d'[ibv ^ fttyvz, ov EXCC-

fadav &zhy[t6v' xal rcc ahku df opoicos TQi,7tA.G)6ccvrs

15 6%o

[iVxccl En,, o0Ks xal 6 ijhos eitihaiipdvEi rolg vd

A/3.

psvroi Ttdkiv 6 "l7titaQ%o<3 ijfa'y&v dito rs rtibv

20 XahdaVxcbv xal r&v xa& favrbv rrjQtJ6C3

fyovra ravra dxQip&s- ditodixvv6t,

cov Eê&Ero rrjQiJGEGOV) on, 6 Jtotbros dQi&[ibs r&v

3. xat] om. D. tooov D. 4. $s] 8' D. 7.

(iEV(p\ KQOKeipsvo) D et supra scr. B 3. *"*] f8 C, T seq. ras. 1

litt.' A, r A^, dipoigov supra scr. D 3, 1$ B, h aUco I vfi o

xui cdrifi'ss mg. B 3. 10. n^fbrov} corr. ex ngbg TOV B 3

. 12.

UVTOV r)(ieQ&v D. GVOT^GOJVTCCI] B et supra scr. D, cvaTâovrcct,

ACD. TQl1t).K6lKGKV~\ TQl7tld)6KVTS D- 13. %at] Om. D.

] D, iiu D 2, fluids U D 3

. 14. l&iUwov corr.

ex l&leiynov D 2. TU aUcc Ss] T&Ucc 8' D. 15. ds] $' D.

16. ? c - 19 - êSff corr. ex Ifrsv A 1. 21.

MA0HMATIKHS STNTASE&Z A'. 271

di oG&v itdvTore 6 ixfamnxos %$6vos iv

foots iirjtilv xccl iv foots XiinljfjLatfiv dvccxvxÊirat^ ku,

6rtv xal enys: r\^L8Qcbv xal Alices cooas i6rmsgivi]S) iv

acts ^vas [iV aitaQriôêvovs vot0xiyd(?if, okas de

drtoxarciGrdGEis Sepoy, q)diaxovs ds xvxAovg 5

OIQCCS f /.' tyyiGxa, o6ag xal 6r^

xvnkovg keCitEi, ndkiv cos tf}S tt

CCVT&V ngbs rovs anAccvets UGTEQo&sv stigfaxsi, xcci rbv ^VLKIOV (JLE'GOV %$6vov

rov rtQoxi,[iEvov r&v fiiiegcbv nAyd-ovs 10

rovs fititfc pypas fiiLEQ&v 6vva i

y6[jLvov K& Ace vi]K

iv [iv ovv TGI ro6ovrc3 %QOVG) rccs cforo EX-

EAyviccxris inl EKkE

dicccfrccGEis artodEixvvEi,, &sTO ttTtoKaftiGrccGftai rr^v <xvco[iccMccv ix, rov itavrore dice 15

rov rotiovrov %QQVOV rovs * rotiovrovs privets

'xccl rats facus xccru

l'6as 7tiA.tt[i(}(Jcv6<d'cci, polkas tvfi /_' <xxoA,ovd"G)s rats

rov ijAiov Gv^vytcus-

EL $ ns pf} rov ana ixkefyEGis 0E^vt,axijs iitl 20

ctQi&yiQv r&v nqvcov titifyrofy, ILQVOV de rov

O tivvodov tj navtizkrivov iril rqv bpoiav

1. IxAetTTTtHog] s- ins. A 1. 2. firioi'v] -v del. D 2

. v.ivr\-

HUGLV~\ nivri- corr. exftrjorfc

D 4. Ji] in ras. A, [ivQiddcov D.

3. tcxiv] corap. B, -v del. D 2. >tcu'(pr.)] t|3

nctl D. rt] corr.

ex ITTJ B. 4. ,tfffg] I).G^ C. __ 9. SVQLG^L] -ft inâs. C.

tov\ tr\v A, rov per D. 11. vrj]

B et e corr. D 2, VT] AC.

13. &cxAn/>u> D. 14. SiaGTKGfis] -i? in ras. D 2, supra -GT-

ras. &Tto8wvvi\ -et in ras. A. Sfiôv] corr. ex dffia D 3.

yivsG&cci C, yevEG&ctt, D. 16. rov'] om. D. roGovrovg]i'covg D. 17. ras I'GK? D, corr. D 2

. 18. fioâg] ante -Q-ras. 1 litt. A. 21. en^rroT in extr. lin. A.

EVQOI civ en ijrrovcc rbv dxoxaraGranxbv rijg re dvco-

[iaMa$ xal r&v ^rjv&v doi&nbv Aa/3cbv rb [tovov avr&v

xowov [isTQov STttccxciidexaToV) o Gvvdyei,

GvcC) dvcopaMas de a7toxara6rd6i 6%$. ovxen

5 6 3tQoxi[ivos %QOVO$ VQi6xro xccl tr\v Kara

drtoxardGraGLVfy yaQ avrajtodoGig r&v x-

rag dia6ra6is povov rov re %QOVOV xal

r&v xard ftijxog TtSQiod&v q)atvro 6c)ov6a rag 106-

rrjras, ovx&i, $ agog rd peytftvi xal rd$ 6[ioi,6rriras

10 r&v btitixotifescdV) dcp7 &v xal rb xAdro$

fidvercu.

ijdrj pivtQi ytôxart^^vov rov rijs

ditoxaraGrarwov %QOVOV 7taâd'îvos JtdAiv

dta6rd6is iirjv&v 6/iOtag xara Ttdvra rag axgas %-

15 AefyfiS %6vrcDV xal rots iieydfteGi, xal rots %QOVOI,S

rcbv 7Ci6xortJ6G)v ,iv alg ovdlv eyiyvero didtpooov

itagd rr\v dvoâUav^ &s &i& rovro xal r^v xard

TtAdros ndoodov d7toxa&i,6rau,vr]v

xal rrjv roiavryv itEQiodov dytaorôêvrjv iv

20

6 [iv ovv rooTtos, w Ttybs rag roiavrag xara-

fyatftiavro oC nab fni&v, roiovros rig yv> on,

de ov% dxhovg ovd' fvitootfros ,(UAa jroAA^g xal ov

rrls rv%ov<5r]s dfdkitvog 7fL6rd0os^ ovr&s av xaravorj-

25 6ai[iv. wa ydo d&pfv dxyiflcbs fcovg aAA^'Aotj rovg

1. IJTTOVCC xov\ r\trov D. a.Ttoy.ara.G'tiY.ov D. 2.

fiWV C. 5. qVQlGKSTO D. 7. TtQOS tU<a SiCiGtOCGSKs] Om. C.

jLtovov] avT&v fiovov D. 10. aqp5

] e corr. D 2. jur/J om. D.

13. ccnoKK-cccGtiyiov AD, corr. A 4. 15. psys&s6i \ -s&eei,

renouat. D 2. 16. syivsro D. diccyogciv C. 18. dsfawaiv]

-v del. D 2. 19. fATjai D. 20. ?gxy] AB 3

, swy BCD.22. e^tyaro A, corr. A 1

. 23. ovds C.

rav 8ia6rd<5eG)v %oovovg voi6K0d'CCi,.)ito&TOV îkv ov-

dw bcpskog TOV roiovTov[irj

KK\ TOV f}Mov TO nagcc

rr^v avopaUav didyoQov vj {lydsv t)TO ctvTo itoiovv-

Tog xatf xccTQCiv T&v dt,a6Tcc6O)v. i y&Q pri rovro

$ rt,, &$ gyqv, naga xr\v avoyia- 5

civrov didgjogov, OVT ambg gdrcu iv rots

faces rtfOLdoonag n^noiri^vos ovrs

<xv yaQ hoyov VXV %aTQdiatiTK6G)v ftfO

1

'

oAovg xccl rovs fcovg

%aovov$ jt^cc^dvrj TO rftiiGv TOV EVLCCV- 10

6iov IQOVOV, v d TGI T060VT& Xi,xxivrjtivog 6

idtfTCiGiv aitb Tij

,XCCTCC $

aitb Trig KCLTCC TJJV IIao&voV) KCCTK [iV ri]v TCQQTSQKV

ka66ov 7iiA,r]cpG)g 6 rjhiog l6tai TOV r][it,xvxMov poi- 15

g&v d [_' d' fyyiGTa, xaTa $ TYJV dVToccv

iftMKVldUov Tcctg avTCilg potocug' &6x xccl Tr\v

v Totg faoig %aovoi,g fteO-' ohovg xvxhovg xccTa

TJJV naoTaccv did(3TK6iv Bitsi^fpdvaL {loioccg QO dr

,

XCCTCC $ TTjV dVTOCCV QTtd i! $'. dlV OVV CpCC[lV 20

TOVTO ito&Tov %iv Tag dict6Ta6ig 7tol TOV ij&iov

6v{i(lf}r]Kbg TO r^roi ohovg CCVTOV xvxhovg itîiîv r)

XCCTK [LV TY]V TQCCV TG)V dlCC6Ta(5G)V TO KTCQ TOV

aitoyzCovi

r\\MKVK/

kiQv iiti'kapft&vBiv, XKTK $ rv\v TaavTO (XTtO TOV TtEQiytLOV, 7J

CiTtO TOV CCVTOV T^tj^LKTOg 25

XKTO(XV TG)V 8ltt<5Ttt6WVJ]

TO

5. yi'voiTO D. TKXQK] pr. a corr. ex s in scrib. D. 8.

SHUTSQCCV D. 9. oiovg] -4- e corr. C, ittovg Kvuhovs D.

10. 7td(X[Lpdvl CD. 12. 7lQ03TriV~\ TtQOTSQCCV D. 14. T7^(alt.)]om. D. 15. 7tsiHr](pd>s]

-- ins. A 1

,-si- in ras. D 2

,-I- corr.

ex d D 2. 16. /.'I v.cu ~L MI D. 19. Ttr\teiyhai D. 20.

iv] corr. ex CCSL D 2. 22. avrov] corr. ex ccvr&v D.

xarQG)d'v r/tot XQV aitoyeiov r)rov 7tQi-

yeiov Kara re ri\v itgoregav eKêityiv rrjg eregag dia-

6rd6&g xal Kara rr\v devregav ri\g eregag. ovrog

yaQ av [lov&g rjovdsv

T}rb avrb yCyvoiro diacpogov

5 Ttaga xr\v av&naMav avrov KCL& sxarsgav r&v dict-

,(Stirs xal I'ticcg rag Jtikcc[i/3ttvonsvag yivsG&ai

ijroi dA,htjA,ccig 7)ual aMtfAaLg xal rcclg

opahcctg.

dsvrsQov ds fiyovpefta, detv xai itsgl rovg dgopovg10 ryg Gshtfvrjg rr\v d{ioiccv iitfara6'iv TtQiEiG&ui. rovrov

yap adiaxQirov pe'vovrog vds%6^vov it&Kiv (pav

rb ncci rqv (jfhtjvrjv jtoMdxig faag 3tQicpQiag

prjxog v rolg fooig %Q6voig zitikaiifiavsiv dvva<5&ai

{irj Ttdvrcog Hal ri\g avoâîag avrfjg d7toxa&i,6ra[ivr]g.

15 <?t>ft/fy'<?r<u $ rb rouovrov, iav re Ka& SKarzQav r&v

dia6rd6G)v dnb rov avrov Kara 7tQ6(5d'6ivfyrov av-

rov Kara d(paio6i,v daopov TtOL^rirai rrjv dQ%rjv xal

^ 7tl rov avrov xara^yrj^ edv re Kara [ilv rr\v

rf

oav aitb rov [i^farov doopov aQ%o[ivr] Hxl rov

20 sA.dftio'rov doopov Karakriyri, Kara d rr\v ersQav dnb

rov eka%i<5rov doopov 7tl rbv iisyiGrov, edv re rb

i'Gov aitB^Gtîv xarQcod'v aito rov avrov &a%i6rov

daopov o re ryg eregag di,a6rd<5(og jto&rog

xai 6 ri]g ere'aag e6%arog. xa6rov ydo rovrav,25 eav Gvyipaivri, 7}

ovSev rtdfovrjrb avrb noiêi Ttaod ri]v

4. yivoiro D. 5. r&v] bis D, corr. D 2. 9. d^] 8' D.

10. opoiav] 6- ins. A. 11. 7^9] seq. ras. 3 -j- 2 litt. A.

]a- in ras. A. 16. KCCTO] corr. ex nctl rd D 2

. 17.

nonfi6i]-tai~] TtQir\ta.i corr. ex aoteiVcu D 2. 18. xaraArjyft D.

20. dQO[Lov~\ om. D. 21. dgofiov] om. D. TOV] TO D. 22.

UFOV] i6- e corr. A 1. ib^fwrm] -we- in ras. A. 25. r\ (pr.)]

om. D. avro] bis C.

MA0HMATIKHS STNTAEESS A'. 275

v avryg didtpooov xal dia rovro rag per Kara

MpfaiQ faces aTtfoyd&rai, , r^v ds av&yiaMav

dxoxaraGrrjfai. ovdsv aoa ovds rovrov r&v

%iv dsl tag 7taQaha[ij$avo[ivag dia-

el iifMrjGovG'iv avro&fv rbv K7toxctTcc6taTt,xbv 5

. rovvccvrCov d' av

dwccpevccs ,sav py oAat neQify&vrai rrjs avo-

K7toxccT(x,6rK6Ei<3 ,iQvrititiv orav ^ ^6vov anb

dgopcov rag KQ%K$ f^to^v, AAo: xal 6(p6dga 10

rjKara ps^d'os r\

Kara dvvaniv, xara ft-

&$ orav xara êv tv\v srsgav didtiraGiv

anb rov sA,a%i6rov dgopov aQ%r}rai, KKLp/ty

siti rbv

lifyiGrov Karakriyri, xara ds rqv ersgav, orav anb rov

psyfarov &Q%Yirai xal ^ Bid rbv hd%i6rov xaraAtfyy 15

ovr&s 6rai, rrjs xara

oAeov xvxAcov artaQri&iiwcov ryg

orav [idhitira reraQrô^Lov fvrj

KKI ryia

Kapftaviiitai, dvtil ror rotg Jtaoa

avG}[iaMav diayogoLg aviG&v r&v dia6rd6G)v iftopt- 20

vov xara dvvaîiv (Jf, o>g orav

r&v dia6rd6&v aitb rov {i6o

anb rov avrov df ftftfov, AA xara {isv ryv

cuto rov nark 7tQ06d'6iV) Kara d rr^v roav aitb rov

dcpaiQ6iv' xal ovro yao rb nfalGrov diofaov- 25

2. aitEQydasrui D. Si] 8' D. 4. TtaQc

-fta- ins. in extr. lin. A 4. 5. fifyUrjtfovffn'] mut. in

C 2, pr. I del. D 2

. <broxcmK<mx6v D. 7. ocpsttopev BC.

(fccvf]6ca B C. 9. ci7tov.oiTa6ra,6r\g D, corr. D 2(comp.). fiovcov C.

10. dgoiicov 11. diacpOQoov] mg. D 2(netiitvov). 12. V.KTK

ju-f'r]corr. ex psv xara D 2

. 16. itteiGTov C. y#(>] y- corr.

ex G in scrib. D. 23. ftsV] ft'vA, om. D. 25. OVTCQS D.

18*

6iv akkrikozv aC rov ntfxovs facovtffai [idhtira [ITJ aito-

r}s avGjpakiag reraQrôQiov pev vbg

i}xal rgifbv BTtiKaâvo^vov [nag dvG)[iaMag

dv6l rots Jtaga ri]v av&tiaMav d(,atp6()oig,

5 de TrraQ6i. dia ravrcc dy KOI tbvff

Iit7iccQ%ov

rcbv rtccQt,A,r)ii[isvG)v SLS xty roiavtrjv

sxhoyf} ual GwyxsxQqiisvov [isv r& rrjv

Kara fifi/ ti]v snlgav diccGraGiv CCTCO rov (is-

10 yfarov dpopov 7t7toirj6&ai, rrjv CCQ^V xal (i^ exl TOV

ekdftiGrov xaTa7t7tav<5&a^ Kara df xi]v TQav ccnb rov

A.a%i6rov dgopov TtsnoiriG&ai rrjv OCQ^YIV KKI[irj

7tl

rbv insyi^rov xaraTtfTtavG&ai,) dioQft&Gavra de ual rb

Ttaga, rriv rov riMov av&naMav yv6(ivov15 xatroi, PQCC%V ov dt,a rb d' fyyitira vb

QLOV xal pr} rov avrov7}

rov rb i6ov Jtoiovvrog

yoQOV rijs civoîa^Cag KK& xarQav r&v

ig 6'Aovg uvxAovg a'AAeAowreWt TYJV rov fjMov aitoxa-

20 ravrcc elitopEV ov

rijs r&v ttQiodix&v a7toKara6rd6G)v

aQitiravrfQ^ on pera îv ri\g 7too6-

7tt,6rd6G)g xal rov xara rb axohov&ov iiti-

xarog&ovv dvvarai, rb

25 si $ nva xal rb rv%bv r&v xr&i,iiVG)v

3. ciVfopaUag] -pec- ins. in extr. lin. A 4, -s corr. ex -v D 4

.

4. 8vci~\ supra scr. D 4. rots TIUQK rr\v KvcopuUav] om. D.

5.Si~\ supra scr. D 2

. rsrccQGi AC. 6. evopi& D. 7. sni-

D. 8. xca] corr. ex i in scrib. D. 10. %ca] suprascr. D 2

. 12. dgofiov] om. D. 13. xov\ corr. ex TO D 2. Y.UXCC-

Q'ai B. di.oQ&a>6uvTa] -v- in ras. D 2. 15. d']

D. 18. ivteloutivai CD, corr. D 2. 20. $i~\ d' D.

MA0HMATIKHS STNTAEE&S A'. 277

pdrcov TtKQBk&oi, dia^V(3&i^6Tat JtavTanatiiv T^g Irti-

rjTOV[ivrjg xaraAitjfa&g, xal on dvGTtooiGTog 6Tiv

rots 8ioQttrixG)<3 3toiov[ivoi,g rrjv rcbv TOLOVT&V rrjQij-

6G)v xA,oyrjv r\ ttobg TO dxgi,($g jtdvTov rcov ocpsi-

ccvralg vitd()%si,v avrcatodoGig. 5

*yovv XT&i,iiVG)v 3tQiodtKGbv Kitoxccrccdrcc-

XCCTK rovg vjtb rov(

l7t7tKQ%ov yfywrjiiwovs iiti-

ovdfvl

vtrai, dityv6yiBVYi r^ cd.y&iccg, i\df ryg av&iicdtccg 10

xccl rov itAdrovg aZiohoyq) nvl dirjiiccorrjuwr], &6T xal

XCCT<X TO <X7tA.OV6TQOV XCCl V7tOQt,6TOTQOV

od&v, ccg vftvg K7todLôîv apa Tfi

xrig avG)[iakiccg nooXT&i,[jLvoi, 15

TCQ&TOV dt,d TO Jtgbg TU Qiig v%QT}6Tov TK Kara

xwtJuciTcc iiijxovg r

ccg xal n^drovg dxoAov&cog Totg

xal ra X rife artodL%&r}6oiivr}g avrcov diooftcbfaog 20

2. KccTcdriiiipfoos C, corr. C 2. tan D, comp. B. 4.

97]

ins. D 2. 5. atccnodoGig D. 7. ysytwrjusvovs AC, pr. v

eras. A. 8. vytw?] C 2D, vyftwg ABC. 10. SLS^VG^VJ]

mut. in distysvîLivT] A 1. rj]

corr. ex si D 2. 12. yeyovevcci]

corr. ex yeyovev D 2. 15. itQ06K&[jivoL D, -6- del. D 2

. 16.

rd (pr.)] corr. ex TKS C 2,TO D. 18. &Y.olovft(os\ pr. o in ras. A.

19. (knoKCLrciGrwoig D. 20. cc7toSi%d'r}6opvi$ A, corr. A 1.

D.

y. Ilfol rcbv Kara, psgos bpah&v

'Eav roCvvv rb artodsdeiyiisvov peGov rov

o v&rj i% ~i

rag rov vbs

x xal rotg ywof&otg Jtao6&&[iev svbg xvxhov uot-

,

r

&>opev, as sv rtp svl pyvl iisti&s % Gshrfvy

xara ^TCOS MOIQCCS md- i xy a xdJ3

A v't,

ravras sitiiieofaavrss sis

10 rov [irjvbs VJIISQCCS %o(iev fftisariGLOV psGov Xivrj[ia

[loiaas Ty 1 A^ v^ Ay A A syyitfra.

rovs <?# KVKÔVS vfjs

itl ras rov evbs xvxhov {lotoccs

poio&v 11 ygo|Lt. ravras [isofaavrss sl>$

15 yivopEvas f){iQKS rcw <5vcc [irjvcov gvift I ^d va jif

lisv xal avG)[iccMas rifieotjîov [istiov xtwj[ia [loioas

y vy V$ xfr faq faq.

t&S f^KY rov ftAdrovs aitoxarccGraGeis

ra rov

1. y'] mg. AB, recisum C, om. D, xecpdlcciov y' B 3. 3.

rot) rjMov H&GOV rîEQ^Giov mvrjfioc D. 4. o] om. D. ty]

supra scr. A 1. ^yy>ra] om. D. 5. v ^] vj\ D, diremit D 2

.

6. yfvoftfvot?] -e- corr. ex t in scrib. D. nvnlov] -v in

ras. A 1. 7. ^|o;fv] seq. ras. 2 litt. A, supra e- ras. W]

f C, om. D. 8. xy] x y D. 9. TrôHftftâs] -sV- corr. ex

?]v D. 12. fff^] Igijxoftff D, dmx/ ins. D 2, mg. c^ D 2

.

TroivTrZactaaavres D. 13. xvxZovg C. 14. (JLOLQMV] ftA CD.

ft C et supra scr. A 1

,om. AB, f @ e corr. D. 15. yivo-

corr. ex ysvo^vag A. t>va] ~G seq. ras. 2 litt. D, vcc

supra scr. D 4.

/~^jj] ^y tp BC. 16. xa] g C, del. C 2.

18. 6/iotcog] supra -ft- ras. A. Deinde xat add. B 3

.

O supra scr. D, r D 2. ^xy] -y in ras. D 2

.

aty

(lOiocbv ft JpGTt. rccvras ^iQi6avrss sis

t tg

ras t&v jvvr] [irjvcov yivo^Bvag rjpzoas ft- ,aoo vr\ vr]

y x '|oftv xal nkdrovs fi[iatf6iov [i6ov1 <x ^ a.At/

1

ftt ttr.

Ttdhiv dnb rov rijs 6A,tjvr]s xara

rb rov iiUov

if} LCC K% fta K L v&. dice [isvTOi rcbv etps^fig, as

ftiiv TtccQahrjcpd'rjGoiiev&v sis rfv roiccvrrjv

scpod&v [cap. YII] TO {isv rov ^KOVQ f}[iQrj- 10

%s8bv ccTtaodAhaxrov VQi6xo[iv red itoo-

xccl rb Tys <x7to%fis drjAovori) rb $ rijs

gkarrov poiQcas oooo lajilg A^, ess

v 1/y y ~vy v^ it, va v&, rb $ rov ithdrovs ntetov

oooo ^ A-9- 7^, cos xccl ccvrb yCv^&ai [lOiQ&v 15

xara ravra drj ra rftiforjcJia Aafiovrss ftfv Zxdtfrov

rb flxoGTorsraorov efcofisv aoiatov ii6ov

xovs ft^v {lOiocbv o A/3 v x xz x/y ft? tf,

ds poiQ&v o AjS AO- ftd v ftd A^- vj A, TrAarovg df ftot- 20

o Aj> <? >cd # A/3 sea A/3 A, cbro^g df [lOiQ&v o A

1. ji

y] ^

c<rB, pvgiddas supra add. B 8

.

y^<] - e corr. A._y |3(73r mg. D 2

. 2. apo^ C. HVQL tg ^90^ mg. D f.

3. x] om. B, xf supra scr. B 3. 4. ty (alt.)] i- ins. D. t] nrj

D.

8. J\\LIV wg Zcpaptv D. 13. ju-ot(>atff] comp. ABCD. oo(pr.)]

in ras. A; pr. et tert. o e corr. D 2. ytVccrihu] -t-inras. A. 14.

LQ&v] comp. ABC, [ioiQa$D. 15. ju-ot^atg] comp. ABC, poiQasD.o(pr. et tert.)] e corr. D 2

. yiyvsc&cci D. 17. ncc-co] KKI A.

18. SLKOGTOxeTUQTOv] K j D. wQcciov D, corr. D 2. 19. ftot-

D, comp. ABC, ut etiam in seqq. 20. Ifi] -fte corr. D*.

21. <?] ins. D 2. I (alt.)] seq. ras. 1 litt. D.

JM? AS jityx /Ltd vf A, tgiaxovtaxis ds Tt

a, xal acpshovrsg xvxkovg fôpev pqvwfav [i-

ds iioigibv Aa vZ vrj rjvs v& A, 7cldrov

AS" v/3 ft-O1 vd wrj Irj Aa, jcoî5? ^ IIOIQ&V

rjv& A.

TCC fip,Qri6ia TtokvTtkaGiKtiavrsg exl rag vov

Eviuvtov fjiispas T%e xal c

viav6i,ov istivv 7tov6iav

10 yioiQfbv $%& Kfi jitg ~iy v A/3 A, d

ytrj w \ xij fia ly v, ithdrovs

?toi,tf<5ccvrs ra wiavtiicc dia TO

<bg

15 r$ o'Aovg xvxlovs

gvz ~v% id Ag xft I A,

Qvg v & ft-91 tO1 A A, asropjg de yioigwv goy

t/3 5cg A^ ^ 7 A.

20 diaygatyoium ovv, &6itg xal inl rov Âtov, xccvo-

1. fty] |x- in ras. D 2. 2. xvxXovg] x D, x D 2

. 4. â]

-a in ras. D 2. 5. \d\ \ seq. ras. 1 litt. D. 6. fZ rj] /Trj

BCD, corr. D. v-fr] corr. ex vp D. 7. TroUajr/lactaffavrfs B.

8. xat] om. D. 10. [IOLQ&V (utrumque)] comp. ABCD. 11.

TTTf] pTtT] BC, 9- eras. C. ^] fzj BC. nlarovs] -e ins. in

scrib. D. ju-ot()wv] comp. ABCD. 12. xs] x- in ras. D.

K7to%f)s~\ corr. ex no%f)s D. /^(H9<m>] comp. ABCD. 13.

TO] om. C. 15. oxtrooxatdxafTTjîôg D. 16. fisv] om. D.

jtt^] seq. ras. 2 litt. A. 17. ÔIQ&V} comp. ABCD. K?]

seq. ras. 2 litt. A. x(3] -|3 e corr. D 2. 18. jnot^wv] comp.

ABCD. p?s] corr. ex g^ D 2. v ^] r^ ABC. 19. tp]

-|3e corr. D 2

.ZJjf] -(3

e corr. D 2. 20. dictyQatpcoiifv CD 3

.

vag y ml tirfyovg pv itdfav ^s^ GeMdia ds xaO-' exa-

tirov 8' rtiv tie <58hidi&v ra pv itQCbra itSQiQei, rovg

%QOVOVS snl [isv rov ngcorov xccvovog rag

ccs, iitl de rov dsvregov ra err} xccl

rag coQCig, enl ds rov y' rovg [i^vccs xal 5

Jtdfav rag r\yiQag, ra ds houta rstftiaga rag

oiKSiag rcbv {loiocbv Tcagad'^sig^ ra {isv dsvrsoa rag

rov iiijxovg) ra ds rgira rag r^g avonaMag, ra ds

reraora rag rov Jthdrovg, ra dl Tte^iira rag rr^g

axo%rjg. xaC etinvfj sx&sGig rcbv xavoviwv roiavrrj' 10

1.p8]ji,ev

C. 2. t&v~] TOO C. 3. TtQmrov] a. B. 4.

B. 5. Tovg] rdg C. 6. tsGGu^ci] // corr. exA D 2

. 10. &nowe] corr. ex footfe B 3.

It

O oJ O oj O

I* 7|

13

oooooo

20*

-s-g

x* -"<fc a> *

^ U> u>

Is? 8 I-

MA0HMATIKHS 2TNTA3E&2 A' 283

O *I O *< O O"<0XO,o!Oxio>JO

*o 'o * V **51 "<*> *>^ X cJ* >

m- ot^co =L

O "< I* O * ^jo

2 *

<*>

.

QO

.

3 a

Q^T-rt 3 ?> 5> Or

s s

o oe o \<*e o r>e

10 wJ.

"S

.

!/><*>

^0 Jk-^

(jf-4

0"<JO ojootf.Or^o

55 a. 3.

4"& e,5

o < o x o >; o

ff 55il^^!

tit

411-

MA0HMATIKH2 STNTASESS A'. 285

JU>->-r s=-

ir

ox o x o

Ooj O<^ O O "J I O ^ O

<*'*'*

813 55 2 U> l/>

x *

<*> g~

<*!. U>

5L *

1l-l| r

3

8

tOi

5V"4

S 5

1-rs

s? ?

a 8 :*.

US- ?

|

I

o

i

MA0HMATIKH2 2TNTABE&S A 287

o it x o :*. x o

2 5

a3^ 06*

U1 ^ VS S

X* ~

a qe_ x.'o *

<*> <J>

* x a

_ .

ls afl M ^3

^'

I1 -

x *

*\**

a x

1/> <v w

sg-s,

r

o a

\ \

*\X

3 3

t-t?

X Uxfc

MA0HMATIKH2 A'. 289

>.u,

20 .

J.J. X

* =0 <*5 "0

xx ! -Vo ** rhr

??*'

22

x05

~I l

-^ >..

1-

rvv stt

<J> 5 2

t rv

$ 2

*$

OOOjOOOOOO'OOO

9.W

1

1-en

*I a i/> a

8J 1 fc S

1

o 2

o <>: o .^ o i <J o

rv fS-l

MA0HMATIKH2 STNTASE&S A'.

$ S g 3 3

^3.

^ 2

HI

O X|5.

291

g.2.S d d g ^i5

jf * X6 *

O oi O >S O

ill:

2^-

O'XOl'XO'XlO'XO

^/> ^ O

tt

^ x^

*^^

*?

o ^rW >. <

<S-

Q

.

-<y 0.

3, X 5L X

x a oc.

O <<*>

aLx<*><*><*>

x6} K- ss-

9

U- I*I

It 4" 13<= to to to 1


s'. "On xal Bitl rtfg aithfig vrtofteGscog ri\g

vrjg tft avrd (paiv6îva vtoiovGivr\

rs xar*

xai

(

EjtO[lVOV $8 rovroig rOV dsl^KL rOV T6 TQOTtOV KOI

5 rqv ityfoxorrjra ryg GfAyviaxiig dvcopaMag vvv

rbv Jtsgl rovrov hoyxccl itdvrss 6%sdbv oi TCQO f][i(bv

$ xr\ xccra rbv

%gvov aTt

10 rccvrcc dt|o^v, ort noilra,i nvcc xcci dfvrfyav avco-

fj (5^vri itaQa rag Jtgbg rbv

rag

dig v

avrdg r rag Gvvodovg xal rag

15 Ovro $ rr\ raêi rrjg artodi%G)g %()r]66ii&a dt,a

rb ravryv [iV avv rijg Ttgcbryg 6vî7C7C^'y}ivrjg ye

avrfl 3idvror [lydap&g VQ&i]VKi, dvvaG&at,,

$ xal avv ryg dvrQag, 7iidtJ7tQ aitb r&v

x&v xA,fyG)v âî^dvfrai^ natf ag ovdfv

-10 ytvrai didtpogov x rqg naga. rbv ijhiov

iitl d rqg 3tôrjyov^v^g dnodLôraig rov &G)Qri[iarog cqpddotg, alg xal rbv

1. f'] om. AD. 2. ij] ri]v ij D, sed r^v del. 3.

AC, HUT' BD. 4. TOV] TO B. 6. TKvtr\g\ ncti T?)g ccvrfjg BD.7. J] ins. B 8D 2

. G%86v\ 6%ov C. 8. enifapri^res D,corr. D 2

. 9. &nov.ct6t(xri,Y.6v A, sed corr.; ccrtOKccTKCziKov D.

10. SfvTôcc C. 11. &TtOY.KTK6Ta.6is D, corr. D 2. 14. TS

Tag Tf D. Mg. rd$ T Tag ([^ (h. e. cvvodovg) D 2. 15.

g D. unodei&cos] anodet'êcog r^v dwrtgav BC. 18. ccno]

s' ccno D. 19. ag] seq. ras. parua C. 21. sni] -C in ras. 2

litt. D. Ss] -i e corr. D. 23. IKÔVTS? D.

xal avTol rgstg sxhsfyeis Gfhrjviccxdg dsôîsv^ OGOV rs

TO itkstGTov didcpoQOV yivzrai nagd Tr\v ê'tf^v %ivv\6iv

xal Trjv XCCTK TO ditoySLOTCUTov iitoyr\v, d)g Tfjg TOKXV-

Trjg dvcopaMccg xa& avTr)v ^soQOv^svrjg xal did Trg

XKT iltlKV^QV V7tO&S6G)S fbrOTfAoV^fV^ff, TG)V

avTcov rtdkiv 6o{iVG)v (pciivoîBvcov xal did Ti]<3

XXVT()6Tr]TCC V7CO&0G)S> OiXlOTQOV d' CIV

dvG)(JLCifaG)V Tfl dVTQ$ Xttl JCCC^d TOV ijkiOV 6V{lflcCl-

OTt, [lVTOl TO. KVTK Ttdfav KCCi IvTKVâ yiVTCCl, 10

VCC di XdT()CCg T&V XXt,{lVG)V V7tO&0G)Vixav arf 1601 cbtfiv ÂA^'Aotg, &67tQ itl TOV rjhtov $-

oi %Q6voi T&V ditoxaTaGTaGfCdv d[icpoTQG)i'

T KCCTK rr\v dvcoîaîccv xal Ti]g ngbg TOV did fte-

T&V t,G)dlG)V XV%A.OV ^(DOOV(JLVr]g^ dM.(X. XCil &67tQ 15

fill Trig Gf&rjvrjg UVLGOL T&V Aoycov ndfav [lovcov vito-

TCOV ccvTcbv, ovTcog uv xaTavor]6ainv in

Trig xxt,[ivr]g cbrAi} dva)[ittMag Tr^

1tOlOV[lVOl Tr)V Jtl6Xtyl,V. Jtldr) TOiVVV

6M\vri TtoifiTca Trjv itgbg TOV did [isGcov T&V tydicov 20

xvxkov dTtoxaTdGTKGiv Trig agog Tr]v V7toxi[ivr]v dvo-

v, v Totg Itioig %Q6voig dyhovoTi, xciTa plv Trjv

sitixvxkov VTtQfttGiv pti'tpva. r}XCCTK TO opoiov

7tQKpQt,av 6 7tixvxhog dd xivrjd-rJGMai, nl TOV

1. rt TO] corr. ex TO xe D 2. 3. fno^v} AD 2

,

BCD. 6. cpcctvoêvcov] om. C. 7. o6ca6r(>oi'] corr. ex

oixiOTjTa D, mg. yp. otxftoTfpov. 9. T$] bv ry D. ini-

Gv[iaivov6r] D. 10. ftf'i/TOt tec ccvra] (JLSV TQIKVTU C. 12.

Y.&V} post r'as. 1 litt. C. 14. TOV] T&V C. 16. povov ndhv D.

18. a7tU]$] corr. ex aitliog D 2. 19. tniidri] corr. ex faei D.

Taîor] A, Tcc%iov BCD. 20. TOV] T&V C. 23. opoiov]corr. ex OÎOLKV D 2

. 24. ini} supra scr. D 2.

KvrQOV x& ^cpdianti KVK&OV Tvjs vjtb tfjs

rbv BTtiKVKôv ajtoââvo^vrjg ,iitl $ rife Kar K-

Kvroor^ra % plv as^vrj rrjv bpoiav rf\ Bid rov Biti-

KVKÔV Kal 7tl rov iKKevrgov xivrj&tJGsrai, 7tQi(pe-

5 $iav, b ds KKvrQOs 7tl ra avra rr\ 6^tjvri iteQi ro

usvrQov rov ^codianov rrjkixavrrjV) fiMxrj /itov 6rlv

'fjKara (ifjuos itaQodog rijs Kara rr^v avG)[iaMav, rovr-

i6nvfj yi,vo[ivr] rov 6[ioxvrQOv 7tQi(pQi,a rijg rov

itiKVKkov' ovrcog yag av ov [i6vov at r&v Adycov,

10 AA xal ai rcbv %oovcov xaroas r&v xivrjGfav b{ioi6-

V apcporeQais ralg VTto&faeGiv diatic

rovrcov dfj Kara rb aKokovftov avro&w

6 [iv b[i6Kvroos r<3 dia {istiav rav

b 4BF 7Col KtvrQov ro A Kal 8id-

15 ILMQOV rrjv Ad, b $ TCLKVKÔS b EZ 7Col Ksvrgov

rb P. vitoKfiG&G) dS) or {t,v rjv b TCLKVKÔS Kara rb

A, Kalv\ 6A,ijvr] Kara rb E anoyfiov rov TCIKVKA,OV

yzyzvriiiitvri, iv r& facp dl %o.6v0'c6g, rjd 0^,tjvrj rr\v J5JZ,

20 Kal 7t&v%&G)6av ai J5Jz/, FZ. Kal jcd {iia)v <5rlv

TIKara rb QIIOIOV fj

AT 7CQt,(pOia ri\ EZ, aiti-

Aij<p&G) fjBF bpoia ry EZ, Kal tt&v%&G) f]

B z/.

on [iv ovv v r& facj %QOVG) Kal b KKvroos ryv

1. xvnAov] om. D. t% (pr.)] corr. ex x& D 9. 3. ini-

v.vv.lov] y.vy.1.ov C. 5. W] 8' D. 9. T&V] r- e corr. D 2.

11. vno&sGBGi D. Sicc6woivro] -01- e corr. D. 13. TW]corr. ex r&v D. tcav] corr. ex TOV A. 14. 6] om. D. 15.

AJ] -A e corr. D. 8t\ d' D. 17. V.CCTO. TO] snl rov D.18. Vsvr][ivri C. tv\ h 6s D. ds~\ om. D. 19. 8if-lrr

-9-cbg D, con*. D 2. 20. iiti&v%Q-(o<>civ BC. at Ez/] ij

rs

EFJ KCU i] D. 21. Tfjg] corr. ex TIJV C 2. a7cedr}(p&ca

-

22. EZ] supra scr. D. 22. rf?] rrjs BC. EZ] EZ 1 D.

tae&vlfaoi A, lTtisv%fro BC, corr. C 2. 23. ort] post ras. 1

litt. C. fynsvTQOs D, corr. D 2. TTJ'V] rj] seq. ras. C.

MAOHMATIKHS STNTASE&S A'. 297

vjtb A4B y&vCav Tijs TGJV rtccgodov a[KporeQ(X)v VXSQ-xccl ydyovsv CCVTOV r6 rs XSVTQOV KOI

TO aitoyeiov iitl Tijs

J3z/, (pavsQov. TOV-

rov d' OVTC3Q %ov- 5

rog xffa&G) tr\ TZfay fj AH, xal 7t-

ZH, xal

H, dia-

T& HZ, 10

6 Zxxsv-

6 Z.on xccl 6

f)

6 CIVTOS 0Tcci, r<p

ds iv\v V7t6&6i,

f'GTCU, TOVTBGTW 6{lOia KOIJ)

TV EZ.iti yap i'0rj itiriv

fyvjtb

EFZ, TtccQccUyMs ten

*ai e<5TW far] r]FZ TTJ

far] T i<5xi

ZH

agogxal KCCT& 15

TO Z 6rnislov

Z 3tQl,<pQlCC 0Tat,

B^JF y&vicc rfj vito

rZ-Tfj AH [Eucl. I, 28]. 20

xccl r]ZH a$cc TTJ

[Eucl. I, 33], xal 6

Hd Adyog 6 ambs T& Tr]s 4F ngbs FZ.

1. AJB~] corr. ex ABJ D 2. ycoviav] yavicc seq. ras. C.

2. ti\ om. D. 6. E*v.Ei6&(o D. rfj] rfji, corr. ex tf\ A,

Tfj C. 7. JH] in ras. A 4,HJ D. xat 8. ZH] om. D.

7. 3*tge^g4to BC. 9. SiuGTriiLctTi ]xal diccGrijficcri, D. 11.

6] om. D. 12. Z] Z wi bteevx(o 17 ZH ktffprfrta$e f] ZB (mut. in 4B] snl TO & D. 16. TUVT^V] corr. ex

Tciv-tarriv D. 17. OT<U nsQiysQi-Ltt D. 20. ETZ] ZTE D.

i] AH rfj rZ D. 21. xat (pr.)] ras. 1 litt. D. <mv]sWtv ^g xa/ D, -v del. D 2

. r) TZ T7j JH] om. D. ZH]HZ D. 23. Tr^dg (pr.)] nqbs rtjv D.

'

TW] SGTL xti D.

7cd TtaQccMrjkos 6nvfj4F TTJ HZ, fay i<5x\v

J)vnb F4B y&vCa, rf? vnb ZH [Eucl. I, 29]. vxe-

XLTO ds xal rj vnb FJB rfj vnb EFZ fay tiers xal

fjZ 7tQt,(pQl,a T\\ EZ O^lOiCC 0TW. V Ttt fa& CCQO.

5 %QOVG) xa&' SXKTSQCCV rcov vjto&fas&v Kara TO Z

6r][iiov yfyovw ^ (?fA^V^, 7ti8tf7t() avrrj ply xv\v rs

EZ rov IniKVKkov xccl ri]v Z rov IKKBVXQOV itQi-

TO d TOV iiti-

XVX&OV XVTQOV TJJV AF, TO dl TOV XXVTQOV Tr}V

10 AB v7tQO%i}v T^g AFn^bg Tijv EZ' oitfp $i

OTL de, KKV opoioi ftd-

vov (btiiv 01 Adyoi ncd[ir]

faOi [irJTS KVTOi ^T 6 X-

XVTQOS TG> 6[IOXVTQG}, TO

15 CCVTO Tt&klV 6VlLfittCvi, Xttl

OVTK>S

XCCTQCC TK)V

Xttl <JTG) 6(A

20 T& dltt HB6G)V TG)V

6 ABF vital XSVTQOV TO z/ y.al dicc^TQov Trjv

,b $ enfavxhoz b EZ nsQi XBVTQOV TO F, ^ ^

TO Z, xal ndkiv b [iev f'xxfVTQog xvxkog b

H&K 7tol XSVTQOV TO A XCCi

1. s'jm] corr. ex inC A. 4 F] FJ D. 2. vnintiTO 6s

v.a.1 i] vnb PzlB] CCQCC D, corr. mg. D a deleto KQK. 3.i'cri]

seq. ras. 3 litt. D. 4. Z@] f)Z D. tW A. 6. avrr^v D.9. fyxtvTQov D, corr. D 2

. 11. Ss, v.av\ COIT. ex dev A. 12.

firy] ins. D 8. 13. fyv,evrgog D, corr. D 2

. 14. TO ccvro] mut.in to. ccvrd D 2

. 16. r](iLv] post ras. 1 litt. A. 22. r) ds

c&r\vri rb Z] oin. D. 23. ce^vi A. 24. H&K1 corr. exHK& D 5

. 0AM] @A D.

(p

iv rc3

TO tov <pdiaxov xevtQOv fatco to M, to de K'

17 6hrivrj, xal nv%&G)6av xst plv aC A TE,

z/Z, v&dd d a[ HM, KM, KA,d b tils AT ngbs TE6 avtbs v& tils A ngbs AM, 5

xal XXt,vrJ6d'a

vnb AAT ywviav xalf]

<S-

^vri ndhv t^v vnb ETZ, 6

df xxvtQos vyv vnb HM0 10

y&viccv xalfj 0^vrj ndhv

trjv vnb AK.I'Grj aga 6tl

tovs vnoxi[ivovs i&v xivi]0G)V Aoyovg ^ y&v

ETZ y&vCtt ty vnb AK, r)dl vnb AAT <5vv-

rri t vnb HM& xal rr\ vnb &AK. 15

tovtov d ovt&s %ovto$ Kiy<a, oti nakw xa&

XatQaV t&V Vnod"6G)V V tG) l'<303 XQOVG) tfjV I'GrjV

6A.rjvr] (pavri<5tai di&r]A.vd'via, tovt-

6tiv oti itiri titlv rjvnb AA 2, ycovCa tfj vnb HMK,

Infidrj xata [ilv xv\v aQiffiv tils dia6td0G)s sxt t&v 20

anoysi&v ovtia17 ^^nvrl xata t&v AA xal MH v-

&iG)v <pawto, xata dl to t&os snl t&v Z xal Kov6a dia t&v Zz/, MK.

2. WML C, corr. C 2. 3. TZ, z^Z] *ca FZ xai JZ

D. de] BCD 2,om. AD. KM] xal KM D. KA]

KA C, xat KA D. 4. SE] ZE D. 6. XSVLG&COGUV C, corr. C 8.

8. AJF] in ras. A 4. 9. nctiiv] om. D. 10. ^8 SKKEVTQOS]

8' fMevrgos D J,8s XEVTQOS D. HM&] H- e corr. D. 12.

WD. 14. rjj] rjv C. 15. HM@])

&AK D. AK]HM& D. 19. OTI] supra scr. D 2. latv\ D, supra scr.

at D 2. AJZ] AJ- renouat. A 4

(oorr. ex AJ?]. 20. $ni~\

cog inC D. 21. ttpccwf-To tt&ei&v D. 23. OVGK MK]om. D.


df] xarQa rcbv &K xal EZxdfav r] BF, xai 3tesv%d'G) j] BJ. ensl rot-

vvv 6riv, ag f]4F agog FZ, r\

KA ngbg AM^ xccl

itQi foag y&viag rag agog rotg F, A Grjiisioig ccC

5 rtfavQal ccvdAoyoV) faoy&viov 0ri, to F4Z rgiycavov

i& KAM tQiy&VG)) nal VTIO rag dvahoyov nfovgag ai

ywviai facet [Eucl. VI, 6]' 017 KQCC farlv % vnb FZ4ycovta if) VTib AMK. aAAa xal % vnbBzIZ rr) vnb FZ4fay [Eucl. I

? 29] dta rb yta^K^yjôvg slvcci, rag FZ,10 BJ [Eucl. I, 27] foav VTCOXSÊVCOV r&v VTtb ZFE>B4F y&vicbv for] KQCC xal

r]vnb Z4B ycovicc rf] vitb

AMK. vnoKSiTKi ds nolr]vnb A4B Tr]g v

TG)V M,Vr\6G3V XT} VTtb HM TOV XXVtQOV

for]' Kal ohrj ago, r]vitb A4Z for] 6rlv o'A?; T\\ vnb

15 KMH' OTtEQ 7tQOXlTO

g'. 'A7todi%i,g rrjg TCQ&rrig xal aithr}g

rrjg 6Arjvr]g.

Tavxcc ILEV ovv ft%^t TOGOVT&V r][iiv

îjÔ-co, 3toir]66iiE&a d rr]v aTtodf^v rrjg

20 Gfkrjviaxrjg av&iiaMag itl rrjg KU.T titiKVKkov VTCO&E-

2. EF] TE D. BJ] corr. ex BTzf D 2. 3. r] KA]

jtat r) KA D. 4. T, A] A xai T D. at ntevQctl ccvcttoyov]om. D. 5. ianv D, corr. D 2

. 6. KAM] AKM D. vno]ai VTCO D. at] om. D. 8. ycoviu] ycoiviK C. Suprapr. vno ras. D. TZz/] corr. ex FJZ B 3

,FZ4 &GTIV D.

9. rag'] corr. ex zd D 2. TZ] post ras. 1 litt. D. 10.

B4] v.cii BJ D. 11. BJT] %al vno B4T D. KQK] torlv

KQU D. Z^/B] Z et B in ras. D 2. TJJ] supra scr. D 2

.

12. vntneno D. AJB] corr. ex ABJ D 2. 14. ftrrj

D. %] ol- in ras. D 2. 15. KMH] -H e corr. C 2

,HMK IGTLV tVrj D. 16. 5'] mg. AB, om. CD. 18. ngo-A, corr. A 1

.

MA0HMATIKHS STNTAEE&2 A'. 301

til 7JV iTtO^LV KITIKV,TO JiV JtQ&TOV Ktp' G)V

ccQ%caoTttTcov sxtefysav TQitii Tatg

doxovGcug avu'ys'yQdcp&ai, 0vy%Qri6a^vo^ (p%ijg ds xal

ccTtb T&V v T& vvv fflovG) TQitil itA^iv tcclg vy' fin&v

avt&v axQi,p6tara tSTrjQrjiisvcus' ovt&s yaQ rjts 5

,dt' o0ov ye [idfaGtct dvvcttbv

xal aM&s (pavsgbv eGtcu, diori, TO

re TtKQct r^v KV&pccMccv didyoQOv TO CCVTO % a[iq)OT-

QGJV T&V dl%0)V fyytfTCt K7(0^6TCC^ KKlf}

TG)V [l6G)V

KKTO, 10

TQCCV dioQ&otiw 7ti,6vva'yo[ivr]. Jtobg drj TJJV

xctl cog %&&' avTrjv &G)QOV[ivr)g

TOV TQOTtOV TOVTOV. 15

T Xttl V TK> KVTGJ 7tt,7lda} Xi[lVOS TG)

dia [i6G)v r&v gcodttov, jrpog dl TOVTOV TQOS tynrnki-

[ivos avccho'y&s TTJ rty&MOT'rjTi, rijg KCCTK TC^KTOS xccoo-

dov Trig 6A,ijvrjs jtoi,q)Q6[ivos oftaAwg ig TCC xoo- 20

7Col TO KSVTQOV TOV dia [ifawv T&V Jcodtov

T06QVTOV, O00V i\XCCTCC TC^KTOg XLWTjGig VTtSQ-

Trig XCCTK iiijxog. iitl \LBV ovv TOV Ao|oi) TOVTOV

{lVOV VTtOTi&yi&a TOV XCCA,OVILVOV Tti-

xvxhov o^ia^&g itdAiv fig Ta itoiiva, TOV xotipov axo- 25

T?I xccTa xAuTog aitoxaTa<5TK6i, rJTig

corr. ex SLTIOL^V D. 2. l>t|^ti/>fa)v corr. exA 1

. 5. yap] D, yug &v ABC. 6. ys] D, corr. exrs B, re AC. 10. &el] om. D. 12. Sri] Ss D. 13. eavvyv D.

17. xftftfvoff] om. D. 18. f'yxfx^t^vog] AC 2D 2, ifHtnlutf^vos

BC (-G- del. B), %SV.UIIEVOS D. 19. ccvcclioyos C. 23. rovtovrov loov D. 25. snofisvcc] -ofiev- e corr. D 2

.

avrbv rbv dia {isG&v r&v Jepdtcav

xarcc [lijxog itoislrai xwriGiv, sitl ds avrov rov

jv &g xccra rr^v ciitoysi

Qi,av fig ra TtQorjyovîsva rov xoGpov rr\v

5 noioviisvriv axohovd'&s rfj rijg av

0t. TtQOS ptVTOi TY}V VTtOKEi^BVTflV dsl&V OvdfV CCV

atjrs rijc;dice rb

rov Gshyviax

ovdspiag ccîoôyov diaytooas rfj xara

10 firJKog jtaoodG) jtoo6>

yLvo[ivr]s BK r^g sitl rotiovrov

G3v roivvv slkrppKiLSv ttahcucbv roicov exhsfye&v fa

r&v iv BccpvA&vi, rsryorjiisvav, j] per Tto&rr) avays-

yoaTtrca ysyovvla rep Ttocora) srsi MaodoxsîTtddov

15 Alyvitriovs (&&& x&' stg rqv X'. riQ^

psra ryv dvaroArjv fttag ftoccg Cxav&s TCKQ-

KOI s&tei'Jtsv oAr]. sxsidrj ovv 6 r

rcc 6%ara r&v 'Ift&vcov r\v ,KOI y vvt, tbo&v

vCbv i{$ k'yyiGra, f] {isv CCQIÎ rijg fafafyscoc; eysvsro

20 dÂovdrt nob d /_' cao&v i6y[iQi,vG)v rov

6 $ [isGog %o6vog, jtidiJ7tso rfteia i\v y

nob/3 /.' mo&v. iv 'j4A.,KvdQia (), 7tidnJ7CQ nobg

rbv di ccvrr}g iieGrnifiQivbv rag ctiaiaLag 7to%ag 6vvi-

i df b dt avrrjg ^0rjîftoi,vbg rov

1. rov] ins. D 2. ^stogov^v^v C. 2. noift D.

om. D. 5, itoioviisvr) B. 7. dia] v.ccrd D. 8.

ô|cb(jfoos] supra scr. D 2. 11. {^xJUtocK D. Deinde add.

ccQ%ri :<^> D, : &Q%ij '.^ D 2. 14. ysyovviui D. MagSo-

vevTrddov D, corr. D 2. 15. ob^] e corr. D 2

. x^'] -&' in

ras. D 3. 17. l&Uitiv A. 18. fy&vm C. 19. tyivsTo]

ytyovtv D, -v del. D 2. 20. //] corr. ex g D 2

; mg. (H D.

21. whipis A, corr. A 1. 22.

/_'] dvo ijfiicv D. 23. tag]-dg e corr. D 2

. lno%dg] mg. D 2.

did BafivA&vog i\îiGi xal TQITG) syyitira {lias cooccg

,6 ptGos %aovog yyovv Tf}

nob y xal y' cogfbv faiHUQW&v TOV

vvxTiov, na& tjv &QCCV 6 ijhos xara TOVQ

vovg rîlv rti,A.oyi6nov$ snsfysv aKQifiCbs t&v 'I%&vcov 5

floras nd L' syyiGta.

r\ds dsvTsga rav ixkefyenv dvctysyQanrai, ysyo-

vvia TGI dfvrsQG) ereu TOV avrov MaQdox[Middov xax

Alyvnriovs (dcafr ir[ els rrjv i&. e&teute de, cpqeiv,

dnb v6rov daxtvAovs y avrov TOV ILZGOVVXTIOV. ens! 10

ovv 6 psGog XQOVOS iv BccflvA&vi (pawsTcci, ysyovfog

HUX ccvrb rb [teGovvxTiov, iv 'AteâvdQGiK oysttsi ys-

yovtvcci, nob /.' nctl y' peoovs pices woas TOV [tsGo-

vvKTiov, xa&>

r^v CVQCCV 6 fjAtog dxetysv dxoiflcbs T&V

'I%d"vcc)v iioioas ly /_' 6'. 15

f)ds y' Tfbv sxfafys&v avaysyQttiiTai ysyovvla rc5

avT& dfVTeQG) Tt, TOV MccodoxsîTtddov XUT'

TLOVS (&a[iLVG)d' t,

f

fig rfv tg'. yo&TO df,

TOV f\iifaov<s. 7tidri ovv 6 ijAios ^^ rfv 20

v t nctQ&tVQV, TO

Tec'

2. ytyoviv] -v del. D 2. 3. y] mut. in r* A 4

. y'] jf

mut. in r A 4

, TQLTOV D, rgfaov D 2; TCQO rgitov v.a.1 rqi&v WQ&V

mg. A 4. 5. Inefysv] corr. ex in/l%ov D 2

. 8. Post tov del.

SfvT^Qov D. MccQtioKeiiTtddov'l -do- in ras. A, -p- corr. ex

v D 2. 9. i&lfinev D, feline D 2

. 10. avrov] TIQO D. 11.

(fctivtrcii ysyovcbg] yiyovEv cbg cpccivercci seq. ras. 2 litt. D.

12. oqpalft] ncchv dgjft'Aft D. 14. 7tet%v ccKQip&g 6 ijliog D.

17. dsvTSQOj] B B, a post ras. 1 litt. D. MccgSo-ufvndSov D.

19. IÂtMMv] mut. in st-sUnsv D 8. 20. TJ^LGOVS] corr. ex

A 1. 21. IIctQ&evov] TICXQVOV C, ut saepius. 22. BKV-

-i add. D 2. IK] i- renouat. D 2

.

TO ds ijiit,6v 1% vvxrbs s L' &Q&V xccl

CCQCC rijs sxAsfysas ysyovs ago Jtsvre

v rov [isGovvxriov did TO para rrjv dvaro-

,6 ds psGos XQOVOS itgb y L' cbp&v, sjtei-

5 dijrtSQ 6 nag XQOVOS rov TrjfaxovTov psyd&ovq rijg

yti6xorij<S6G)s tQicbv syyi^rcc COQCDV ocpsttsi, ysyovevai.

sv 'j4A.t>ccvdQi(x nakiv KQK 6 [isGog %()6vos r^g exfai-

il>SG)g aTtstskeG&ri ICQO d KKL y' G)QK>V itirnLEQiv&v rov

IIE60VVXTIOV, KK& 1JV &QKV 6 ÂfcO SttSfySV O.KQifiG)<S

10 rrjg nag&svov [ioiQcc$ y d' syyitircc.

v ovv, ort dnb [isv rov fif'tfov %QOVOV rrjs

ni' vbv rrlg devrfyKS neKCvritai 6

xalv\ ê^tjvrj^ {letf ohovg xvxkovg [io-

TII& 7?, ccTtb ds rov rijs dsvrsgccs

15 %QOVOV 7tl rov ri]s rqirriQ [IOLQUS Q%& A. AAa xal

j]rtibv [isra^v ^QOVGOV did<5ra,6i KTCO psv rov

snl rov dsvrsQOv ftfiSQas it^d%Bi rvd xal CDQCCS

USQivag ccTthcos psv ovr&g &sa)DOv<5i,v dvo iJiuGv,

ds rov rcbv 6[iccA.G)v vv^d"rjîso(DV STtihoyiGiibv dvo

20 ij[it,6v Ttsvrsxcudsxarov., dnb 3s rov dsvrsgov snl rbv

rgi'rov fftiBQCcs QOZ xccl COQCCS farjpSQivas aitAwg [isv

x/_', dxQifl&s ds x Ttsîtrov. xivslrca ds 6ft-

agog yaQ rbv roGovrov %QOVOV ovdsvl

dtot(?ft, xav rats tivvsyyvg rcov

2. nivts\ s BD. 4. r)g%&ai] corr. ex dai D 2. 6 -

C.^

mg. A 1. 8. Kitors'keGft'Ji C. 9. S7ti%v 6 ijkios D.

11. rov] ins. D 2. 15. I] ins. D 2

. Post xcu del. fast D 2.

16. Sid<5tKGi<s\ ante GT ras. 1 litt. D. Ttgrnrov] a B,,

TOV C. 17. TOV] corr. ex TO A 1

, rrjv D. dsvrsQccv D. 18.

dvoijfiicv'] ft [_' BD. 20. ij[LL6v] om. D, /.' BD 2

. m-vrs-

is D, is" D 8;a {_ Is supra scr. D 3

. 24.

D, corr. D 8. Gvv\syyvg A, Gv\veyyvs A 1

.

MA0HMATIKHS 2TNTABE&S A'.

V tth

305

l cbgcug i6rnLQi,vaig /3 /_' IB' ccvcoîaâg [isv

okovg xvxAovg

v $ ralg $o<5

r? x, prpiovg d [toiQccg rjie

K

,ai df rr^g dvrQag 10

# xcctii, rr\g [iforjg

- 5

fitfavxhog 6 ABF^ 15

rijg

OV fV V

rijg 6^tjvrjg inl

rov ETtiKVKkov yLt<x,fiK6ig &g onto rov B iitl rb A xal

b rov A 7tl rb JT ivoifvr &6r riv iv ATB

rb 20

7tl

rr\g rtQGyrrjg sxfafyf&g 25

V ov6av rg KB 7tQO<5n%'8vat, rfj

1. &KoJtt*0ifari D a, &*olov&j*n ABCD. 3. olovg] -I- in

ras. C. vu\ v$? D. 5. (JLOLQCCS (pr.)] om. BC. 8e]ins. D 2

. fioiQag (alt.)] om. D. 14. TOVTOV] xovzcov ovv D.

16. 86T(o] vitOKi-iG&aj D. xa#'] e corr. D 2. 22. aeMvrig A.

23. xai a^ro rov A] supra scr. C 2. 24. T] corr. ex r^trco C 2

.

26. x?] mut. in nd C 2,%^ D. TrôfftrtO'fWt] post -- ras. 3 litt. D.

[toioag y xd, rqv $ BAT, r^v XEXivqrcci, axb

rr\g dsvtSQccs exfafys&s iril rqv rgirrjv,

~gv xs K(paiQlv tils iisGys poioag o AJ, SIK rovro

xal ryv plv onto rov B sitl rb A ndgodov5 ovtiav vy Af cupaigslv r^g peGris VMS ccvras

xd r^v de aitb rov A 7tl rb Fori, ovv ov

dvvarbv eitl rijg BATQiccg rb itegiyewrarov elvau rov

10 eTtixvxkoV) (pavegbv ex rov dcp-

\v re avrqv vTtdêiv xal

flliixvxhiov rijg

xara rb

enel $ TtKvr&g eitl rijg

15 BET, iA,rj(p&a) rb xtvrQov rov re

dia p6G)v r&v fcodttoz/ xvxkov xal

rov yegovrog rb xwroov rov eitixvxhov xal eGrct rb 4,xal jt^v%d'C()6av an' avrov 7tl ra rcbv y exkefye&v

Gripeta ev&elai at 4 A, 4EB, 4 JT. xa&okov roCvvv,r

iva

20 xal Jtobg rag bpoiag deCêug evEitifiokov rty peray&yriv

rov frfcoorifiarog itoicoêQ'a^ edv re dia rijg xar eitCxvxkov

vjto&<jG)g avrag cog vvv deixvvcopev edv re 8ia rijg xar7

exxevrooryra rov 4 Xvroov rore evrbg

\iia \Jiev rcov

25

2. r^trrji;] supra scr. D 2. 3. QV] seq. ras. 1 litt. D. 6.

ds~\ re D. 7. ^] jit-e corr. D 2

, pfl BC, corr. C 2. 11. rs

Ss D, sed eras. 14. tnef] corr. ex Ini C 2, InsiS^ D. 15.

BET] corr. ex BT A 1,PEE D. 19. JEB] wl JEB wi

seq. ras. 1 litt. D. 20. evi-nipolov] mut. in fvBitôlov D 2.

21. noica^Q'ci] A, corr. ex noiovpE&a D 2,

7tOi/

r]6co^Q'ci BC.22. 8siv.vv(o^fv cog vvv D. 24. ft/a] corr. ex (iLccg D.

MA0HMATIKHS STNTASE&2 A'. 307

it\ rb Edjtb rov B rijs dsvrsoccs fafatifjecog, rd ds koma dvo

6r][ita r&v extefys&v srti&vyvma) svd-sla CDS v&dds

t\ AT, xal ditb tils ywopwys ropijs vnb rijs s^ftsft^-

fisvrjS) olov rov E, e7ti&vyvv6d'G)6ccv psv snl rd koiitct 5

dvo Gypsta ev&eiai, cog sv&dds at EA, ET,ds ayfa&Mdccv sal rag onto rcov kont&v dvo

7tl rb rov ^codiaxov usvraov smfevyvviisvccsM plv tyy AA ri EZ, M ds ryv F4 % EH, xai

srt anb rov srsoov r&v sior][isvK)v dvo Grjiisicov, cbg 10

sv&dds catb rov F, xd&sros a'yeGd'G) STtl rqv dab rov

srsoov avr&V) olov rov A, STtl rqv ysvopsvrjv VTCO rijs

disxfiohiis 7csoi,66^v ro^v, olov rb E, smfevx&stGav

sv&stav, &s sv&dds iril rrp AE i\F' drto&sv yaa

av %or)6G)[isd'cc rr\ ri}s xctra /

yQcc(pijs ctywyfi, rovs ccvrovs 15

fxflccivovrccs Aoyovs dux rcov rijs dst&cos

rijs Mhoyijs nobs rb v%or]6rov p6vov xarcc-

7tl roivvvfjBA jtsaicpsosia vitorsivovGcc

rov did ii6&v r&v fydiov nvukov poious y xd, sty 20

av xcdi\ vitb B4A y&viK nabs t& xsvraa avrov

ovtia, of

i(Qv [iv i6iv CCL d ood'al r, roiovrov y ^d,

OLCOV ds at dvo oafral r^ roiovr&v ? prj. &<3rs nut

1. diKpaM.oii8vr}v (post ras. paruam) s'^o/ifv (post o ras. 1

litt.) avTO&fv D. 5. olov] tv&stces olov D. ra, konta\ -a fol-

ia ras. minore D 3. 6. sv&sfai] -stcti e corr. D 2

. at] ^ rs D.

EA] AE C, EA*ctiri D. 9. ini (pr.)] post ras. 3 litt. D.

jitsV] supra scr. D 2. 8fr] ins. D 2

. 12. A~] e corr. D 2seq.

ras. 1 litt. 13. rb E] supra scr. D 2. 7te&v%d'i6av D,

corr. D 2. 14. r<9] e corr. D 2

. 16. BV^GCO^BV BC. Myovs]-ov<; in ras. 2 litt. D 2

. 21. ctvrov] om. D, rov avrov suprascr. D 2

. 22. OIG>V\ olov CD, corr. D 2. at] om. A. 23.

ol'(ov] corr. ex olov I)2

. dvo] B B.

20*

ij fti> itl rr}g EZ sv&stag TteQiysQEia TQIOVT&V i jitiy,

olov 6 itol TO 4EZ oo&o'y&viov yoa<p6[ivos xvxôg

f)EZ v&ia TOIOVTCW o,

X. 6ôto>, f'jtfl$\BA

v 6Ttv vy As, sft? v xat17

#6 5?^ yewCo,

OV0K

d avrcbv i\v xalfj

iiitb B4A[Eucl. I, 32] CCQCC r\

i)7tb EAZ[i. &6r Kal

i] pv itl

10 Trig EZ itQLCpBQia TOLOVTCOV faxlv ^ ftf, oicov 6 Jt$l

TO AEZ QQ&o'ycaviov xvuhog T|, ufai] dfjEZ v-

TQIOVTCDV[l Kf\ A, OtW <3TLV % EA V7tOTlVOV<3CC

' xal OLCOV 6Tlv CCQCC i\ plv EZ eti&fia 5 ^ o, 17tie

TOIOVT&V 6T<u xalf)AE v&ta 1% v A/3.

15 TtK&lV) 7tLr\ BAT 7tQi(pQia VltOTLVL TOV

lioiQccg o AJ, i'rjav xal

v\ VTCO BAT y&vicx, it

XVTQGJ TOV CCVTOV OV6d^ olov [lV l6iV CCi d

T|, TOLOVT&V O Af, OIG)V $ Kl SvO OQ&al T%, TOLOV-

TOV a id. &6T xalf\ fisv iitl r^g EH 7tQi,<pQi,a

20 TOIOVTCOV 6TW a fcd, OiCDV 6 TtQi TO AEH1. g] iarlv s D. 2. oi<av] corr. ex olov D 2

. 3. o] 6

ABC, om. D. 5. tcriv} comp. B, -v eras. D. sir] 6. fa]

mg. D 2. 6. oi'a>v] corr. ex olov D 2

. 8. EAZ] EAJ D.

9. sanv] comp. B, -v del. D 2. siti] corr. ex vno C 2

. 10.

EZ] EZ fu-9-fiag D. sartV] comp. B, -v del. D 2. oioov]

corr. ex ofov D 2. 11. ÊZ] A, E^Z BCD 2

,AZ D. _12.

corr. ex olov D 2. E-4] -^ in ras. A 4

. 13. f o] o A,

o BC, g D. 14. Ez/] zfE Idthfrri D. fdt<*] |r^ D,-v eras. Ê] E^4 D. t-v&siai D, corr. D 2

. 16. o] seq.ras. 34 litt. D.

17] supra scr. D 2. Bz/T] corr. ex EA D 2

.

ycovicc] -i- ins. A 4. TOJ] TO D, corr. D 2

. 17. Y.EVTQOV D,corr. D 2

. TOV avrov] supra scr. D 8. OVGUV D, sed -v eras.

18. o] in ras. D. 19. a id] corr. ex cci 8' D 2.

D, -g eras. 20. tQiycovov] oQ&oymviov D.

MA0HMATIKHS STNTAgESiS A'. 309

avrri de fjEH sv&eta roiovrcov a it, A,

titlv

BAT 7tQi(pîa {lOlQWV 0TIV ^V X5, sify aV XalJ]

vnb BET y&via, jroog t$ itQi<pQia ov6a roiovr&v

~QV xg, 0603V sfalv at dvo oo&al v%. rcov d% avr&v 5

^v xalr\vxb EAT ynvtcc a ~id' xccl lom^ [Eucl. \ 32]

ccga j]vitb ETA rcov avtav stitiv QH& ip. coGre xai

?l iilv sill rijs EH itQiq>SQicc roiovr&v tirlv QII& ij8,

otcov 6 TtfQl to FEH dgftoyaviov KVKÔS r|, avri\ de

fjEH v&ia rocovTfov ^n jUa xa, oicov 6rlv 17

TE 10

vitorivov6a QK' xal oicsv sGtlv agct ^ ^ V EH v-

&ia a 1% A, ^ dl AE ^x, roiovrcov i&xlv rjFE v-

K x wy. r&v $ ctvr&v dt%&rj xal i\EA sv-

fj AT jtQi(pQia poiQcbv fdffy&r] gg 15

i/, elrj av xali]vnb AEF y&via rtgbg rr\ 7tQi<pQSia

g ^VK, olcov sfalv at dvo ogftal T%.

fj [lV 7tl tr\$ r 7CQL(fQia TOIOVTCOV

6rlv gg va^ ol'eov 6 7C^l rb PE& rgCyczvov r|, ^ îitl rij$ E 7tQHpQia t&v AoiJt&v [Eucl. III

7 31] tg 20

TO rjiiixvxfaov ity ft' xal ai v7tOTivov6ai aga avrag

v&lai, ftiovraii\ plv F TOLOVTCOV 7t& jiig td,

3. 86TLv] comp. B, -v eras. D. 4. ovocu D. 5. tie] 8' D.

7. EFJ] ETJ yatvta D. eGTiv] comp. B, -v eras. D. 8.

TCfQicpsQsLas D, -s eras. 9. 6] supra scr. D 2. 10. EH] E-

e corr. in scrib. C. xa] -a e corr. D 2. 11. ^x] -x e

corr. D 2. xat] corr. ex xot C 2

. 12.if] D, seq. ras. 1 litt. A,

Iri BC. Post z/E del. iSti^j] D 2. IdrtV] comp. B, mut.

in icxi xat D 2. 13. x] supra scr. D 2

. de] om. D, <?MD 2.

15. Ante Tra^tv eras, s D. 16. 17]om. A. 17. dvo] ]? B.

19. Qg] corr. ex 9 D 2. r^tycovoo'] dôycbvioi' xvxAog D.

8s] d' D. 20. ni-QKpsQeiK] om. D. 21. jty F] con*, ex

ny o A 1

, ny& CD.

TE V7tOTlVOV6CC 03C , f]^ E r^v CCVTG)V

oO* A vs. xal oicov CCQK 6T\vfjTE ev&ela a % xy,

TOIOVTOV h'tixai xcclf] psv T sv&EZa a o 77, f]

d

E OIIOL&S o ~vy me. T&V ds CCVT&V f}v % EA oArj

5 tj v? A/3' xal koLTtri KQK t\A roiovrov etitlv i^ /3 ta,

OLG3Vf\F di%%"Yl a O ^. KKi 0TiV TO {llv KTtO Trjs

AS tttQdy&vov 6$ id t#, rb d coco r^ F0. O ij, a 6VVT&VTCC 7tOLi TO KTtO T% ATvov [Eucl. I, 47] <5c,cc id Ag* p,rpii aga 6Tiv

r\AT

10 TOIOVTCOV l 7 V%) OICOV 0TiV fj [lV 4E VfriaJ33C,

j]d TE T&V KVT&V a % wy. S'GTI d\ KCCI, o

r

i(QV fi TOV

7CLKVXA.OV diK[lTQOg ^5C, TOLOVTC3V f\AT

jUg id' VTtoTivi, yag Tr\v AT nQi,(pQiavovtiav gg vcc. xccl olcov aga 6T\v r\ [iv AT v&la

15 7t& ^ig td, i]$ TOV 7tt,XVX&OV 8iK^LTQOS ^3C, TOiOV-

TO)V 6Tttl KOl % plv /IE V&tCC %A.tt 1/y ft^, f]d TE

T&V CCVT&V P V' K)(3T KCclf] [LV rf CiVT^ XQl,(p-

Qia f\TE TOIOVT&V g (id a, otov fVrtv 6 7tfavxA,os

T%. TO)V d aVTG)V VTCOKfiTKi XCci BAT 7tQl,q)Qltt

20 ~QV X?' X(d 8A^ [lV CCQK fl B TE 7tQl(pQia pOLQ&V<3Tiv Qvt, la, fi

d vit avTqv v&laf]BE TOIOV-

2. ^] I- ins. D 2. 3. xat] om. D. 4. 8s] S' supra

scr. D. 6. 17] %al r) D. o] e corr. D 2. SGTW] comp. B,

icn D. 7. A] -& e corr. D 2. 8. a] e corr. A. o] corr.

'ex ft D. a] corr. ex a D. TO] corr. ex TOO D seq. ras. 3

litt. 9. o9a] c9 D. Is] e corr. D 2. 10. sv&f-icc] ev&ficc

vnotsivovca D, vnoreivovocc supra scr. B 3. 12. Totovrov -

15. ^x] mg. D 2. 13. [loiQ&v] om. BCD. 17. ph~\ om. D.

18. roiovTcov] roiovrcov icriv D, -v eras. % pd a] ^L doc D.

oi(ov]_oiov D, corr. D 2. s<ntv] om. D. 19. ^] S' D.

20. pv negicp^QBLcc] bis C, corr. C 2. xca

']. (pi'iore loco)

comp. ins. C. 21. r oj Tec ABCD. 8] d' D.

TG)V A/3, olov 6rlv % plv rov BitMvxkov did-

t pw ovv j]BE v&ta l'6r] r)v BVQ^BVVI rrj

rov fitixvxhov,id avrfjs av

on rb xvroov ocvrov, xccl ccvro- 5

&V av cpaivro r&v

avrijSi &&66nv o\ noliiBTE

7CQifpQia rilLMVxMQV, d^Aoi/, OTt

TO Kvroov rov IrtMVKkov Krbg 10

7t(3sirai rov BATE rpijuaros.

vjtoxstctd'G) dy rb K 6r][ilov,

KOI BTte&vi&G) KTCO rov z/ %vroov

rov dia {ifa&v r&v ^coduov uvxhov

dice rov K v&Zct ^ z/MKA, co6r 15

TO [iv A 6r][iZov yivsG&ui rb aito-

yBiorarov rov fjrwruxAov, TO $ Mrb TtSQiyBiorarov. 7ti ovv rb VTCO

faov 0rlv rc5 vitb r&v 20.

Ad XCtl Z/M JtQl%OllVG) OQ&O-

[Eucl.111,36], dedeiKrui d'

on,, O'LCOV 6rlv rov eiti-

r\ didiittoos, rovrfanv

) ^5c, roiovr&v farlv ^ f*^ BE v- 25

fjd Ed r&v avrcbv %la ly prj, rj

r\ARM

&tcc it

3. BE] corr. ex KE C 2. 4. Irvy^ccvB A. 7. d'] 8s D.

8. Ante SB del. i<n D 2. j]\

ins. D 2. 11. Post BAFE rep.

9. TtSQifpfyzict 10. iniy.vY.lov D, corr. D 2. 13. KEVTQOV] e

corr. D 2. 15. K] a e corr. D 2

. 4MKA] AK, M4 D. 16.

yiyvso&ccL D. 20. iotlv] comp. B, scrL D. 21. JM] corr. exAM D 2

. 23. rov] rj rov D. 24. rf]om. D.

ds B4 oAr] dyhovort, typy va K, yivzxai rb vnb rcov

xal 4E, rovrfarw TO vitb r&v A z/ xal AM,n _

OQ&o'ycbviov r&v avr&v M fify xal

s A/3. rtdhv ds, ejtsl KOI rb vnb A45 xal AM [ira rov dnb rijs KM Ttoist rb ditb JKrergdyovov [Eucl. II, 6], 17

^ KM sx rov xsv-

rpov ov0cc rov eTCLXvxôv r&v avrcbv i<5nv %, lav ra_2% rov an' avrijs rsrgay&vov 7tQ00d"S)^v rats M fity

A3 %oiv rb CCTCO AK rfrdovov r&v avr&v_

10 My gr A/3* xal pyxM aga b'tirat,

rjx rov

rQov oi)6a rov (pfyovros rbv sitiKvxkov O{IOXVTQOVx& dice [isG&v r&v ^G)dic3v xvxAov roiovr&v yc, xal

%r)xo6r&v y /Lt/3,oicov 6rlv % KM x rov xwrgov

ov0a rov Ijtixvx&ov ,ijxovra. &6rs xa^ OICQV 6rlv i]

15 X rov Xvrgov rov cpfyovrog rbv fitixvxhov bpoxw-

1. x] xy BC. TO] agcc TO D. 2. rovrsGnv'] comp. BT

tovrion D. Ad~\ dA C. 3. r&v ctvr&v] -&v avr&v in_ _ _ _ms. A 4

. M flip] BC, p By D, pvQidStov p $ty D 2,

p 8%cnuiAia>v (postea del.) TQIKKOGICOV (sire- supra scr. postea)in ras. A 4

, ty postea add. mg. xal ?]-]in ras. A 4

. 4.

end v.ai\ om. D. AJ~] T&V AA D; seq. ras. 1 litt. B; AJK A,K del. A 4

, ylz/xj, in fine lineae C. 5. xat dM~\ corr. exxa ijp D. XM] KM xBXQKymvov D, Tfrguymvov supra scr. B 3

.

4K] rfjs 4K D. 7. I"]corr. ex I D 2

. 8. ,y| ri D,jU? _ ^f/1

/r5J D 2. rats] om - C, irarg ngoy,i^vccig D. M î/Tj ft |3t/; D,

^t ,(J_^_D*.9. 4K]rfe JK~D. 10. M] mut. in ^ uvf D 2

.

75r ^] mut. in

ys r F D 2

. z/A^] -X supra scr. D. ex 12.

xwxiov] mg. D 2(yp.), ^x roi) KVTQOV et TW îa (JLSCCOV r&v ^w-

xvxlov etiam in textu. 12. TW] 'scripsi, TOV ABCD.

r e corr. D 2. 13. 77] i\ CD, corr. D 2

. Post ^supra scr. MOTS xca' D 2

. KM] del. D 2. 14. OVGCC 15.

om. D.

B

toov tri oî xvxAov Qtjxovta, toiovt&v 6tai xalj]

ex tov xvtoov tov tmnvxhov ~iy gyyitita.

%%&& dr) 7il tijs dpoias xataygayils aito rov Kxvtaoy xd&tos itl tyv BE fj KN&, xal im&vyftG)

f)BK. siisl roivvv, otW 6xlv

r\4K jfc rj ^/3, roi- 5

ovtcov i\v xalf] [isv /IE sv&sia

%&cc ly jZ^, f)ds NE fftifasia ovtia

rrls BE [Eucl. IE, 3] T&V ccvr&v

vrj ^/Y] fig, &GTS xal oAyv TYJV

4EN r&v ccvrcbv yivsGftui yfi xal 10

Ad, xal oi&v aga rj

6rw ^x, roi-

OVTG)V xali\ [isv 4N 0tai,

vr\ v, i]d 7i avail

QOTJ ft fyyitira, O'LOV 15

tcbv

<3tlv 6 7Col tb

viov xvxAos T|. co6t xal % vno

dKN yavi'a, oi&v [iv sfaiv at

dvo OQ&al T|, toLovtcov i&xlv

Qoy /3, oicov $ aC d OQâl rj, 20

toiovtav nd1 a. xalfj [iv &J\

ago, tov 3tixvxA.ov

pOiQCOV 6tlV ltd1

,

iS tb fjiuxvxAiov 9 v&. tcov ds avt&v

Jtai,(paia inii6ia ov6a tils B&E pot,- 25

4. BE] EB D._ 5. Wv] om. D. JK] JK sSttz&T] D.

r[\ ins. D 2. 7. Jâ] -K e corr. D 2

. 12. JK] J- e corr. in

scrib. C. 14. ^] S' D. in3

} corr. ex bn D 2. 16. JNK]

corr. ex JHK D 2. 17. acre 19. T|] om. C. 19. EGTLV]

om. D. 20. at] in ras. 1 litt. D 2,om. ABC. 21. K] [ii&s D.

23. SGTIV] comp. B, -v eras. D. 24. loina>v~] bis D, corr. D 2.

Ss] om. D, 6' D 2. 25. B] B3 D.

orj Aa, ^sidr^TtSQ % BE~i eyyidra' xul koutri agcc i\

AB rov

r^v anefysv f} (Ss^tjvri rov anoysiordrov

xara rbv xxi[ivov pitiov %oovov rijs devTSQag x-

5 Aefyscog, poiQ&v fativ ij$ xd. b[ioicos df, endfj VTCO

4KN y&viK sdei'xftri TOIOVTGOV 7t& a, ottov sfalv ai

d OQ&ccl T|, xal koiTtfi stirou,17vnb K4N y&vtcc, ij

rrjv a(pKLQOvêv^v rijs {ifays xara

7teQ(,(pQi,av sx rfi TtccQcc TTJV AB rov

10 xvxhov ywoiisvrjs avKt^Kîa,^ r&v tontfbv sis ^nv

do&riv [Eucl. I, 32] ^LOLQ&V o v&. nctl Kara, pijxog

UQCC yiB6G)$ STtstyev fj GsAyvr] xara rbv psGov %QOVOV

rils dsvreoag sxfafye&s IJaodsvov poious id ^d,

dijrteo axgifl&s exsfye [IOIQKS 1/y jiZf, o6ag xal 6

15 Iv rots 'I%&v(5i.

,(bv siA.ri<pcc[iv roi&v exksfyscov sx r&v 7ti-

v\\iiv iv 'AkeôtvSQsia rfrrj^^

yfyovs rat 1% k'rei 'AdQiuvov xccr'

Ilcivvl K SLS rijv xa', rbv d yidGov %QOVOV20 7tA.o'yi6diid-a ysyovivai itg/Q yjifaovs xccl rsrccgrov

ifS^BQlV^S fOV [ISGOVVXriOV XCtl %A.l,rtV

JV COQCCV axoiflcbs yfl%v 6 rikio<s rov Tccv-

oov {lotoccs ^y ^' ZyyiGrcc.

fjd dvrocc yzyovs rw id"' srei, 'AdQiuvov xccr'

1. Ifo^tfr] D. 2. A B] BAD. 5. icxiv] comp. B, eon D. 6

AKTL D, corr. D 2. 7. \ontr\\ IQIUJ\ &QO. D. 8. ag>-

D, corr. D 2. 9. A E] -E e corr. D 2

,corr. ex AAB A

11. o] corr. ex ov B 3. 15. I%&VGIV D. 20.

-Q-cc BC. 21. f<5s]~

g J' D. 21. |&eurermut. in B'gilmsv D 2

. 22. sitsfysv cMQifias D. 24. dsvrsga~B B. ys'yove] yiyovsv sv D, iv del. D 2

.

MA0HMATIKH2 STNTASE&S A'. 315

AfyvTtriovs Xo'Cax ft' slg rfjv y', rbv de [i6ov %QOVOV

STtshoyrfdiisd'a yeyovBvai ago a &QCCS farj[iQi,vijs rov

H6ovvxriov xccl %Ai,7tv ait ccoxrcov rb L' xul yr

rijs dia[JirQov, xa&' r^v COQCCV itt%v 6 ijfoog axQifi&s

r&v Xrj^cov [IOLQCCS %e %' syyidra. 5

i\ds tQifri r&v exfafyeov yeyovsv rtf x

e

srsi,

rbv de jieGov %QOVOV sitsAoyiGdnsd'cc yeyovsvcci,

d &QCCS faqpSQwas rov peGovvKrCov xccl s&teirte rb

rftiitiv rijs SiuyisrQov cut' ccQxr&v, jtsZ%e $ ucci xaroc 10

rccvryv rrjv &QKV 6 ijfoos r&v 'I%&v(ov [IOIQCCS id i$'

ovv, on xccl

&itb [iv rov [i<5ov %QOVOV rrjs

rbv [i6o

6 TJAtOff, [IOLQCCS OCC V,

CCTtO

rov rrjs dvrQas fti rbv rijs rofarjs [tongas Q^fj vs.

<5uv $ xai b [ircc,v %oovos rrjs (i&v rtgcorrjs diccGrcc-

<?o>g fvtavrov AiyvitnKKov svbs xal f}(iQG)v (>|g xal

wa&v far)[iaivK)V ajth&s pw ny L' <^'? axQisfl&S $ ny 20

/_' j\ , rijs & dmrsQccs diaGraGs&s wiccvrov it&Kiv Ai-

v vbs xccl fj[iQcbv Q^ xal MQ&V fa

1. Xoia. *$ A. 8e] con\ ex did D 2. 2.

lie&cc BC. a] A, (iL&gECD. 3. ttteuc$v] mut. in

Tfsv D. 4. ctKQifi&s 6 jjhos D. 6. T(>mj] F B. yg'

-v eras. D, yeyovs B. 7. Qccqitovd'C] supra -9- adp. A8. 7iJioyriad{ji&(x BCD, corr. D 2

. 9. Qeleine] ABC,DB 3

,itlint D 2

. 10. int-fyf-v D, -v eras. KOCTCC]

V.K C. 11. id] supra scr. D. 15. Ttgrnrrig] & B. (JLSGOV

%QOVOV] om. D. SSVXSQCCS] B B; et similiter saepius. 16.

Kteiipcos~\ om. D. 17. glLy] corr. ex QKTI D. 18.

comp. B, -v eras. D. 20. d' -- 21. /_'] om. C.

ply s, axgifl&s ds ~s /.'. xivsltai, ds ndkiv17

o'Aovg xvxAovs iv \L\V t& svl stsi,

xal r)[iSQai,s pi-g xal CQQCUS falftteQW(&$ xy L' y' &VG)-

liaMas [isv [IOLQCCS ~gi MX, nyxovs ds poiyu5 fyyitira, iv ds rc3 svl srsi xal fipSQcus pAJ xal

Ad syyiGra. dôv ovv, on ncd cci p^v

6G)S tOV STtMVKkoV [IOLQCCI, ^H MX,

a<prj(>ijx(x6i,v tijs xatti pjxog [ifaqs Jtccpodov

10 ft/?,ai SI rrjs dsvTSQag diccGTccGscos potQai, TW, Ag

xccra pijxog peGy Ttaooda) poiQas a xa.

TOVT&V OVV V7tOXSlêVG)V S0TG) 3t(X,klV 6 SJtlXVXhoS

6 ABF, xal to psv A Grjpstov vno-

ov fjv i\ GsAtfvrj iv rco (idtiq) %$6v(p tys

15 itQcbrys extefyscos, to d% B to tijg devtzgccg

to ds r to tils tgitrjSi VOSLG&G) ds caGavt&s

f}cc6iS tys dshijvrjs &S ^Ttb tov A iiti to 5, sita iitl

to r yivo[Levr], &6te tfjv [isv ABOV&KV ^l xa atpcciQslv, (b? s'(pct^sv^ tys xccta

20 iisGys itKQodov [tongas |tt/3, trjv ds BF poiQCbv ov-

6av act Ag ttQOGti&evcti t<p ^tjxsL [IOIQCCV a xa,

ds tqv PA ILOIQ&V ovGav ^)|^ y TtgoGtiftevm to)

tas hoiTtas ponces S *"*

ovv snl tys AB

1. /.'] ins.J)2

. 3. i' r)'~] lj\" e corr. D 2. 6. is] *e

supra scr. Zg v8 D 2. 9. &yr^r\v.uGi BD. 10. nQOGtsft

KctGi BD. 11. îGri\ corr. ex (IEGCO D 2. 12. $GTCO ndliv b

^jrtxvxAog] 6 inUvAlog ndUv SGTCO o D. 13. JBT] AB D.

14. G^lv\vr\\ corr. ex GfJLrjvi A 4. 16. -9-co ds ebff-] in ras. 4

litt. D 2. 17. to?] postea ins. D. slra] om. C, fTmra D.

21. TCQOGzi&evat] post -^- ras. 2 litt. D. 22. PA] AP D.

C, sed corr. 23. raj] in ras. D 2seq. ras. 2 litt.

MA0HMATIKHS A'. 317

TCCTOV slvat, del, (pKVfabv x TOV pyre iitl rife BF el-

fitJT STtl rife FA di& TO sxarsQciv av-

TG)V T iVKl Xttl

cog p

Xl[lSVOV TOVTOV TO XSVTQOV tOV 5

v xal rov xvxlov, eg?'

6 fWxvxAog, xai

S0TG) TO Z/, STtS&VX&OGKV TS

ait' CCVTOV sitl TK T&V y IK-

Ev&etcu at 10

KCCi 7ft-

BF rj%&G)6av

aito TOV E Grjjisiov v&tcci, iitl

lilv rcc B, r at EB, EF, mld rag 5z/, z/F eb&eCus xa&- 15

roi CCL EZ, xal EH, xal Tt,

CMO TOV F 7ti Tty BE Xa&-

T0$ %%&& rjF. 7t\ TOIVVV

fjAB 7tQl,(pQ(,a V7tOTLVi TOV

&V Xtti 20TG)V

i\VTtb A4B y&vicc Ttobg rc5 XWTQG) ovGct TOV

oicov [iv i6w ai d oQ&ccl rj, rotovrovft/3

at dvo oa&ttl r^, TOIOVTCOV H- xd. &6T xccl ^ plv 3ti

T^g EZ 7tQi(pQi,a TOIOVT&V farlv T xti, oicw 6 TCfol

TO 4EZ TQfy&vov xvxhos r|, avr?? $ 17 EZ v&ia 25

1. Set] corr. ex dq D 2. 2. pip D. 4. dt] 8' D.

4EA] corr. ex ^^4 D. 4B, z/T] xai z^B xal z/T D.

^v^fta^g D. 14. B, T] BT B, B *ul F etfotcii, D.

xal EP D. 15. rag BJ] corr. ex ra 27Bz/ D 2.

Tz/ D. sv&8ictis D. 22. ^] fiin ras. D 2. 23.

(5BD. 24. ^0rtV] comp. B, -v del. D 2

. 25. iQiyavov]ymviov D.

11.

EF]

TOLOVTCOV ig d ^/3, oicav 6Tivf}zJE vnoTftvovtict ^rx.

bllOl&S') 7tiI]AB 7tQI,(pQl,a [iOlQG)V 0Tt,V J3>7 %tt, #)?

av xaloj

VTtb AEB y&via Ttobg Tf) jtSQitpsgeiK ov6a

ToiovT&v QI, sea, OLCOV sfalv a[ dvo oo&al T%. rcov d'

5 avr&v r]v xccli\

vjtb AAB Is %d' komri [Eucl. I? 32]

CCQK f]vjtb EB^J ycovicc r&v avrcbv iGtiv d v^. caGxe

XttlJ] pV 7tl tils EZ 3tQl(pQSLCC TOIOVTCOV 6tlv d

vt,, oicw 6 3t$l TO BE2^ xvxto$ T|, avtr} dt- ^ EZ

v&iK roiovrcov ay jcg tf, oiov 6rlvi\BE

10 vovtia ^K. xccl oi&v KQCC itixlvi\ pw EZ v&ia

x TOLOVTCOV &rlv xcil BE

PEA 7tQl(pQl,a V1tOTlVOV6tt

TOV dia ii6a)v r&v Jradtov xvxAov iioigccg & jca, sty

15 av xuifj vitb A^JF y&via JCQOS TG) KEVXQG) ov6a TOV

fydiaxov, oicov piv ffaiv ai d oQ&ccl T, TOIOVTCW ?

3t, oi&v 6* ai dvo OQ&al T%, TOIOVTCOV ifi ft/3.&6re

XCtli\ [lV 7tl TyS EH 3tQl<pQlK TOIOVTCW 0TLV L$

^/3, oi&v b ttQi TO 4EH dgftoytiviov xvx^og T%,

20 O.VTYI $f}EH V&ta TOLOVT&V ~iy tg fc-9

1

,Ol&V 6TLV

V7tOTlVOV6K ~QK. 6^0iG9ff, 7tl ^ ABF 7tQltp-

Gvvdymai, noig&tv Q$a vt, , fy av nal q VTtb AEFycwia agog r^ jtQitp()La ov6a TOIOVTCOV Q$a v^ oicov

dvo ofral r. TMV <5f avT&v iv xai

3. AES] corr. ex AEH D 2. 4. dvo] BD. 5.

E ycoviK D. lQinr\\ otai lomv] D. 8. ot'cov] ol'cov iatCv D.

BEZ] BEZ 6Q&oyot)Vt,ov D. 9. sv^f-fa] om. D. TTTJ] rj

nri C. 10. SGTLV a$a D. 11. ^] tSf-fy&ri ^_D. SGTLV]

comp. B, sGTcci D. 14. TtvxAoi;] om. D. xa] seq. ras. 2

litt. D. 17. ofav T|] mg. D. dvo] {3BD. 18. &>TtV]

comp. B, -v del. D a. 24. dvo] ^ BD. *e] d' postea

ins. D.

A/1F ycovCcc i$ fift- xal Aown? [Eucl. I, 32] agcc % vjtb

EF/1 rcbv ccvrcbv i6nv po-fr Is. cotirs xal $ {isv iitl

rrjs EH 7teQicp8QiK roiovrcov 6rlv QO& 7f, otcov 6

itSQi rb FEH r^Cyovov xvxAog T|, avrr] dsrjEH

v&ia roiovr&v 6rlv QL& v& v, oi&v B6tlv % FE 5

vrtOTivov6a 'QK. xal otcov CCQU s6rlv17 pfv EH sv-

fteta ~iy Tg t-fr, f]ds 4E edeix&r] ^sc, roiovr&v e6rm

xcclfjFE sv&slcc 1/y Ig %. rcov ds avr&v sdsi%d"r] uccl

YIBE sv&stcc xa ^ v&.

:r/Uv, srtslrjBF 7tQi<peQSia ILQIQ&V 6nv xa Ag, 10

ty av xal % vjtb BEF y&vta itgbg rgov6a toiovT&v ncc Ag, oi-W ffalv at dvo ogfral

G)6f XalVI [lV 7fl T7JS F 7tQl(pQlCC XOlOVtO

no, Agr, OLCOV 6rlv b TCSQL rb FE tQiy&vov

T%, % ds srtl rr}g E rcbv Aoiitcov ig rb r^iLXVK^LOv 15

[Eucl. Ill, 31] 9^ nd. xccl r&v vn' avras &QK v&i<G)v

r\ iilv F sdrai, roiovrcov 'brj xd Ag, oi&v stirlv ^ EFvnorivov6a ^c, f]

d E r&v avrcbv 9 v xf$' KOI

otW agci farlv % FE Ev&sta 1/y 7g sc, touovrov xal

rj psv F k'&rai17 ji jc, ^ ds E bpoicos T p fid

1

, rcbv 20

ds avrcbv i\v f\EB oAty >ca Jirj v%" xal AotTTiJ CCQCC rj

B roiovr&v street, lajiZg I, o'icov xccl

j]F ijv rj p

K. xai 6nv rb [iv CCTCO rrjs B rfrgdycovov

1. t^j e corr. D. 4. TEH] -H in ras. D 2. TQiycovov]

oQ&oywviov D. 5. SGTIV (pr.)] om. D. v] seq. ras. 5 litt. D.

6. &mV] om. D. 8. ds] d' D. 10. Is] corr. ex L D.

12. dvo] @ BD. 14. IffrtV] om. D. r^tycovov] 6Q&o-ymviov D. 17. rj (alt.)] ins. D 5

. 20. F0] corr._exFE D 2

.

E@] corr. ex HO D. T ~] e corr. D a. ^] corr. ex

^ D. 21. de] ^' ins. D 2.

i] (pr.)] xat i]D. 22. ia] -a

in ras. D 2. T, oi'cav] ins. D 2

. 23. fortv] comp. B, SGTL D.

-?] e corr. D 2.

la, rb ds artb rijs F r&v ccvr&v o i$ x, a 6vv-

rs&EVTa noiel to coco rfj$ BF rfrodyovov [Eucl. I, 47]

6iy ~p/y A??'

[HJXt, CCQCC 0rlvi\Br rOlOVr&V id A I, (HOI/

6rlv r] plv /IE zv&eia jpz, ^ ^ Ê o/iotcog Ty 7g jc.

5 foxiv de xat, otcov ^ rov STtMVKkov didpsrQOS ^?c,

TOIOVTCOV % FB sv&sla o^ xd A' vitorewsi, yap r^vBF 7CQt,g)Qiav [lOiQ&v ovtiav act Ag* xal o

f

icov aga0rlv ^ plv BF v&tcc o^ xd Af, ^ df roi) eitMVKhov

dlKllTQOS ^X, TOLOVTGOV 6tttl Xttl V\ [lV 4E V&tCC

10 wy Ag AO1

, ^ $ FE rcov avrcov oa Ta d. &6T nccl

r\7t' ccfaiis itQi><pQitt fi

FE roiovtcw 6rlv o/3 jilg I,

o!W 6 frtixvxhos t%- t&v df afa&v f\ TEA vnoxsi-

rcct, Q%rj y* xccl Aotjr^ plv KQK f)EA ttQt,tp()(,K poi-

Q&V i<5nv 9f 7g v, 17$ i)ri ai>r^v fti&tia ^ AE

15 roiovrcov ;r^ ^ t, otov cVrlv 17 f*^v

^ df Jz/ i)frsia yjpy Ag

aAtV ^ EA 1tQl(pQl,

, dijAov, ort TO XWTQOV rov fjtixvxtov x-

rbs 7t6trai, rov EA rpârog. Mtjtp&a) di) al Zero

20 ro -K", xal tTte&vffiG) fj4MKA, &6r itaKiv rb ply

A Grftislov yivsG&Ki rb aitoyuorarov ,ro dl M rb

7tQLyt,6rarov. 7ti ovv rb VTtb Ad xccl dE

1. Se]_d'D.

x^]corr. ex x(3

D 2. 3. jiy] A 4B 3

, Â CD. ^] corr. ex t D 2

. 4. x] corr. ex xf D. 5. SGTLV]

comp. B, <>rt D. 6. FB] EP D. 11. TISQ^QSLU] seq.ras. 1 litt. A, nsQicpsQi-icii C. ^crtV] om. D. 12. fo'J d' ins. D 2

.

13. 0!?;] corr. ex p| D 2. 14. v] corr. ex

rjA 1

. 15. 17]

ins. D 2. 16. EJ] 4E C. 19. EA rûrog] E KT^ZOS D,

EA Tj&rjrog D 2. 20. X] K arîsiov D. xa/] supra scr. D 2

.

AMKA\ corr. ex 4KA D 2. 21. ^1] corr. ex A D 2

. ytyi/f-aO-at C. rb 8s M xb itSQiysiorccTov] mg. C 2

. 22. Post UJTO

add. T&V C 2. Trfpie^d/tifvoi'] corr. ex nQi%o(iEv D 2

.

MA0HMATIKHS STNTABE&2 A'. 321

%6{isvov ogfroycbviov i'6ov itixiv real vjtb t&v A z/ xal

4M [Eucl. IE, 36], dedeixTat, d' rjîlv, on, oitov

etirlv AKM TOV btucvxlov

x, ToiovT&v stirlvr\

AE ev&ela nrj p tj, r\de 5

Ed T&V ccvr&v ipy ACT AO-, ^ ds

Ad ohy driôvon tykfi 7g vs,

yivsxca ro v

rb vnb Ad xal <dM, r&v

avxcbv M ardjitg tf. ndfav de, iitel 10

ro vnb AdM psrcc rov anb KMjtotsi TO ciTtb rr}s 4K rstQccycdvov

[Eucl. II7 6], ri de KM sx TOV

X8VTQOV OVGCC TOV 7tiXVxA.OV [s^tj-

XOVTO] Ttoist TO KTC ccvTrjs /y%, 15

/* _ _Tats Tcgoxeipevais M p,x jilg tg,

jilg i'

lav Ta /y%

v TO curb 4K TSTQaycwov T&V avTCbvM

1. IffrtV] comp. B, -v eras. D. ro5] corr. ex TO C 2D 2. xca]

om. D. 2. d'] postea ins. D. 3. AKM~] A- postea ins. A,corr. ex AKM D 2

. did[itQOS tov ITCLY.VÔV D. 4. fffriv17]

corr. ex Ivtt D 2. 5. if] t?^ D, corr. D 2

. 6. JWKJ --9- in ras. D 2.

8. ytVfrat] yt- in ras. 3 litt. D 2. 9. XOVTSGTIV] -v eras. D,

rovrsOTL B. VTTO] -UTTO TWV D. Ad] Ad CD, corr. D 2. 10.

/u d

M] mut.in # p D 2. TraZtv dt, Inei] -naliv ABC, Tra^w; d'

tni D, TraAtv ^' inet D 2;conf. p. 312, 4. 11. A4M] r&v AA

xalJM D. KM~\ xf\sKM TSTgdycovov D. 14. f|?jxovra] deleo.

^'xoiTa 15./y^J mg. D 2

;in textu TWV avr&v ioriv |f, quae

del. D 2. 16. ,72] -^ in ras. C, y- e corr. D. Deinde add. rov

Lt^~

v D. M] mut. infi [i

D 2. t^] t? D. 17. ccito] anb

D. TgTpccycoycovov A, sed corr. M] mut. in ft fiD 2

.

^^] corr. ex J&S D 2.

xal [iijxfi, aga street, rj4K x rov Xvroov ov6a rov

roiovrav %7t& rj, O'LCOV 6rlv ^ KM ex rov XEVTQOV

ov6a rov Znixvxkov Qtjxovra. &6re xat, olcov etiriv

5 r\ [israt.v r&v xevrg&v rov re dia p&ov r&v ^cpdC&v

xal rov srtixvxAov e^xovra, roiovrcw sGrcci, xccli\

sx

rov xevrgov rov STUxvxAov id. xaC fanv 6 ccvrbg

Adyog r& dia r&v TtaAaioreocov sxfafyecov

10fjjtd'G) dq Ttukiv 7il rrjg ccvrijs xarccygccipiig KTCQ

rov K xsvrgov xd&erog enl rty AEA v\ KNE, xal

7t%SV%d'K) $1AK. 7tl OVV, OLG)V

rj4K

i?, roiovrcov i\v xal ^ ^V ^E sv&tfa

d NE ruiiGeiK ovaa rijs AE [Encl. HI, 3] r&v av-

15 r&v (Snv pd xrj,

caGrs xal o/b?i> rr\v 4EN rcbv av-

r&v %it^ ~v$ ft^ xal of

i(ov 6rlv aga y 4K vitorsi-

vovGa ^jc, roiovrcov xalfj4N <5rai, QI& ^ AST, f}

de Tt avrijs 3toi,q)Qi,a roiovrov Qoy i lyyitita,

oinv 6rlv 6 xsgl rb AKN OQ&oy&viov xvxhos r%'

20 &6r xal17

vitb 4KN ycwia, olcw pw ti<5iv ai dvo

OQ&al r%, roLOvrov 6rlv ooy tg, oi&v $ ai

T|, roiovrcov 6rlv jrg A^ /.'. xalfj ^sv ME&

rov STCixvxkov tti(Qt,a loi&v <5ri,v :rg A A

2. tptgovTog] corr. ex nsQLyeQovros D 2. 4. OVGCC] om. D.

5. xs] om. D. 7. s] e corr. D. 8. TW] TW g* D. 10.

ccno] ini D. 11. 4EA~\ AE D, J add. D 2. 12. ini-

&v%fra> B. 15. t<>riv\ comp. B, om. D. x ^] xrj BCD,corr. D 2

. uvrcbv] avr&v yiveG&ca D. 16. iTg] -g e corr. D 2.

K] -K e corr. D 2. 17. rj (pr.)] ^ fisv D. 4 N] -N e

corr. D 2. 18. df] S' D. In] corr. ex bn D 2

. 20. &GTE] in ras. D 2.

w<7T 21. T^] om. C. 21. iariv] comp. B, fGTca D. 22. ievfv']

om. D. f] ^g BC, corr. B. 23.1] A, /.' BCD.

MA0HMATIKHS STNTAEE&2 A'. 323

AA& r&v hoiit&v is rb YiyunvKfaov 97 xa A. rav d

avtojv idnv fj A$ 7iQLfp0ta Y}{ii6ia ov6a rijs AE[Eucl. Ill, 30] [loiQcdv ft A^ A

fyyiGra' xal Aotjri) aoa ^ -AA7tQl,(pQia [IOIQG)V ititlV \IB fty.

vitmsiro d xalj]AB

avr&v QI> na' xal

AB 7COi(pOLa^ r^v

GfArivr] rov aitoyeiordrov

rOV XKt[lVOV

rav

OCQCC %

xccrcc

10

yiv VTtO

y&vfa fatedEt%fhi TOLOVT&V TCS Ay

,oiwv at d OQ&al T|, fj

15

[Eucl. I, 32] el ^n

Ufa V1tXirO d KOIfj

A4B 0^77 T&V avrcbv % ^t/3,xccl koutii aga fj

vitb A4Bijtig V7torivi, xv\v acpat,Qov[ivr)v xi\g ^0rj xara 20

TtaQodov rov dia pfaov r&v <pdfav xvxAov

7tQi(pQi,av x Ttjg itctQa xj\v AB yi,voiivrj$ rov iiti-

&vm(utJifa$y poiowv fatal d K. Kal Kara pijxos

aoa fieti&s iti%v % ffe^wj xara rov pfaov %o6vov

1. i] A, /_' BCD. 8] S' D. 3. i] A, L' BCD. 5.

comp. B, -v del. D 2. jte] -8 in ras. D 2

. 7. xcu]*a D. ago] om. D. 8. AB] corr. ex AB D 2

. 13.

corr. ex Int D 2. _ r\\

ins. D 2. 14. i8s%r\ D. 17. stg]

corr. ex ^g A. 18. y] in ras. D. vnonsiro C. xat] seq.ras. 1 litt. D. 19. ^4z/] -z/E in ras. D 2

. olrj] seq. ras.

1 2 litt. D. 22. AB] corr. ex 4B D. roi)

D.

21

tils dvtoccs sx&efys&s tov Koiov ILOLQKQ x& A,

dtfxeQ axQip&s zitetyev poious xe t, otfag xal 6 ijhog

tcbv Xyhcov.

,'. Ilol tijs dioQfr&Geas t&v5 tils 6A>ijvvjS [iijxovs rs xal avopcchtag.

'Eitel rotvvv Iv p^v rri devrsga r&v Ttakai&v sx-

attdsfi-ccusv r^v tieAtjvrjv xara rbv [is<5ov

7te%ov6av 6Â? Kara pijxos [isv IlaQ&evovid ftd, Kv&paMas de ano rov aitoyetov rov

10 STtMvxAov poiQag t/3 xd, iv ds rfj dsvtsga r&v xa&

tQi&v sxhefysiDv dîoicag it%ov6a ftfVog CCTCS-

Kara pijxos i&v rov KQLOV poisons x& A,

$ dttb tov ajtoystov ^lOi

on, xccl iv tip [ista^v %o6vG) TK>V XQOXsipsvcov

15 tyG)v STteAccfls [ifaas v\ GsArjvr] ftcO1'

o'Aov?

[iijxovs [isv /itotâg 6xd pg^ avcsîaîag ds [loioas vfi

id. AA' 6 iiTa%v %oovos TOV rs devrsoov srovg Mao-~

I'YI lg rrjv i&' rtab /_' ual y' a

tov {i6ovvxTiov xal tov i&' tovs'

20 vov Xo'Cax ft' fig t^v y' nob fi

tOV [IBGOVVKtlOV 3tQiB%l, j4fyv7ttlCCXK trj &vd Xttl

O/ KKl COQCCS i^^fQLVag CCJtA&

xal jtobg ta oîcda

2. sitei%e D. 4.']om. AD. diogftwcicog] om. D.

ivriGt&v D. 5. rfjs <TfArjv7j?] diOQft&Gfcog D. 6. na-Ttaîai&v TQI&V D. 8. nata] seq. ras. 2 litt. D. 11.

C. 13. lr[\ corr. ex As D. 14. xca'] supra scr. D 8.

15. BTtslKfisv D, corr. D 2. 16. JUTJXOVS] supra p ras. A.

17. 6] seq. ras. 3 litt. D. 18. a &QUS] rjpsQccs D, del. D 2,

mg. roâj D, piae wyccs D 2. 20. Xvdv. D, corr. D 2

. y'jC. 21. Irtt C. 22. ndUv] om B.

MA0HMATIKH2 STNTAEE&S A'. 325

/la

y'9 rtddag 6% f)[iQag M xal ptyyty xal agag

vag xy y', aig VQfaxo[iv BTtifiakhovdag [16&

xvxhovg 7tov6i'ag x rcov 7tQOxr&t,[iva)xara rag Ttgb rijg dioQ&mGf&g V7to&6i,g

jioiQccg 6xdjiTcr, av&iLaAiag d [loigccg vfi 5

Aa, ag r^v plv rov [iijxovg itov6iav

fog (paiiv, fvgriG&cci, TTJ dice r&v XXLÎV(DV

i)<p ruicbv Gwajfoefari, tyr ds rr^g avcDpccMag

&iv QqxoGtoZg 1%. o&v itgb ryg r&v xavovt&v K-

&<5G)g vXv Tijg T&v ri^f^îov^dQo^cov diog&aGfcog 10

ra L^ %r]xo6T(x 7ti,[iQi0ccvtg fig rb TtQoxeiyievov r&v

fiHSQ&v TtA.ijd'og ra xd&rr] f}H>Q(x iti(idMovra o o o o

lajiZ?

A-91

acpA.6vrg rov xgb rr^g dioQ&coGf&g xari-

[p. 2787 16] VQO(iv [p. 279, 14] rb di&Q&coiiwov poi- 15

pwv Ty y vy 1^ tj w 1/-91

, alg axoAovfrcag xal rag

r&v xavovicw

r&v bîa^&v rijg

xivirj<3G)v [itjxovg r xal av&paAiag.f

'Ivu $ xal rag 7to%ag avr&v 6v6rrj6(D[id'a fig rb 20

avrb TtQ&rov rog Na(lova66d()ov xary

(daft u rijg [i6r][i(l()iag) Ad(lo[iv rov ivrsv&ev

vov p>%Qi> rov ii6ov rijg dfvrfyag SxAefapecos r&v

Ha1. M] (ivQiddccs ha D. 3. TJ/^rjfftW] j]plv rjêQrt 6i(ov C.

4. rag itQO T^J] rijs ifQatris B. 8. Ttteovdfeiv] -dfew e

corr. D 2seq. ras. 5 litt. 10. ^ftf^rjatcotj 17- ins. D 2

. Sg

dLOQ&motas] mg. D 2,in textu fa&saemg D, del. D 2

. 11.

KQGTO.S D, corr. D a. 13. dto^cofffcug] seq. ras. 2 3 litt. I).

14. rf]s ccv&iJicdiKg] supra scr. D 2. 18.

rj'~\om. D. 21.

D. 23. T%] seq. in ras. 4 litt. B.

xal eyyvrdg&v rgi&v, r\n^ cos <paiiv, ysyove

^7tddov xar' Alyvnriov &&>& itf

/.' xal yr

a cngag farjpSQwIjs rov pe-

(SovvxrCov Gvvdysrcci ds ovros zrtibv Alyvitnax&v x

5 KOL f}[ieQG)V l^ XKi G3QG3V CCTth&S T XCCi C

Ice 5', xal ttccQccxsivtcci, T& roGovra) XQOVG)

eitovtitas [iijxovs [isv [lotQcci, guy x/S, d

ds ILQLQKL ^7 A' as &v a(pe&G)[iev r&v sv

10 ay' sxccrfyas oixsi&s, %o[iv ig to TtQcatov stos

xar Alyvxriovs cod' a trjs pe'dcos ity 6&rivriv xara plv pijxos Tavgov

Ta Xj8 5 dvaiittMccs $ dftb fov dnoyfiov rov

7ti,xvxA.ov ponces 6^1 f*^5 djto%fjs $ drjôv6n

15 o AJ, litfidr^TtsQ xal 6 rjAtog t$ tbv avrbv

r&v '!&va)v itG)v loias o i.

diOQ&G)6G)S t&v xard

jtaQodcov rijs Gskiqvris xal r&v 7to%wvavrcbv.

20 Tds plv ovv rov [irfxovg xal r^g dvco[iaMas

MQiodixas xwtf(3is xai n rds iito%a$ avrcbv did r&v

roiovrov <p6da)v GvvfGrrjtidnf&a, Irii ds rcbv xard

xal avrol

1. syyvTEQco D. TJVIS] ^trt C, faHefysmv ijtis D. cpupsv D.

yeyovev B. 3. y' a] ya C. 4. ovroos C. Mg. (H D. 6.

g'l t? B. ncnQKyiKitKi D. 7. snovafa D. 10. NUÔVVK-GCCQOV D. 12. ju,7]xovg C. 13. d] supra scr. D 2

. 16. &TIO-

8sl%frri C. ane%cov D. 17.-8-']

om. D. 18. ce^rjvrjs]

comp. AC. rcbv BTCO^&V] rfjs sno^fig D. 21. 810. rmv~\ -cc r-

renouat. D 2. 23. diriûgra.vo^v'] SL- in ras. 3 litt. D 2 et

supra scr. D a. 0vy^9a>ftfi/ot] -vy- et -co- e corr. D 2

.

%gd)[ivoi, Kara rbv "IititaQftov rtf rr^v 6A.ijvr)v %axo-

6idxig fiei> xal rtfvrrjxovrdxig fyyitira xara[irolv rbv

ffiiov xvxhov, dig de xal f}[ii,6dxi,g rbv rfjg 6xiag xara-

HTQiv xard rb ev ralg Gvtvyiaig p&tov ditoGrrjiia'

rovr&v ydo vitox^^dvov xal rijg Jtrjfaxorrjros rrjg sy- 5

rov Ao|oi) xvxhov rtfe Gshijvrjg oi r&v Kara

avriig sxtefyscov OQOI didovrai. 2.ccîftccvovrg

ovv dia,6tK6i$ xtei,7tri,xag xal dnb rov ^y^d-ovg r&v

xccra rovg ps'tiovg %Qovovg 7ti,6xorr)(3G)v r&g dxQifotg

xara nhdrog itl rov Ao|oi) xvxAov naoodovg d(p dno- 10

roov rcov 0vvd0^G)v fmôyi^^voi did rs rijg aito-

xara rr\v dv&iiccMccv dictcpooag dytb r&v

rag 7toi,odt,xag diaxoivovrg ovr&g

rdg r xarti rovg [i6ovg %g6vovg rcbv xfofyG)v tito-

%ag rov TtEoiodixov nhdrovg voi^xo^v xal rqv v 15

(p ftf^' oAovg xvxhovg ixwtifav. vvv

%aQie6rQai$ ecpodoig xal iiydwbg r&v

&i,nVK)v 7tido^8VKLg Ttobg rqv rcbv

xccrd^îv rtjv r $t' XiVK>v STtiksko-

rov nhdrovg itdgodov VQO^,V di^v6îvr^v 20

xul dnb rtfg vvv x&olg XIVCDV xarihr]ii[ivr)g xal rdg

V7tod'6ig avrdg rdg 7tol rd [if'y&r] xal rd

fiara pr} ovr&g %ov6ag ^ f>yâvrg di>G)Q&c

rb $ opoiov rt7toirixa[iv iiti r r&v rov KQOVOV xal

D. g|axo(TtaHts] m\it. in |axo<7ioireoug C 2,

e corr. D. 3. TT;S] tf) D. 7. xlel0a>i> (-vcorr. ex g D 2

) avr^g D. SiSovui D, corr. D 2. 8. rcov] corr.

ex rovs D 2. 14. re] supra scr. D 2

. 17. %ttQiGTiQOis C.

18. vTtoTi&stitvcov D. 19. inikl.Q'yiG\\Ltvifiv A, f7rt^Zoyt|(7ju,-

vi\v A 1. 21. natiJir}[L[isvr]s~\ pr. -rj- corr. ex 1 in scrib. C.

22. v.a.1 rd] Kurd C. 23. diOQd-caGdfis&a CD, corr. D 2. 24.

8s] d' D. in] xal ini D. r&v] rov C. xat] xai r&v D.

TOV(

EQ[IOV VJtO&GG)V XWtJGaVT^S TlVtt TG)V JtOOTOG)V

ov itccvv axaificbs efari[i[ivcov di& TO v6TQOV ddi-

6TttXTOTQCCl,S TrjatJGfGl, 3tQLTTV%r}X8VCCl,.

rotg t<p OVTL <pi,A,cchvjd'G)s xccl fyryrix

5 ftfooQia 7too<5Q%oiivoi,s pi} nabs [tovqv rv\v T&v ita-

r&v litl rb adi6TaxT6tQOv VQ1,6x0[isvcav

xal yfobs TT)V rcbv idicav^ av ovr&s h'%G)<5i,

10 7tcc'yyMaSi xav vn* aM&v xalfti) [i6vov T&g?' av

TilS && VO <XXQI,(l<3TQOV TV%G)6l dlOQ&TLVK [lV OVV TQOTtOV SKK6TO, TOVT&V K

V Tots (p%ijs trf's 6VVTK&&S xar& TOVS

T6rtOVS <X7todd)60llV. TQ^6^ld~CC $ V TG)

15 KKOkoV&iCtg VSKGV 7tl T^V T^S XaTK TthttTOS

CpodoV TOLCCVTrjV.

TtQKtTOV [lV OVV 1$ ify ttVTi]S T^S [l6V]S

TG)V

20 JtfaiGTOv %aovov, xa&' as TCC T îyd"rj T&V 7ti6xo-

Tt]6ov faa ydyov xal 7tQi TOV avTov Vvvdetfpov, xal

d[i(poTaas iJTOi, an aaxTcovtjdnb î6rjî^QLag^ xal STL

(ol TO l'6ov] iiv dnoGTriua. TOVTCOV dw ov-

1. vno&EGtav} mg. B. TCQOTSQOV D. 2.

corr. ex adicczcrxTorsQccis D; deinde del. KCLTO, D 2. 7. r&v~] corr.

ex TOV C 2. to] supra scr. D 2

. ccdiacTayiTOTsgov D, corr. D 2.

8. ovrcos] supra scr. D 2. ftrjd' D. 12. TQOITOV] corr. ex

D 2. 14. ds~\ d' D. 16. St-l&iv A. f] ^ D, T D 2

.

20. TO] corr. ex Y.KTO. D 2. ^fyf-9-ft D, corr. D 2

. 21. L'GK]

in ras. D 2, mg. t'. ysyovtv BD, corr. D 2

. 23. TO] TOV C.

f}v~\ seq. ras. 1 litt. A. ajrdffrjjfia] &.- in ras. A 1. drj]

yd$ D, non male; corr. D 2.

rcog %6vT(av ccvdywr] TO KBvrQOv r^

rcbv sxhsfyscov iitl ra avra

rov ccvrov Gwdfapov xccl dtd rovro rr\v axQiflij

ccvrrls oAovg xccra nAdros xvxAovs sv trca

jtQt,%ei,v. 5

plv eKteityiv rrjv enl dageiovrov jtQ&Tov rerrjQrjiis'vriv lv BccpvA&vi r& jtg&TG) xal

G) ccvrov erst, xccr' AlyvitrCovg Tvftl y' fig

COQCCS %' |it<?^g, xcc&' TJV diaGcccpstrcci,) on J

|-

fj 6&v\VY\ KTtb vorov daxrvhovs /3.10

sQccv ds rv\v rsrrjQrjUEvrjv iv 'AK&>av8Kia, r&

b'rsu 'Adgiavov XUT' Afyvitriovs IIa%G3V i% stg rr\v

yiQO rpi&v aQ&v faYjpSQivcov xal rgi&v

&Qccg rov peGovvKrfov, na& r^v oftotojg

rj 6e^vri rb sxtov [legos ffjs SiayihQov aito n<5- 15

]v ds xal fj [iv Kara jt^drog TCccôdog rye;

TCSQl rov xccra{}i,(ldovTcc 6vvd<5[iov iv xarQa r&v

rb yKQ rOLOVrOV Xttl IK rCOV dA.06%Q6TQCOVV7to&6G)v Kur&.'kapft&vsrvii. rb d aTto^rrîcc fyyiGrcc 20

i6ov Keel utxQco rov p6ov itfQiyfiorfQOV xal rovro

TG)V 7tQOCC7toddl,'y[lVC()V 7tQl Trj

1. avdywr)] -y- corr. ex i in scrib. C. 3. TOV avrov] corr.

ex TOV D 2. 5. %qov(p"\ corr. ex XQOVCQV D. 6. Mg. a D.

fyla/3oft D, JAaôft D 3. drj] corr. ex ovv D 2

. itQorrjv C.

fiev"] ins. D 2. 8. trsi ccvro^ B. Atyvmiovg'] -ovg in

ras. D 2. Tv/3t] T- e corr. D 2

. 9. s'] om. D, wrr)s D 2.

dtjaffaqpffrca A, dia\aacpiTai A 1. ^|e7ft7Tv] supra -8i-

scr. i D 2. 11. Mg. {3

D. trca]corr. ex T&V D. 13. rgi&v

7li\LTlX(QV\ TQLTOV V.O.I TCSflTtTOV D. 14. ^^L7t8V D. 17. jWfV]ins. D 2

. 20. ds~] 8' D. 21. nsQiytiottQOv] -to'- in ras. 4litt. ]3

2.

yivtrui dr\kov. Emid^ ovv, OTCCV ditb VOTOV

V\ 6h?jvr]) floQl,6TQ6v B6TIV TO XEVTQOV CCVTriS TOV

, (pctvQ6v, on xal xafi'' EXCCTEOKV T&V x-

i'Gq) TtoorjyEtTO TOV xaraf$i{ldovros 6vv-

5 ds6[iov TO XVTQOV Trig Gehrjvrjg. dhhd xciTa yiev rr\v

aitsfyev fy 0e^rjvrj TOV anoysiov TOV

xal %r]xo6Ta i-9" 6 ycco 4u(?og

sv BaftvAcbvi,i

y8iyovv nob riyu&Qiov TOV ILB&O-

vvxTiov, v 'Ake^avdQEiK d ttob [lias TQLTOV (boas

10 i6rniEQivYis, ual 6 ccTtb Tijs tito^s Trjg 7tl NafiovccG-

6&QOV XQOVOS 6VVKy8i TVl 0VZ XCil f)[lQCC

thcbs per I rS, nobs ds TK

i d', xccl dia TOVTO EAccTT&v rjv r\

S TtSQLOdlXrjS 71BVT8 [lOLQCCtS. KCCTCC $ Tr\V

15 dsvTBQKv Exteifyiv ani%ev j] Gfhtjvrj TOV aitoysiov TOV

7tixvxA,ov lotott 6vcc w' xal v&dd ao 6

Trj C3occ Kul fjpsoas 6v<5 xal wooes t6r][iQi,vas

[iv rj xal dvo jr^jrra, dxQifi&s $ n xa

20 did TOVTO $ xal ^ dxQififjs rtdoodos TtfaCwv i]v Tr^g

%OOVG) TG)V

i XCCi

2X mg. D. 6Tw] comp. B, ICTL in extr. lin. D. 3.

[isocav] (IG<QV T&V fadtoov D, corr. D 2. %at] corr. ex Y.&V D 2

.

6.rj] ins. D 2

. 7. ^] seq. ras. 1 litt. D. g^xocrra] om. D,

^|a BD 2

. 8. iv\ fv pv D. ysyovs D. 9. ^Zflavd^fat A,

'Ateccv6

D. 10. NapovvctGciQOv D. 12. r*] ^ BD, / AC,

dt' supra scr. D 2. 13. TOVTO] corr. ex TO C 2

. skaTtco C,corr. C 2

. T\V ri\ corr. ex fl'r] D 2. 15. ctntiitv] untile fisv I),

ptv del. D 2. 17. rjjg] rfjG\6 D. 19.

rj (alt.)] corr. ex o in

scrib. C. xca (alt.)] comp. supra scr. D 2. 21. ~S vy] post

ras. 1 litt. D, 8vy AC. 22. nEQitxovTi\ -i in ras. 2 lilt. D 2.

MAOHMATIKHS 2TNTAHE3S A'. 331

xal cogag farjiiSQiv&s KM [_' y' rj (lev CC

xata TtAdtog rtdgodog tf}g 6^vrig okovg 7tSQie%i,

, 17$ ItEQloSiXri VAt,7tV s$ ohovg XVX?iOVg

taig fj an,<potQ&v t&v avco[icdiG)v Gwayoiiwaig poi-

gcug # vy. eAfofasL de ex r&v itQOSXTS&eiiievcov xaxa 5

rag tovc

lTtita^%ov V7to&6i,g [ifa&v Ttagod&v sv rc3

G) ?g ohag attoxaTcc6ra6t,g iioiQccg i xal

a fyyitfra /3* jrAftov agcc yiyovsv TIKQCC rag

rj iL6rj xccta Jt/Unrog rtdgodog QqxoGroig &.

ovv 7UiiQfaavrg fig to nkri&og r&v x rov 10

y.fi

7tQOXl,[lVOV %Q6VOV (JVVayO^VOV f]{lQG3V M %& fy-

ytfra xal ra x rijg 7taQa($ohrjg ysysvruiEva o o o o77

AO- Irj 7tQo6d'vtg TG3 xat' Ixuvccg tag V7to&6i,g ngo-

ajcoddi,'y^VG) fjHQr]GiG) p^GG) xivrman [p. 279, 4]

VQO[iv [p. 279; 16] to dicoQ&KHLBvov poiQCbv !/y ~iy ~\Tz

15

AO" ^ ~v% AJ, alg TCukiv axo&ovd'&g xal tag

t&v KKvovCwv litiGvv&BGEig 7tQai

yiiatv6d[id'a.

d$i,'y[iivrig d ccTtafc, tov tgditov tovtov ti\g

dixfjg xata rthdtog xwYjtif&g ,fjg xal ig tqv t&v

avtrjg <5v6tct6iv ^rjtt]&a^v nafav dt,d<5ta<5iv 20

1. rjfiSQUL D. mQca l6r]peQivul D. xa C. y'] seq.ras. 3 litt. D. Supra ajt^tfSrjg KKTK ras. D. 2.

iD, post -do- ras. 1 litt. nsQisfytv D, -v del. D 2

.

3. svehnsv D. 4. poigaig GWKyo[ivcit$ D. 5. vy] v y A.

ds ex] corr. ex 5J

Ix D. 6. rov] supra scr. D . sv\

ins. D 2. 8. |3] dvo corr. ex 8va D. y^yovs D. 10. ovv]

per ovv D, corr.D 2. 11. M] ADB 3

, ^ BC, *J3 D 2.

^-9- CD, corr. D 2. 12. TO: ex] corr. ex raaex D 9

.

D. o (quart.)] ins. D 2. 13. rm\ ins. D 2

.

corr. ex tnovaff C 2. 14. ^fpijcioo] -co corr. ex -oav in scrib. A,

^- corr. ex v D 9. 15. SioQ&cofisvov CD, corr. D 2

. 17. em-ult. corr. ex t in scrib. A. 19. xca] comp. A.

8- postea ins. A.


txksfys&v dvo, xcc&' as rcc psv

rolg TCQOTSQOV Gwdfiawsv, TOVTS'GTLV TK TS aito-

rife GsAtjvys syyiGTa faa syivsro xccl aC siu-

facu, rs xal JJTOI TfQOs CCQXTOVS 1} Jtgb

a^(p6rEQa,i^ 6 $ tivvdeGpos ovxsrt, 6

6 svccvrtos.

xal rovrwv d% rcbv txfafys&v itQ&rrj

'K xal 7CQO$ r^v tfjs avco^ct^ccg

ds rc3 /?' srsi MagdoxsiiTtddov xar

10 TLOvg cod' itf slg tnv l& & ^ v BafivAcbvi, rov

de 'AksâvdQeia ago L' y' pi>&1

'

r^v diaGccyeZrai, Extehoiitvicc fj

ccjtb v6rov daurvAovs y.

devT8Qcc de, ri Keelr

'l7t7tccQ%os 6vve%Qri

15 Tc5 K' erst, dagsCov rov pera Ka[i{lv6r]v xccr' Atyvit-

sis rfv nft' rijg VVXTOS TtQOsh&ovGrjs

y', KK& tjv Oftotog s$sA.st,3tsv fj

aitb VOTOV TO rzrccQTOv ti]g dia^BrQov^ xal i\v

6 [i6os XQOVOS sv iiev Bafivk&vL XQO Svo Ttsînrcov

20 [lias &QKS l6yiiQ(>vfis fov psdovvxriov ,snsl TO î-

vvxnov i\v TOTS MQcbv^forjusQivcbv g /_' d' syyitiTcc, sv

'AAsâvdysia ds TCQO cc d' CDQCCS faypSQiviis TOV

VVXTLOV.

D, -cc- eras. 2. GVV$UIVEV\ -v eras. D.

comp. B, -v eras. D. 3. I'GCC ^yytcra D. sys-vovro D, t supra scr. D 2

. 5. ovntri] corr. ex ot>x ?Wt D 2.

6. all? D. 7. TtQwrriv D, corr. D 2. 9. Ss] comp. ins. D 2

.

11. HQO\ -6 ins. D 2. 14. l7tncc()%o$] 6

r

'ImtccQ D. ysvo-

(UfVrj CD. 17. tj y'] % T C. Q&tmiv D. 18.

d' B et seq. ras. 4 litt. D. 19. uip-jitov D. 20.

VVXTIOV D. 21. /'I in ras. A. 22. 'AHEâvSotcci A.

ins. D 2.

TBQK

E dl xal TOVTOV rcbv sxfofyecov EXKTEQK T^g

negl TO frfyttitov ovGqg ajro'tfr^a, aMarj [lev

TOV avccpi,pdovTa GvvdsGiiov, % de dsv-

rbv xccTapifid^ovTcc, csg xccl EVTCCV&CC T& i'6c)

sivcu rov dia [is'dcw sv avralg TO KBVZQOV 5

6x03 dr\ 6 Ao|6g ccvrfjs Kvxko<s b ABP TCEQI did-

TO [lev A Grftistov b

G)v tivvdeGpos ,TO

ds F b xaTccfiipd&v, TO ds 10

B (loQi6TaTov 7tQccg, xal

aTtElAtfcpd-GXyaV fcai, 7tQl(p-

QiKi d(p' XCCTQOV TfOV A, F6vvd6[iG)v as JCQOS TO B /3d-

QIOV 7tQCCg Oil Ad KCcl FE, 15

&6TE KCCTK {LEV TVJV ItQOTSQKV

Kara TO A ivca TO

/3' XCCTK TO E.XBVTQOV

fiv iitl

TK)V 6TIV

KCCTK

Kttl tj Xttl G)Q(bV 20

v catkcbg TE xccl ccxQifi&g la gr

,xccl dia TOVTO

cc7tl%v rj GEhtjvr] onto TOV anoyEiov TOV Eitixvxkov

t/3 xdj jtfaicov TE %\v ^ JtEQisodixrj ttdgodog Tijg

ig v&' b dl litl Tqv SEVTEQCCV E'K-

bpOLcog T&v AlyvTtTiccK&v 6{i xccl YULEQ&V TX^ 25

xccl a)QG)v v catk&g {ilv ~i C d', ds

1. s*lfytcov D. 7. 6 (pr.)] postea ins.D.^

Ho6? D. 11.

E] B TO D. 12. TttQicpsQsiui] cone, ex nsQiysQua. A. 13. A,

T] AT B, A Y.&.1 r D. 17. TO (pr.)] TOV D. 18. TO] TOV D.

&U' D. 20. IOTLV] ins. D 2. 21. Ante 5' eras. F A. 22.

ccTto] om. D. 24. 6*6] 8' D. 26. i'] corr. ex [_ A 1. /.' d']

in ras. 1 litt, D 2. dx(uf3oog Ss T d'] mg. D 2

.

Id', xal dt,a rovro aitsfysv fj 6s^vrj cbro rov aito-

ysiov \rov srtixvxAov [IOLQCCS ft ^d, itteicw rs i\v rj

Ttsoiodixri itdoodog rijg dxoiflovs sfyxoGrotg 1/y. xal

6 iiera^v ds r&v rrjotftisav %oovos Ttsoisxcov Alyvit-

5 naxa srrj Wiy xai ^BQKS r& xal &QKS faypSQivac; ny

i$' Gwdyei, Kara ryv aTtodedei'ypsvqv rov

enovtiiav ftotâg p xal

ovv dia ra exxsipsvcc xcclr\ [is0rj jr

rov xsvrQOv r;jg Gshtjvrjs sjtl [iev rijg Ttgoregccs

10 i[>G)s xarcc rb Z, snl ds rijg devrsgas xara rb H. xal

i\ [isv ZBH itZQifpegsia. [IOLQ&V s6nv Q% xal

, r\ds 4Z sfyxotir&v v^, r\

ds EH s%rj-

Ty, 6vva%%"ri<56rai xal ^ Ê TtSQiyegsia [ioi-

v. xal 6vva[i(p6r()a{, per aga ai Ad, ET15 r&v Aoirt&v slow sis rb r\îxvxhov ILOLQ&V i& I, sxa-

rsga ds avr&v, sitsl faai sidCv^ r&v avrcbv ^

fj axQiftrjs itdgodos rrls GsAtfvrjs xara psv r^v

sxAsiiluv VTtshsfasro rov avafti,ftdôvros

xara ds r^v dsvrsoav rov xarapifid&vros

20 xal O^TI ply aoai\A Z rtsoiysasia JIOLQ&V s6nv T Ad,

dsrjHP poiQ&v ft xfi. &0rs xal

fj

rijs 6s^vrjg xara [isv rr^v Jtoorsgav

rov avafiifla&vros 6vvds6pov iioioaig 1 Ad

1. xal i&\ in ras. D. ano] om. D. 2. sniv.vy.\ov] -xvx-in ras. D 2

. Tt^ftcov] -ft- in ras. A 1. TF] 8s D. 4. F'TTJ

Alyvmiana, D. 6. cvvdysi] -a- supra scr. A 1. ajrodf^ftyjjttf-

vr\v corr. in encoded i\ynevr}v A. 7. ^j]v.oGr&v D. 11.

ZBH] ZH D. 12. EH] E- supra scr. D 2. S&KOGT&V]

comp. B. 14. ET] v.al EP D. 16._^] om. D, 8' suprascr. D 2

. stGiv} comp. B, -v del. D 2. #] corr. ex o D 2

seq.

ras. 1 litt. >U] /I- in ras. D 2. 19. itgoriyeito rov nctra-

fit,pdf;ovto$ D. _ 20. poiQ&v] om. D. GTW] comp. B, -v

del. D 2. 23. Id] i j C.

MA0HMATIKHS STNTAgESS A'. 335

xal U7tl%v aitb rov B jSoofiov 7toarog [loiaag tfjr

Ad, xara $ r^v dvroccv Ttaoyytfro rov xarafiipdôv-

rog yioiQttis & xfi nctl aitetyev rov avrov fioQZiov vtBQa-

rog [loioag it Ay.

rov pfaov ryg 7tQoroccg faAffyfcog 7tov6iav

jtAdrovg ôigag 6xg ift, ravrccg

Kara ryv iito%r\v ryg

avrccts Zva nvKkov, ô^v xai els to <*>'

srog NccftovccGGaQOv xar' AlyvxrCovs wO1 a ryg 10

li6ruifiQia.<s r^v rov jtSQLodixov nhdrovs 710%^ aito

rov floostov ttSQcctos {loiaas rvd 7f. xccl ngbs rag

de rCbv Ttsol rag Gvvodovg xai itavGekrivovQ

^qqiocpoQicbV) sitsidrj Kara rag rotccvras

ovdev 7tQo6drjd"r]66[i&ci rijg anodeix&rjGo- 15

devreoag &vtopcdfa$, x&fjtf6n&a r&v xccra pe-

QO$ T[ir][ittta)v xavoviov dia r&v yQapn&v itahv,

xccl 7tl rov ^/U'ov, r^v itQCfyiiccreiccv avr&v

xotl 6wy%Qr}6dnvoi, pv r<p r&v Qtfxovra

xccl d' A(5y, dieAovtes ds catiavrcos ra plv 20

r& ctTtoysicp rrccQrr][i6aia dia ILOIQ&V s1

,ra ds

trc5 itfoiyfiG) dice ^loiQCbv y, cog ndfav rr\v rov

xavoviov diccyaacpriv bpofav yCvstiftat rf} iitl rov rjMov

1. &nefysv] corr. ex &ne%iv D 2. 2. ngoriyti D.' 3.

iBi^s D. 5. Ss~\ 8' D. 6. &d,eog] rfbv fatefyfaw D.

8. GTC Ad corr. ex Gnk d D. 10. NuowaudOv D. a']

D; similia saepe omisi. 11. 6.7to%riv D. 12. niqaros]corr. ex niqug D 8

. 13. xi] v.al rds I). 15. 7tQOG8ei]6Q-

HS&K D. 16. r&v~\ TO r&v D, supra -d ras. et ante -&-ras. 1 litt. 19. ffwronadfievoi, D. rw] seq. ras. 1 litt. D.

t&ptorca] I D, g D 2. 20. wC] om. D. Adyw] -w e

corr. D 2. SiMovxss BC. Ss] d' D. 23. T#] T'TJS D!


V, TGJV

dvo 7tQi%6vrG()v rovg aoi,&iiovs r&v rijg

rov $

5 yi,vo^vrjs Kara r^v tyrppocpOQiav iiti t rov

xal rov Ttkarovs, orav 6 rffc dvG)[iccMag aito rov KTCO-

ysCov rov itMvxhov Gwayd^vog aai&tibs &S ^[loiQ&v ft, ri}$ d 7tQo6&6G)S) orav rag ^

v7tQTtfarr}. nai tGriv rb navoviov roiovro*

1. GEliSicov] -li- supra scr., -8- in ras. A. tQi&v] y B,y D. 4. itQOG&cHpcciQSGSLs] -&- corr. ex o D 2

. 5. yivo-

^f'rTji^D, corr. D 2. 6. 6] 6 ccno D. 7. sag] corr. ex tog D 2

.

8.TI jaot^ag] supra scr. D 2

. 9. v-JtSQitinriri] -y corr. exft D 2

, vntQwninTy B. EGTIV] CD, comp. B, isxi AD 2. toi-

ovtov CD. Deinde add. in imo mg. fol. 93V : inzl^v j\

ro5 a ETSL vafiovvaGaQOv rov daft vsoprjvfa elg TT\V \

\L IK X

&no%f]g |/ ft o A nldrog fiogsi TISQ p TVJ Ts : ?-

|4^

\D.

MA0HMATIKHS STNTAgE&S A'.

Ktt.1

337

Y.OIVOL

(T

itQOG&acpcci-G

v

TtQOG&CtCpUl-

TUT]

Y.& QY. Ice

is

30

I

Is

3

vy (JH-91 Gld

Gun]

GY.S

n

X

6^8

G7C1]

QV

oogGO

gvsQV&

Gift

GLS

GiyGl

y

y

y i

G8GK

is

vy

35

40

ty

c,y

<f

90

GVK]

Gve

vy

45

te

tTJ

1.(,'] B, om. A CD. V.KVOVIOV 2. Gslijvris] om. D. 3.

Offt. f at '1 T\iiQK(pQGi.s D, nQOGvcupKiQ C. 4. cc p y J om. D.

Ha] corr. ex X D. 13. va] corr. ex v D. 31. cl8] Gla D.

35. ffx(5] postea ins. D. Omnia sub uno capite codd.


id. "On ov Ttaoa rag diatpogag r&vnaoa rovg EitiAoyiGiiovg 8ir\vyxev xard

rbvf

'Iit7tao%ov r\ ytrjAixorrjg rrjg

5 Tovrcov ovrwg aitodsdsi'ytiEvcov Eixorcog civ rig

sititfitYiGeiS) dice Ttotav alriav EX r&v vnb rov

%ov 3taQKt&ei[iva)v Gshyviaxcbv sxfofyscov xgbg

rrlg roiccvrrjg avG)[iaMag eititiKstyiv ovts 6 avtbg

TCCL hoyog r vg>' f][iG)v KTtodsdsLy^sva) ovrs

10 6 TtQ&tog Keel dia rrjg xcct' HxxsvTQorrjrcc

r& devrsQC) KKI dice rijg xarJ

ertfavxhov vno-

3ti,foA.O'yi,(j[iVG). xata filv yap r^v jtQcotrjv

dwdyei rov hoyov rfjg x rov xwtgov rov EX-

xwrgov agog rv\v pEru^i* rcbv XEVTQCOV avrov rs xal

15 rov dia [lEti&v r&v Z&di'cov xvxhov, ov E%EI ra yQ[id

Jtobg ra rxt, rB syyiGra, cai Adyw 6 ccvrog 6rt,v 6 r&v

| Ttobg ra g Z?, xara ds rrjv dsvrEpav Gwdysi rbv

Aoyov rrjg EX rov xsvroov rov dia [lEGcov rcbv ^radtov

pEftQi' rov XEvrQov rov ErtixvxAov itobg rr\v BX rov

20 xEvroov rov Eitixvxkov, ov E%EI ra yoxfl [_' ftobg

//, G> hoyc) 6 avrog fanv 6 r&v \ nobg ra d

Ttoisl ds rb JtAEiGrov rrjg dvK)[taMag didcpooov 6

rcbv 1 itgbg ra g 8' k6yog poiQcbv ftO1

,6 8s r&v f

B, om. A CD. tag] seq. ras. 1 litt. C. 7. naga-D. 8. loyos yCvEtai D. 11. vrto&sofas] -g in

ras. D 2. 15. /j^ttf] yy- corr. ex FA 1

, r mut. in I) D 2.

16. ^tj] rt D. r*] r ABC, r B D, Si? D 2

. scnv]icriv g' D, corr. D 2

. 18. Adyov] alt. o in ras. 2 litt. A. 20.

^(^(3] jT Q-x.pD.

[^~\in ras. D 2

. ngog] nqbg rd D. ffj^//]e corr. seq. ras. 2 litt. D. 21. scnv] sen xca D, xat del. D 2

.

23. r&v (pr.)J supra scr. D 2.

ta d~JLS [loiQcbv d Ad, KK& faces rov T&V

ra~

d' koyov poiQcbv syyitircc XOIOVVTOS ttyv wti-

[lV OVV OV TtCCQK rrjV T&V 1)710%'6 G)V

G)S ol'ovrcct tivs, fj TOiavrrj TtaQrjxoA.ov&rjGsv 5

,xal t& Adyw yiiKQ& jrpdfrfrfv tpavegbv fair

yfyovev SH rov x0-' MCCTSQCIV uvr&v ra avra <pcuvo-

psva GvpfiaCveiv ditccQccM.dxrcos, xal dia rfbv aQi&p&v

fo', el ftshriGccinsv TOVS eitiAoyiGiiovs TtoislG&ccii rbv

CCVTOV CCV VQOl[lV yiVQ\lVQV AoyOV f'| tt[KpOTQG)V TG)V 10

)si rots ccvrotg \iivrQi

p exccregas xccl ^dvvccTov y&Q ovrcog k'tircti

TtCCQCl TOVS T&V dlCC6rCC0G)V 3tlAo'yi6[lOVS ify K^KQtLaV 15

Qr^6o^v yovv xal iit Xiv&v r&v

TCCS ^V 6vvyiccs vyi&s TfT^p^jifWg xal

j^vccs rcctg v(p'

xal rijg dvcoîdôv xivvJGfcos V

$ i&v dia6Td(3ov iitiKQyiGpvvs, 81 d)vf} itî- 20

rov Adyov SeiKwrai) ^ liti^^&s^ &S ^vi pd-

ysyevYiyisvQvs. dfiôpfv ds tovrcov

ditb T&V

1. <?(alt.)] A D. U~\ seq. ras. 3 litt. D. w&s rov t&v] -s

tov T- e corr. D 2. 2. [IOIQCQV] {* D. 10. yivofisvov] om. D.

11. fqp' SKccreQccs axoAov-^Tjaaififv D. 12. diacpogois] dia-

qpoêog D. 14. v7tOT8&inVG>v D. ccvrds'] -tag add. D 2.

rug T7]-] e corr. D 2seq. ras. 1 litt. 15. ^môyiGôvg A,

sndoyi\6}iovs A 1. 16. evQioo^sv C. 18. -s tats v-] in ras. D,

rat's supra scr. 21. TOV loyov] rovrcov B, rov C. SVL] e

corr. D 2. (idhcrcc] ft- in ras. 2 litt. D 2

. 22. rovrov C.

TCCVTCCS [iv di) rag rgsts SfJltty&g

KTtO TG3V X Bafivh&VOS dIKXQyilG&eLGcbV O)g Xi

syovzvcci ds TVJV TtQcorrjv KQ%OVTOS

vv\6i <&avo6TQKTov [irjvbs IIoGsids&vos xal

5 Ttsvat r^v 6^vrjv fiQa%v IIQOS TOV xvxhov

Qivr[$ dvatohijs rijg VVXTOS AOITCOV ovro$

xal hi, <pri<sCv, xA,faov6ccr

dv. yivtiui toivvv

6 %(>6vos Kara, TO T%$' rog aitb NccfiovccdtiaQOV

Atyvjtriovis ^f, cos ccvr6s (priGiv, cod" x<s' slg xi]v v^'

10 \JLSrCLf /.' &QO,g XCUQlKCiS TOV llSGOVVKtlOV , 7tldlJ7t()

i\v ffjs VVKXQS fjiM&Qiov. ahAa rov fjAiov ovrog

tec k'<5%attt TOV TOÔTOV v BafivAcbvi, fj Tils

%QOVG)V <5TiV1/Tj' ^ yp VV%

Kttl dlJO ItfyltTOV' CCi 3tVT ij[ll,6V CCQCC

15 XKigwal tivvdyovGiv iGyufQivas &QKS S KKL TQLK

Jt[MtTCC. $1 KQ'xfl KQK T^S xA,fyG)S yfyoVf (JLTa Irj

l,6 [l

CC L'

20 k'yyiGTK, 6 $ [i6os drjhovoTi, [iT<x tO* y' CQQKS

QIVKQ. v 'j4A,%avdQic{ Ttakw aQa yfyovfv 6

XQOVOS Tils xfafyG>s f*^ t^ /.' COQKS l<5rniQiva$ Tils

iv TV} x$' ftfî/ft/3()tag. KKL i^tiv 6 anb Tils wtu TO

1. ^TJ] ovv Set D. TtccQutid'fG&ccL D. 3. Trpcbrrjv] a' B.

mg. D. 4. IIoGide&vos D, corr. D 2. 6. XotTtov] -v

corr. ex i C 2. 8. TO] ins. D 2

. NKÔVaGGa.gov] -CCGG- in ras. A,GccQov D. 9. dz] ft-aft v& D, alt. -O1

postea add.

b'] om. D. 12. tfjs] -fj- e corr. A 1. 13. lmtv\

D, comp. B. atgiav ZGTIV iGrnisgiVcav D. 14. nevte

ypusv] ?/.' BD. 15. rgCci] -i- ins. C 2, y corr. ex ty D. 16.

nsfiTtTK] F D, e" D 2. 17. %cct] in ras. 1 litt. D. TQICC

itsfjintcc] y D, y t" D 2. 18.

|u,s'(>og]om. D. 19. eoâ?] comp.

AC. 22.trj] corr. ex 73

D 2.

MA0HMATIKHS STNTA&EgS A'. 341

'

frog Nafiovao'o'dQov eTto^g %Qovog ^#pt fov i)ito-

STtbv Alyvitnax&v r% xal Y^LSQ&V us xal

ftLQiv&v aith&g [iv Trj /.', dxoip&g d Irj

''itobg ov %QOVOV 7ttôy^6}ivoi xara rag *xxt,[ivag

V V7tO&6ig rOV {llv yklOV VQfaxO{lV aXQlfi&S 5

Toôrov [toiQctg xrj Irj, rrjv d

xal xara rrjv av&iiaMav aittysi rov

rov 7tixv%Aov [LOLQas 6x jUy.

JJV %ijs xA,tipiv (prjGiv yyovvai, aQ%ovrog 10

<&avo<jTQaTOv

iv, djtb &8Qivi\g avaro^g rijg jc^corrjg cngag

yCverai drj xal ovrog 6 %Q6vog xara

to T|S' f'zog anb NafSovaGGaQov <&a[tVG)d' xd' ig xrjv 15

xe' Ttgb ? /.' CSQCOV {idAiGTa xaigixcbv TOV [i6ovvxTiov.

aA,A,a tov îov ovrog Ttfgl ra 6%ara r&v 4t,dv[jiG)v

y rqg vvxrbg figa iv Bafivtibvi %QOVG)V 6rlv ifi' au

aga /.' xaiQixal agon TtoiovGiv foqptytv&Q d xal dvo

n[iiira. q aQ%r] apa rqg &cteAfrGti ytyovtv pierce f 20

fioag t<5r]iiQt,vag xal rgta ne^nta ryg iv rrj xd'

1. (H mg. D. NCCPOVVCCGKQOV D. TtQOHflllSVOV D. 3.

comp. e corr. A 1

seq. ras. 1 litt., om. BC, del. D 2.

4. itQOs ov} corr. ex nocov D 2. 5. rjp&v] corr. ex vp&v D 2

.

~

TOV D. 8.

corr. ex sl%e D 2. 10. qpijeti/] -v del. D 2

. &Q%OVTS<S D, -s-

del. D 2. 11. 'A&i]vr]6i BD. cyu&QotpoQi&vos D, corr. D 2

.

12. St] supra scr. B. l&Jiiieev D, -v del. D 2. 13.

a B. 15. NKÔVVKCKQOV D. 16. pcikiGta. MQ&V D. [ie-

GOKTLOV C. 18.17] corr. ex i\i A, om. BC. tart D, comp. B.

_ 19. "/_' KQK D. KCCI] -K- in ras. A. dvo nlînrcc] ft? g' D,

^ F" D 2. 20. yeyove BD. 21. coâ?] 5- in ras. 2 litt. D 2

,

-a- in ras. A. TQICC nf^nTa] y' s" corr. ex y s D. -r^g]

corr. ex rfj D 2.

rj[if}()icis- &W fad o n&s %Qovog rijs

tQi&v <xva<yQK<psTcci,, 6 ^<?o dyhovoti ysyovssvvsa xccl dexarov cogas fttyptyttri}?. iv

'

CCQCC oysifoi, yeyovsvcci [ista vjd' syyidrcc Syces

5 Qivag r^g ev rij xdr

iLsGrjuPgias. xai i6n ndfav 6 dnb

TG)V S7CO%G)V %QOVOS TG)V AfyvTttlCCX&V T^S KO,l i\^QG)V

&y xal MQcbv tor}(iQt.v&v uicA&s y&v n ^'> KKQI^&Q ds

5 11 y'm

ftQOS ov %g6vov svyfoxopsv rbv per ijfaov

axQijS&S 7ts%ovta ^didv^cov [IOIQCCS xa jilg, tf}v 8s.

10 6s^v^v [t6(QS [lev To^6rov [tongas H/y ^vr^ axQip&s$ lOiCCS MX L( &C1$1XB XCCTcl x) dvCOCiîKV CCTt-

rov K7Coyiov rov

(5vvKyrcci ds xal$} $ufartKft$ j]

coco rv[ rtQ&vrjs sx-

fofyG)S fal inv dsVTSQCCV f}[lQG)V Q0% XOi

15 xccl rQi&v TtfyrttGOV i6r][iQi,VG)v, [loiQcbv d, as o

Qoy xrj^ rovr

Irt7tccQ%ov TtoirjGa^vov

cos tfj? dt,K6Td6&s fiiiSQ&v ILSV

far]HQiVG)V 1/y H d\ ÎOLQ&V ds

rb oydoov [ISQOS [lifts [loigas-

20 rfjv $ tQitriv (prjtilv yfyovsvcu CCQ%OVTOS''

Evavdpov [irjvbs IIo6i,dsG)vos tov TtQorsQOv xccrd

2. peGog] post (i- ras. 1 litt. A. 3. EVVSCC] & BD.

tov] FED, i" D 2. IcTiiiSQivfis] ABC, corr. ex IGT]^QIV(X.<S D 2

.

4.rfi ri KCCI D. d'] mut. in 8" D a

. 5. 6] ins. A 1. 7.

cry] in ras. D 2. iGr}[LQiv&v] corr. ex lc TIÎSQIV&V D 2

.J\ ^']

in fine lineae add. D 2,in initio sequentis f) d' del. D 2

. 8. y']in ras. A 1

. ngbs oV] corr. ex noaov D 2. 10. xy] -y in

ras. D 2. 11. &7ti% corr. ex iTttfytv D 2

. 13. ngwrris] a. B.

14. fovTffttv] B B. 90^] (isv QO D. 15. TQI&V nsfjiTttmv]

sy" D, f" TQI&V D 2. 18. famovccav] -G&V in ras. D 2

. 19. rb

oySoov] i] D, j\" D 2, mg. yg. rb oydoov D 2

. jttôe] jcW^m, -si

in ras., D. fuag] a B. 20. cprtGi D. ysyovsv D, corr. D 2.

21. rov TtQorsQov (irjvbs TIoGsidscovos D. y.ctra\ ncer' C, Kara, df D.

MAOHMATIKHS STNTABE&S A'. 343

00)0- i$ els fty *'' &teut6V de,

dnb &SQI,V&V avccrohcbv d agcbv. ywTat, d?) xal ovrog 6 %QOVOS Kara TO

r' hog drtb Napovattdgov (bO- i$' ig r^v i itgb

]3 // ftaAttfra COQ&V rov iisGovvxttov. aA.A.a rov fyCov 5

ovrog itSQi ra dvo [isQiq tov TOÔTOV sv BafivAtivi, fj

rilS wxrb$ aya XQOVWV itiilv Irj b'yyiGta,' ai KQCK, @

i' GDQCCI xaLQixal xoiovtiw fayiUQivag &Qas y. &GTE

rflg sv rfi i$' lUtiypPofae. aM.a sxsidfj 6'A^ s&AsiTtsv, 10

6 ftfv itas XQOVOS syyitita ysyovsv GOQ&V d

yb ds [i6os %QOVOS drjAovori, îra la cogag

6

sxrov

rrjg iv rf/ i$ ps&r$k$Qfa$. xa i&nv 6 anb t&v 15

r|g xal

xal &Q&V l<5rnLQW&v aith&s plv Ttakuv I

dl -91

/.' y'm

itgbc; ov XQOVOV t&Qfaxapev xbv fiv ijfaov

Toôrov {lotgas tj A, rr}v ds <?aA^'-

[i6G)s pv ^didv^KDv [lOiQag tj ncc, axQip&s ds t 20

^, dia TO xaTa TJJV ava)[iaA.iav UTtiyziv TOV axoyftov

TOV 7CLXvxôv oia jta i. (3vvdTai $ xal f

1. ts'] corr. ex ty D 2. ii-ttutsv D, -v del. D 2

. 2.

KQ^Kfisvri] om. D. <? cb^cov] corr. ex SOOQCOV D 2. 3. Stf]

$ D. 4. NK$ovvttGa.Qov D. tg'j corr. ex v.' D 2. 6. sv]

ndliv sv D. 7. Ivtt D, comp. B. ^ /_' CCQK D. 9. fV

Mtfjscos A. ytyovs D. ft] corr. ex p D 2. ^ffrjjtisptvag]

om.D._

10. &U.'D._ iîlinev D. 11^ yc'yove D, corr. D 2

.

14. F snrov (OQUS] t? D, F g" D 2. 17. T?'] corr. ex Ig D 2

.

18. 7tQO$ ov] corr. ex TTOGOV D 2. 19. TO|OTOV axî^cog D.

20. xa] -a postea ins. D, supra scr. x. 21. TOV] <Jbr6

TOV D.

cbro trig devttQag STtl xv\v tQiryv sxAeityiv did<5ra6ig

V [lV Q0% Xal l0r]^lQiVG)V COQG)V /3, [IOLQ&V $

tovr

Iji7tccQ%ov Ttdkiv v7tod'^Lvov xal rccvrt^v

yilv po xal &Qag a rB

5 ds (>o ^. cpccivsrcci, ovv v rots t&v diaGraGecw iiti-

koyitiiiots dt,si(jvc>[i8vos iitl [isv r&v rjusg&v g' re xal

y' pias G)Qa$ t6vuLQivi\<3 ,itl dl r&v poig&v xgiffl

Tti\LTi'tQi fyyiGra KCL& XCCTQCCV [lifts poiQas, aitQ ov

rrjv rv%ov6av v TTJ jnyAtttdr^Ti rov koyov10 cc7f^ycc6a6d'cct, dvvarcu.

a dfj xccl iiti rag v6tQov

rovrcov d rv\v rtQ&rrjv cprjtilv

rrjs dwrfyas xccta

15 KKT' AlyvTtriov

TtQO

CCQCC

dl G)Q&v KcuQixcbv Tov prfovvxriov, itQQ roGovrcw

20 xal farjiifQivcbV) $Xid4ptQ 6 ijhog itQ\ ra

1. SSVTSQKS] dsvrtQag IxAffywg D. f'jdfityiv] om. D. ^t-

corr. ex dtaffTaffet? D. 2. OJQ&V IGTIUSQIV<QV D. 3.

*Init- e corr. D 2. 4. atQccg] wq&v D. rs

~\ J^ Ar

r BCD, mg. a r" D 2. 5.

73]%at

TJD. 6. du-if>VG\[ievos A,

8itf)v\G[ivo$ A 1. 5'] g wZ D. 7. y'] pwt D; mg. ?HTO>

TS XCU TQltCj) D 2. 8. TTSflTTTOlg] D, f" D 2

. jtUCJs] B.

9. 3rr]/l(.x6T7]trt D. 12. a-urai T^ftg] KVTWV D. (jprjatv] ^? D,/J add. D 2

. 13. TfTTje^ffahu] corr. ex rriQfLG&ca D 2. qprjatv]

comp. D, ex parte renouat. 14. hsi] U,' D, U'st D 8

. Kal-hntnov D. 15. %ar'J xara D. (ASGOQL B. 16. TJJUOOJH'OV] corr.

ex (>ag D 2. %6%ctTov] -c- e corr. D 2

. 17. r^tVTjff] corr.

ex f D 2. 19. TT^O] Tr^dg BC. 20. Tstevrai C.

MA0HMATIKHS A'. 345

cotirs [isra cogag

iv rr] tg' [isGyppQiag iv 'Aks^avdQsCa ydyovw 6

rijg SKAefyecctg. 6n ds 6 KTCO rav xccra TO

frog NaflovccGtidQov STCO^&V %Qovog ir&v Al-

yvmiax&v cpii<5xal r\yiQG)v rJLtf xal MQ&V fariiLSQiv&v 5

ov

rvxg g, t^v d GEJitfv'rjv [ifo&g ^nlv '!%&V(DV ^ot-

Qccg xfi) axQiflcbg ds [IOIQCCS K% ^, dia ro Kara TY\V

avco[iccMccv d7t%iv rov aitoyfiov rov fitixvx&ov {loiQccg 10

t xccl

rijg avrijg

$

Xttl

wary

xcc y

V COQCOV XCCl

CCQCC

Tec xal y' cogag

7tidiJ7tQ itdfav 6

dice TO

6tiv 6 dnb r&v 7to%<av

Jjg X- 15

rijg iv ty

g 7t$l ra

X-

rov- 20

2.TJJ~\ A,

ras.

xy A 4, rrji D. tg'] COIT. ex comp. xat D 2

.

D,"

add. D 2. 3. BGTIV D, -v eras.;

comp. B.tfe']

ds Y.KL D. 4. tTOg] t, D, t-,' D 2. JTWV]

corr. ex TWI/ A 1

, comp. D, 5? D 2. 5. TILS] rpz D, supra ?

atQ&v] corr. ex r}(ieQ&v D. 6. /_'] e corr. D 2. 10.

?] bis D, extr. et initio pag. 11. sr]v.oGTd ] |a

D.

12.qp7]fft] tpj]Giv B; 9 D,

spostea add. ra] rcot corr. ex

rco AD. v7

] e corr. D 2;

v8' Ideler Hist/Unters. iib. d.

astron. Beobacht. d. Alten p. 216 sq., qui deinde p. 346, 13 ccvtti

deleri uult. ?rst] e corr. D 2. 13. MS%LQ B. 14. ngoa-

tk&ovG&v D. TQtTrjpOQLOv] r D, mg. yp. TQixruLOQiov D 2. 16.

IK] renouat. D 2. v.ai\ om. D. 17. Jvcm?] ^ BD. faeiSy D,

corr. D 2. 19. %at] supra scr. D 2

.

346 KAATA10T HTOAEMAIOT

rov %aovos ir&v Afyvrtriax&v <p/i xal

xal d)QG)v ior]iiQi,v6)v djt^&s r xal aKQ

1/y y' nabs ov %QOVOV KHSavrcas BVQI^KO^BV rov [isv

ijhov anal/Seas it%ovra r&v 'I%&vov fiotpco? jc? tj, rr\v

5 ds 6s^vrjv [items [iv Xqh&v poiQav a, axQifi&s dl

v poiQas x? 7?, ^td^jr^) Kara ryv dvoâ-

a7ti%ev rov anoyfiov floras Q& xrj. GwayBraidl xal r] anb ri}$ Ttg&rrjs Mfafyfcos litl rqv $vrQavdideraGis YI^QK)V goy xal MQcbv i6r][iQiVG)V g {_' y',

10 yiOiQ&v df ^ la9

rovf

Ijt7taQ%ov JtOirj(3a^vov rrjv

dl%iv G)g rrls diaGrddf&s ravrrjg rîBQ^v [ilv

00?} K0

rr\v df roirqv tpytilv MteityLv ytyovivai ro5 avrcp

VB BXBI r^s dvrQas XQi6dov xar Alyvitriovs Me-

15 Goorj B', iJQâro d rys vvxrbs TtQOBk&ovticav c)oa)v i

TO Kal ^^l,7CV oA^. Kttl XQV ^LB&OV

%QQVQV cprjol yfyovEvai, TIBQI &oas

roirrjuoaioV) rovrttirw pra /3 rgCrov Soag

rov ii6ovvxrtov. dMa rov fjMov ovrog Jtol rd

20 ri]3 IIciQ&Bvov BV 'AXBâvdÊia i\ rr}g vvxrbs &oa

v&v BGrlv i,d xal dvo ytBiLitrov ai dvo rofaov aga

G)Qat, xaioixal TtoiovGiv farjii0ivd$ EyyiGrcc dvo r-

raorov. &<jr yfyovw 6

1. rcor] U D, U D 2. 5. fioiQuv] corr. ex [toiQfbv D 2

. 7.

-v'del. D 2. 9. joorj] psv QW\ D. 14. STSL] \& D,

*'add. D 8

. MSGOQI B. 15. itgotldovGj}g coâg D. 16. r*]

lo ABCD, /> A 1. liêwev] mut. in i&ucev D 2

. 17.

qpTjtftV B, comp. D. Y.GLI tQirripQQiov] r D, yQ- KKI TQurtfioQiov

mg. D 2. 18. tovTSGtw] comp. BD. TQLTOV] r' B, p D.

21. iariv] comp. BD. dvo n^nrcov'] ftse D, J3

s" f" D 2

.

xqirov ago] yaq D, y' &QK D 2. 22. dvo Tgra^rov] (3

^'" D.

23. ftara] |u, D, ut saepe; fta D 2.

oivas rijg v rr\ s' [t0r][t^giag. xai

6 ditb r&v 7to%<DV [t%oi rovrov XQOVOS

Afyvnriaxcbv <pjt xal rj[tQG)v rAd xal MQ&Vv&v artAcbs [tv id d', axQifl&s de 1/y [_' d'' JVQOS ov

%QOVOV VQi6xo[tv rbv psv tfAiov sitfyovra

[taigas Tf t/3, t^v 81 GsAtfvrjv [i

T xd, dxgifl&s $ [IOIQCCS is

xccta xv\v ava)[iaA,iccv KTtetye TOV cutoysiov rov

[IOIQCCS 6ll& &. GWCCySTCCl 6s XCtljj

(XTtO

sfyscog iiti r^v tgirriv diKGrctGis ^f- 10

Z xal dvo 7C^,7Cr(ov {iiag G)Qag

xal Tavrrjv rrjv diaGratiiv fipSQ&v QOS xal îiag rgi-

rov Sgag farjufQivrjg, poiQ&v ds (>|^ Ay. xal v&dd

aQa g)aivrai di^VGtîvog eitl [iv rcbv [IOIQ&V $' xal 15

y' eyyitfra [nag [taigas, iiti $ rcbv fi[tQG)v f)iti6i xal

TQixcp xal dsxdrG) k'yyi&ra ^tiag cogas farj[tQivfiS) a xal

avra dvvarai diatpOQav at>i6A.o'yov Ttfgl rbv ri\g VTCO-

ditQi

yd<}a6d'ai.

1.-rf?] tfj D, tr\i D 2

.

f(Trw;]_comp. B, -v del. D 2. 3.

i&v] corr. ex ctirv D 2

. xW\ -18 e corr. D 2. 5. &n-

s%ovrcc B. 6. Gsl^vriv'] D, ut saepe; ^ D 2. 7. ax^tjSws]

bis D, corr. D 2. 9. fiotâg] seq. ras. 12 litt. C. 10. Ssv-

tQccs~] H B, p D. TQiXj\v~] y' B, y D. 11. xat] corr. ex

xa D 2. dvo ntpnTfov] ^ s" D, corr. mg. D 2

. 12. vs] supra

scr. A 1;v& A, -& del. na.liv\ TtdUv

r\A. 13. 90?] psv

Q0<5 D. pi&g XQitov copag] ccyoQOJV D, ay" top'D2

. 15.

/u-ot^cov] ^ C, ft C 2. 5'] ABCD, supra scr. u C 2 et sura) D 2

.

16. y'] ADC 2, y' |5 BC, o> supra scr. C 2

, Tattoo supra scr. D 2.

eyyiata fttag] e corr. A 1. rjfifg&v^ ftf^cov C.

Tjju-tityft]xat

D,' D 2

. %t] om^D. 17. TÎ'TW] r D. _*l tfexaroi]

post ^f- ras. 2 litt. A, tgw '

D; supra scr. ip A 1 et tj3" C, {_ r" i"

cog 'v riGl ccvtiyQa D 2

. fttag] a supra scr. D, fnas D 2.

348 KAATA. IITOA. MA0HMATIKHZ STNTAEESS A'.

yeyovev ovv fftiiv VTI oipw r6 re rijjs

alnov, ual on &ccQQOvvt$ civ In

snl r&v Gv^vyicbv r^g ffe/tofV^g xal avrcov

5 Tovrcov r&v ijttefymv Gvpcpcbvav iidfaGTcc rats

1. fipfv D. 3. Gvv%Qj]6ctipQ'a. D, corr. D 2. 4.

D, ([ D 2. 6. vTto&tGSGi D, corr. D 2

. In fine: Klavdiov

GVVTK^ECOS 4 AC (KkuSiov C), Kiccv-

diov ntofoficclov ^(x^Tf]^a'tiY,fig Gvvrd^ftos fiifiMov J B, KKccvdiov

D.

'.

Tads sv6riv v ret) e' rcav rov IlToA.[iafov

a'. 7tQi xaraGxsvijs a<7rpoAa/3oi> oyydvov.

rijs itQOs rqv dinfo]v dvco[iaMav rijs

y' . stegl rijs jr^AwcoT^rog rijg Ttccga rov f/Atov dvo-

rov A,6yov ri}$ sxxevrQorrjros rov

xov xvxhov. 10

sf

. itSQi rijg 3tQo6vev68G)$ rov rils GsAtfvys sitixvxkov.

g'. Tt&s dice T&V yQcciin&v ditb r&v itSQiodix&v xi-

vrJ6SG)v fy dxQLJUrjs rils Gshijvrjs ztdoodos kccp-

pdvsrai.

'. TCQayncirsia xavovos rils xa&oAov tffA^wcmjg dvo- 15

?)'. xavoviov rils xcc&oAov Gskyviaxils dvco[iccMas.

'. nsol rils xadohov GsArjviccxils ipqcpotpoQias.

i. on, nydev d&oho'yov ywsrai, didyooov Iv rats

Gv^vyiais Jtaga rov SXXSVTQOV rils GsArfvys 20

xvxAov.

1. E'] om. ABCD. 2. r&v [Lcc&riiiccTiyt&v] rrjg

KfrrjiittTLnfis 6vvrd^(os B, om. D. 4. a'] et numerosceteros om. D. 6. vito&sGEcos] om. D. 9. ivY.EVTQo-ir]TOs D.

11. Supra ae^ijVrjg scr. ([ D. 12. y.iv^Gfcov] sito%&v D.

15. avcoiaMag ccv D. 17. Y.KVOVIOV avcoK^Cccg om. D.


ia'. TCSQL rc5v rrjg

i xara6xvijg ogydvov JtagaMaxrixov.r&v rijg GsAijvrjs aTtoGrrjudrcov.

id', 7tgl rijg TPYjAixdrrjTog rojv v ralg 6vvyiaig (pai-

5 vo[iva)v dia{irQG)v j]^iov xal GsA.tjvrjg xccl Gxiccg.

is', itegl rov fjfaccxov drtoGrrjparas xal r&v Gvvano-

dMVV[lVO)V CIVTG).

1$'. Ttegl [isys&cav fjMov xccl 6^vY]g xccl yijs.

it,'. Ttegl T&V xccrcc pSQog 7tccQaMd%SG)v rjh'ov xccl

10

iv . xccvcov

T&V

a'. Ilsgl xccraGxevrjs ccGXQokdpov ogydvov.r

'Evsxvju,v df) r&v agog rbv ijfaov Gv^vyitiv 6vv-

15 odixcsv t xccl ytccv6^rjViaxcov xccl T&V XCCT' ccvrdg

ctefyStQV %CCQXOV6CCV

7tl t^ JtQK>Trj$ XCc

xav ccvrb povov ovrcog f][iiv

itgbg pivTQi rag xard pfyog nl rcbv aMov ngbg rbv

20 tffaov 6%yiiaTi,6[i(X)v itagodovg ovxer' av avrdgxy rig

1. TtBQi 2. Tra^aHaHTtxou] om. D. 5. Siay, D.G- postea ins. A. 7. wurw] avr&v C. 8. icsgt yf}g] om. D.

11. TtKQuMcc'X.TtKos] pr. x coTT. ex 1 D. Post indicem add.

'EfiitedoKifis dm^KGiov aTti^siv ri]v ([ anb rfjs y^S sdoi-ccfev,Ol 8s &7t6 t&V [LK&riUCltl'X.&V &KQlpGTQOV 1tl,pdM,OVT$ (sitl-

v' D) 6Kta>y.aiSWJila.Giov : (: om. CD) 'EQaTOG&gvrjg

a7t%eiv Grccdiav ccnb rrjs yfjs (ivgidScov r ncci omanis>

( : no om. C) xr]v ds Gfl'ijvrjv &7t%iv rfjs y^g (ivgid-8(ov tydopfaovrct oxrcb GrccSioov BCD 2

. 13. a'] om. AD,rag. B. Trf^t] nsQi Tfjs C. Post ogydvov add. s A. 14.

o; mg. D 2. Gv^vyi&v] Tijs cs^vrjs Gvvyi&v D. 18. iaja-

D, corr. D 2. 20. nccgoSov D, corr. D 2

. ovvtri, BC.

MA0HMATIKHS 2TNTAJEJE&S E'. 351

avryv evooi, dia rb xal devreoav^ cos <pcc(iv, xccra-

AapfldveGd'ai, r^g Ge^vr^g dvopaMav naoa rag ngbgrbv iqkiov drtoGrdtieig d7toxa&i<3ra[jivr]v jiv els rfv

uar dîfporeoag rag Gv^vyiag, pzyiGrrpt de

diKporeoag rag di%or6{iovg. xarr]V%- 5

ds sg rqv roiavryv snitiratiiv rs xal itiGiiv

axo re rdbv vjtb rov 'IititaQiov rerygrjuzvcav xal ava-

6e^tjvrjg nagod&v xal anb rCbv fi[Liv

dia rov ngbg ra roiavrcc J^LIV xa-

ra6xva6&vrog bgydvov, 7tQi%ovro$ de rbv rgonov 10

rovrov.

dvo yaQ xvxAovg Aafiovreg dxQift&g rerogvevfievovg

rergaymvovg ralg jliticpavfiaig xal 6v[i[irQOvg [lev red

7tavra%6&sv de fcovg xal bpoiovg d^t]ôtg^

xara didêtQOv itgbg og&ag y&viag &ri 15

r&v avrwv eTtupavfiav ,&6r rbv êv eregov avrcbv

voftG&Ki, rbv dia peG&v r&v ^codtcoi/, rbv d' eregov

rbv diet r&v Ttok&v avrov re xal rov i6rm,Qivov yi-

6r][ipQi,v6v' s<p ov A,a($6vrg cforo rijg rov

Ttfavgag ra rovg rov di,a pfacov rCbv ^cpdL&v 20

TtoAovg acpooi&vra 6r]iiia xal epTtoMGavreg a

K xvfavdQioig e%%ov<5iv ngog re rfjv exrbg xal

evrbg eititpdveiav xara [lev r&v exrbg evenoMtiaiiev

2. itgog 5. &ii(poTEQtts] in lac. complurium linn. ins. A 1.

3. ano6td6eLs] ccTto^ccrccGtccGet-s B. ano-Ad&iCrcc^vrjv] -iGrct-

e corr. A 1. 7. r&v] -fa- in ras. A, supra scr. D 2

. vno]om. D. 9. KutacneciGd-evTos D. 12. JLuppdvovTSs C. 13.

eiti(puviai$~] 7tQicpQiaig D. 14. 8' I'GOVS corr. ex dsGovg D 2.

16. rov\ corr. ex to D 2. 18. x6v] r&v B. nokav] -H-

corr. ex 8 A. 20. rd] supra scr. D 2. TOV] supra scr. D 2

.

21. tyitoHfaavTee] -U- in ras. D, 73 supra scr. D 2, Ipxod&ttiTOG

BC, corr. B 2 C 2. 22. Qfyovei D. 23. r&v] rijv D. sv-

] -M- in ras. D 2, rj supra scr. D 2

.

xvukov axroiisvov 7tavra%6&v dxQificbs rr\ xottr] avrov

7ti(pavia t% xvprifc rcbv 6vvrjQno6iiVG)v dvo KVK^&V

Kal dvvdpwov TtZQLdy^&ai, Kara ^xog 7tol rovg i-

QrftLBVovs 7t6hov$ rov did pôv rcbv a>dtW, Kara de

5 t&v svrbg 6ôtrag aMov nvxhov SVSTCO^CC^SV aicro-

{isvov psv %KL avrbv 7ta,vxa%6&ev cwQip&s rrj

ccvrov titicpavsLqi rij^ zotA^g r&v dvo xvxh&v.,

y6[ivov de 6/KHwg XCCTCC [irjxos 3tQi TOVS avtovg 116-

Aovg t& e^cdftev. dizkovrzs d rovrov rs rbv

10 xvxhov xccl In IQV avrl rov dice pfacov rcbv

XKi 0<? Vd%ZO tOVTCOV ^Q^ VCpTr]Q[l66a[lV CiXQl-

fajttbv xvxMexov dnag fyovra, xccta dia-

OV(}aS VTtb TOV VTOS t&V dvO MJXk&V)

15 07CC3S dvvrjTcci itccocc(p()<5&cci Kara to avrb XLVG) eni-

TtsdoV &S ItQOg XaTQOV T&V XXL^lVG)V 7t6&G)V VXVrqs Kara Tt^drog ytccârr]o^6C3s. rovrov d* ovrws y-vo^,VG)v anoGrriGavrss rtl rov di' d[iq)orOG)V rav

itok&v voovjisvov nvxhov a<p xaroov rcbv rov &-

20 diaxov jroAcov rrjv yLsra^v dfdfi'y^vrjv 3tQicpOiciv

rcbv dvo TtoAcov rov r dt {ifacov r&v tydicov xal

rov I^ÔLVOV ra yv6^va 7toara Kara did^rgov

dM,t]A,OLs V7toM6a[iv xal avra nobs rbv

2. GvvriQ(ioa\iisv(ov A, 6vvr]Qô\Gêv(ov A 1, LQ[ioG{ievmv D,

D 2. 5. r&v] rr\v D. KVKitoMGKiitv] A]B 9 C 2

,

BCD, IvsnoîJGKfjiev D 2. aTtTopsvov] -(.LSVOV

add. A4. 6. (isv v.al ai)xov\ om. A. jtccvrcc%6Q'tv\ nav-

add. mg. A 4. HV^T?) corr. in xv^nyi A. 9. TW] corr. ex

T&V C 2. 10. TOV] x&v C. 11. yLvopevov CD.

'

14. rov]e corr. D 2

,t&v C. 16. cog] corr. ex 6 D. ^yntLîevcov D.

17. d'] ds D. 23. ivEnoliGctptv] -U- in ras. D 2, -)b]- supra

scr. D 2, ivsnodtGupsv BC.

MAGHMATIKHS STNTAEE&S E'. 353

opoiov [ie6i][ifigLVOV T&V v ao%ri rijg GvvTd&cog VTCO-

itgbg Tag Tijg ^sra^v T&V TQOXLX&V TOV

7tQicpQtag Tr}QtJ6ig, &6ts TOVTOV Kara

&<5i,v XiVG) xaraGra&svtos ,TOVT&TIV

oo&ov re TtQog TO TOV ooi&vTog zitfasdov xal xara TO 5

oixsiov aia rov 7t6Aov rijs vrtoxi[ivr]g oiKij^fcsg nctl

5 TOV <pv6si [i0r]iLf$Qi,vov 7tiitdG),

Qia,'yG}f

yriv a7COTA.Z6&ai, 7tol

TOV iGriyiBQivov Ttohovs a7t avaToh&v 7tl dv6[ias

TG)V oAcov TtQKtTr] tpooa. 10

TOVTOV dij TOV TQOXOV KK&L<5TaVT TO OQâVOV,

<paiv6&ai, qdvvavTO o T

xal fj 6&rivY]) TOV [iv ^cod'fv T&V a^TQO^d^covrtl tr\v KO.T Xivrjv TJJV cooav

TOV Âtov iLQiQuv xal 3tQi,ij'yoiiv 15

TOV di,a T&v jtohcQv xvxAov, OTtcog Tfjs xaTa T^V yfoaxjjv

lioioav T&V xvxkov TO^S agog TOV rjfaov

TQ7to{ivr]g Gmd^GHSiv avTOvg apa 01 KVKk

o T dia [ifocov T&V tydicov xal 6 dia T&V itol&v av-

TOV) ty CCV7tQ CC(3trjQ i] 6 dl>07tTVO^lVOg? OTtCOg TOV 20

vbg T&V ocp&cc^&v naQaT&VTog Tfj TQa T&V ntev-

Q&V TOV Xad'6Td^lVOV ^G)^V XVXhoV VTtO TJJV VTtO-

xt,[ivr]v avTOv xaTa TOV dia pscicov T&V t,a)diG)v KV-

xAov potQav xal dia, T^g aitwavTiov xal ytaoaMtfkovTOV xvxhov ttfavag &6ii XxoMrivo a(oTat, 25

1. t&v] TCOL D. GVVCC&OOS D, corr. D 2. anodsdEiyî-

. D 2.vcoi D. 5. xat] supra scr. D 2

. 7. naQKUtjlovs D, corr.

9. avcnroôov] -act- e corr. C. 16. Kvyikov] corr. ex uviiJicav C.

Trig] corr. ex TS D 2. 18. GKidgovaiv C. uvrovg] A, avrovg

BCD. 20. i) idvnsQ] tav SI- 6 D, 6 del. D 2, T) iavnsg CCCTTIQ

rj mg. D 2. 22. -AUÎGTK^SVOV B. vno] ini D. 23. TOV}BDA 4

, roTA, T&V C. 24. ccnsvavrtov] -vav- ins. A 1. 25. tov

xvttAot;] om. D, rw supra scr. D 9. xfttoHT^vatg D, sed corr.

avr&v ralg iti<paviaig 6 a6rr\Q iv r& di avr&v s

oj dioitrvrirai. rbv $ sregov Kal vrbg rcov CCGTQO-

KVK&OV 7taQ(pQOn,v itobg ri\v GeAtfvriv T)Kal

n r&v fyrovfisvov, ojreog apa TTJ rov r\kiov

5 rjxal aMov rov vjtoxs^vov diOTtTSvtisi, xccl

r\

rjKal aMo n r&v fyroviisvcov dia rcbv Kara, rbv v

ovrco$ ya$, XOLOV r Kara ft^ôg Ttd%i rov dia

rcov tydi&v r^â^ tTtiyiyvcaGKOpsv x rr\ Kara

10 rriv rov faodvvaiiovvros avrd KVK&OV diaiyztiiv yi-

rov vrbg KVK&OV ropi]g, Kal notiag avrov

y&rriKSv r^roL XQOS aoxrovs ^ ngbg ii6rftL-

figiav G)g 7il rov dia rCbv it6kcov avrov KVKkov, did

rs rils avrov rov vrbg adrgokdpov dt,ai,Q6G)g Kal

15 ri\g VQt0KO^vrjg diadrdtifcos dnb [i0r]g rrjg vjtQ yi\v

OJtf}s rov vn avrov TtaQayoyitvov KVKkCtiKov iiti rr}v

v rov dia î6G)v r&v %G)diG)v XVKÔV.

bs rrjv

20 ^Jth&g ftev ovv yivoyievrig ri\g roiavryg

ai ri\g Gfhrjvrjg Jtgbg rbv ijfoov dt,a6rd0i,g, K re

2. Sionrsvrirca] -o- e corr. A 4. de] d' D. 3. TICCQCC-

v BD. 4. roiv r]Tov[isv(Qv] corr. ex to r)rov[ievov D 2.

6. rc3v fcqtgvp&Gv] corr. ex to ^tovêvov D 2. x&v (alt.)]

-&v e corr. D. nuta tov] supra scr. D 2. 7. KWX.UGKOV] -li-

e corr. D 2. vnontevritca B. 9. ^jriytyvebcitoftfv] A, iiti-

yivwGKoiiEv BC, 7tyivmGKO[jiv D. 10. Icodwapovvros] anteS ras. 1 litt. D. ccvto C. SIKIQSGIV} KKta. rj]v diuiQSGw D.

14. &Grgold$ov] actQoldpov KVY.IOV D. 18.f3'] rag. ABC T

om. D. TIBQL 19. vTto&sGfag] hie om. D, qui x-yxô-u lin. 17

et cc7tla$ lin. 20 coniungit (x-u|xAov a), diremit D 2(xvxiov | a);

TtfgC vno&86co$ mg. superiore D 2 et addito ^ $ mg. ex-

teriore D 3. 20. Tf)g] supra scr. D 2

.

MA0HMATIKHS 2TNTASE&2 E'. 355

6r

'Iit7taQ%og avccyeyQccfpsv ,xal s$ av fipetg irv\-

TCOTE [ISV (J^tt^POVOt XaT&a[l(ldvOVTO TOig XKTK

xal didcpoQoi, 7COT8 [ilv bUym, nors

$' r\lllV Kttl 7tQl,Q'yOTQa$ Ttjg 7H,6TCC6G)S 5

cc TO <5vv%s yivouwys 7i$l rrjv TCC^LV r^g rot-

iiakiag xccrânftccv6î^cc^ on 7tQi pv rag

6vvodovg aiel xal rag Jtav6^tjvovg

dia[iaQrccvrai, 1} jSâ^v, xal o6ov av ai

ryg 6^v^g dvvawro itoitv didcpOQOV, itQi ds rag 10

rdvrai, r^g 6eh$vijg xara TO anoyfiov T)

TOV BitixvxkQv Tvy%avov6r]g ,TtfoitfTov d', orav

Tovg ii6ovg dgopovg OV&K nfaiGTOv xal TO Ttaga TYJV

XQCQTrjv av&paMav didyogov 7101%, xal OTL uyciiQe- 15

Tiling pv ovGyg T^g JtQ&rrjg dv&iiaMag iv 6itoTQaT&V dlOrOÔV Tl &d66G)V 6

rijg Ttg&Trjg dcpai,()6G)g

cov d)6avTG)g xal

rfjg itQcbrrjg TtQOG&acpaiQfaf&g, (bg dia TavTqv 20

TYJV rd&v r^dr} GVVOQ&V ^ kag, on, xal rbv

nl MXWTQOV xvxKov q)Q6&ai, v

yivoutvov TtzQi Tag Gvvodovg xal

1. 6] om. C. 2. ftfV] -EV renouat. C. 3. de] corr. exD 2

. 4. Siccfpogoi] Sidcpcovoi D. 6. ytvo/LtfV?]s] om. D. 7.

ucdiug] KVGj{iaM(xs yivo^svj]? D. Hie mg. itsgi p. 354, 18- 19 v7to&6(D<; D (TIQO?] ttg). 9. dia^ccQtdvei D, corr. D 2

.

$QK%V<S BC, corr. C 2. 10. SVVKITO D, corr. D 2

. 12. uno-

ycciov D, corr. D 2. 14. dgopovc; ovGu\ corr. ex dgofiovccc C 2

.

15. noifL CD. 19. nUlov BC, corr. C 2. axyavTcog] -co-

e corr. D. 20. jrôaâqpat^^fcog] -at- in ras. D. 22. fVxtVTpov] corr. ex HSVTQOV D. vnoJi^Ttrsov^ post r\

ras. 1

litt. D.

23*

rocs 3tav6Atfvovg, itEQiyuorarov de Jtepl dî(poToag

rag diôroôv g. Gvpfiaivoi & av rb roiovrov

v7to&<3G)g roiavryv rwa t^v diooftcs

vosfa&G) yap 6 [jilv 6ii6xvroog r& dia \it6&v r&v

5 (pdiK>v xvxAog v r& Aojep r^g 6%rivrjg ZTti7tB

co6nQ xal vtQorsQov, VKv rov

tovg rov dia {ifacav r&v ^cpdicov tt6A,ovg rodov-

rov, o<?co v3iQ%i, r^g xccra [irjxog mv^saxs % xccra

jtAarog, df 6fajvrj rov Kakovyisvov Infavxhov TIE-

10 QiQ%oiivrj xdfov a)g xar& rqv a^yuov avrov

tpQi,ccv fig ra ytoorjyov^vcc ryv [irccf}cc6iv

axoA.ov&G)g rfj ryg 3tQ(brr]g ccvG)[iccMcc

v drj rovra) r& Ao|w sitiiteda) dvo xwiJGfig svavriag

dMijhcug vjtori&[id'a duahtig xal ftfol rb rov dtcfc

15 p0G)v T&V fydfav Kwrgov diHporfyag, (bv piav \L\V

rfjv 7tQidyov6av rb rov fTttxvxkov %vroov fig ra

rcov ^(pdi&v dxoAov&og rf} xara nAdrog m-

iav d rqv ttaidyovGav rb xsvroov xal rb

rov Iv r<p avra iitntt$& Aa[i(lccvoiivov BK-

20 KBvrgov Kvxkov, tp ov ndvrore rb xwraov 6rcci, rov

7tQi,d'yov6av df fig ra xoorj'yoviiwa r&v

xal rotiovrov, o^c? v7tQ%i rr}g Kara ithdrog

tA,G)d't6a v\ dyto^tj^ rovrstinv ^ vrtQO%rj rqg

xard [irlxog 6&rjviaxrig [i6r]g iuvyJ6cog Jtobg rqv fjhia-

25 MQV. &6r v rri pia ^^Qa hoyov VKev rb [ikv rov

1. T(Xg] Om. D. TtCCVGfkljVOVs] 7tOCV( D.

rov A. 7r(u] Y.CIX' D. 2. cvfifiuwsi D, corr. D 2. TOLOVT.O D,

corr. D 2. 5. ro5] ran corr. ex T& A. Ttyoriyoviisvrjs B. 1.

v] fadicov uvnUov D. 8. OGOV D. rf] i\ B. 10. Kara]ra. C. 15. xsvtQOV a/Ltqpors'-] in ras. D. 16. rov] -v

eras. A. 19. avro5] avrov BC, corr. C 2. la

-ov in ras. D. 23. r) (alt.)] supra scr. D 2. 25.

ras. 23 litt. D 2.

MA0HMATIKHS 2TNTASE&S E'. 357

t7tiXVxA.OV XVrQOV XiVOVflVOV Tag rOV

iy id eyyitira elg rd 7t6[iva r&v ^cpdC&v sill rov dice

li6cov r&v %G)diG)v yaivsG&ai Ttao&dsvxbg rag rov [iij-

xovg poioag Iy Ice did rb okov rov Ao|6v xvxAov avft-

sig td itQO'r}'yov[iva rd rijg vTCsô^g 5

rgia, rb ds K7t6ysiov rov sxxsvrgov avruts-

i, n&kiv slg ra nQorjyov^sva H.OLQKS la ^V7teQ%ov6i,v aC diitkatiioves rrjs ajto^S polyou

wy rag rov nhdrovg [lotoag iy td. ovr&g yap BK

a[ig)oreQG)v rcbv xwtJGstov avriTtSQwyco'yijg nsgl rb 10

cog scpaiiev, rov dia [istf&v r&v ^cndtcov yi-

rjdia rov xevroov rov minvKkov rijg did rov

xevroov rov sxxevroov JtQo6ajco6rt]6

Htvyvr

x re rcbv Iy td xai r&v la # fioiQ&v

osiav dinMjv yivoptvYiv r&v dnb rijg aito%fi<5 poiQ&v 15

i|3 la {_' syyiGra. xal did rovro dig iv r&u,t<5<p prj-

viaiG) %QOVG) rov Z'xxevroov 6 srtixvxAog TtsoisAevGsrai,

ryg Ttobg rb aitoyeiov rov sxxsvroov voov[ivr]g dnoxa-

ratirddscog ev ratg [ifaog frewooviiwaig 6vv6doig re

xal 7tav6sA.ijvoig vjtori^sfjisvrig aTtorsfoiGd'ai. 20

iva ds jiaMov fftitv vit otyiv ywrjrai rd ryg vito-

oefa&G) it&Kiv 6 v X& Ao|w rijg 6^tjvrjg

d) did ^6ov r&v (pdicov opoxwroog xvxhog

1. rag] post ras. paruam D. 6. S^KOGTO] âa

D.

corr. ex TQITU C 2, r B, y' D. 7. ôtâg] -ot- e corr. in

scrib. A. 8. dmlaoiovss] -es e corr. D a. &no%fig\ -no- in

ras. A. 9. id] -d e corr. in scrib. D. ovrco D. 12. siti-

yiv*lov 13. HSVTQOV rov'] om. BC. 15. dmJifjv] Si- in

(Hras. D. ano] om. D. 16. /.'] corr. ex t> D 2

. /* mg. A.

17. IxK I>,vadd. D 2

. 22. votiG&aii D.

10 TO Z/

K06TO,

6 ABF4 TCBol XBVTQOV TO E XCil dld[lTQOV TYJV AEF,VttOXl6&G) $

a'flO:XUTO, TO A 6r]lLlOV TO T

TOV BXXBVTQOV KOI TO XBVTQOVTOV Bnixvxkov xccl TO j$6Qiov

5 itoag xal rj ao%rj TOV KQLOVxal b [i6og fjAtog. v TOLVVV

TTJ f){iQy6ia naoodc) TO [iv oAov

uvsltiQ'ai i TK

G)S KTtO TOV A 7tl

7tQl TO E %VTQOV %rj-

y eyyiGTct, &6T TO A7tQag yfos6&tu XKTCC Tag

LiOLOCig X& V^+ TG)V

vxb Trig b^iOLag r EA v&icig jfol TO E15 Tt&Kiv TOV dia pfacav TGJV ^cadtcov XBVTQOV

a7tOT^OV^lVK)V 7tl T^g l^Q^GUodov Tqv {iky dice TOV XBVTQOV TOV BXXBVTQOV

Ti] EA 7tQia%&i6KV bpahcog ig TCC Ttoorj'yovpwcc T&V

%G>dlG)V G)g 7tl TYJV E4 TO [lV KTtOySiOV TOV XXV~

20 TQOV (pBQBiV 7tl TO Z/ XCCL yQK(pl,V 7COi TO Z XBVTQOVTOV 4H XXVTOOV, TJjV $ AA 7tQl<pBQiaV TtOLBLV

lioiQGtv ice ^", Tqv ds dia TOV XBVTQOV TOV BTtixvxkov

nBQi TO E itdkiv bfjicch&g TiBQiccffiBiGav ig Ta BTCO^LBVK

TG)V t,(pdi(QV O)g T^JV EB (pBQBiV [lV BTtl TO H TO XBV-

25 TQOV TOV BlllXVXkoV, TT]V ds AB 7tOL(pOidV

TG)V V7tVOCVTtG)V

1. AET] seq. ras. 3 litt. D. 3. SHMVTQOV] fa D, ^K8 D 2.

xtvtQov] om. D, Kov

supra scr. D 2,item lin. 10. 10. |rj-

xoota] g|a D, g ||a D 2. 15. KSVTQOV] tf D,

8add. D 2

. 21.

TOV] AD, TO BC. fxx~D, ?xx01 D 2

. 22. poiQ&v] ^ D, tu D 2

,

et similiter saepe. 24. TttQLcpegeiv D. uivtQov] -VTQOV in

mg. transit A 1

,% D, K

r D 2. 25. TOV] --D in ras. 2 litt. A 1

.

MA0HMATTKHS STNTASESi2 E'. 359

Ty td, &<5ts TO H xevTQOv rov mxvxA.ov aito

(iv rov A POQMOV nsoarog drtfyov (paCvs6&ai rag ly

id pOLaas rov ttldrovg, anb $ rye; aQ%fjg rov KQLOV

rag iy ia [toioag rov [irjxovg dia rb rb A (loofiov ns'oag

iv rotiovrcp ysyQvivai Kara rag r&v 'Iffivcov poioag

x& i>, ajtb $ rov A aitoyeCov rov XXVTQOV rag 6vv-

ayo{ivoig 6weepyorsocw rijg- r AA xal AB 3tQi(p-

wy noiotts, ai 16'iv dt,7tA.a6iovs r&v

{i6r]g d7to%r}g. ovrcog ovv, itidi

ijT dice rov B xal ^ $!& rov z/ XLvrjGig v 10

rov psGov ^VLaCov %aovov rr\v \iiav aito-

itouovvrai Ttobg akkrika^ dijAov, ort iv rc5'

rov avrov %QOVOV xal h'n iv rw i\\ii6Bi nal re-

rccorc) ndvrog dia^r^ôvGLV aAA^'Aag, rovrtGriv Iv

rcctg ii0G)g fi-f&oovpwaig 8i%or6ôig^ rb $ dia rijg 15

EB KBvrgov rov itixvxA,ov dia^r^âv rb dia r^g

aTtoyfiov rov fxxevroov Kara rb itfoiyfiov avrov

(pavQbv de, on xal rovrov ovrcog fyovrcwv avrov rbv XKvrQov, rovr6n,v r^v avopoior^ra 20

ri}g 4B nQ(,(paiag nobg rr\v 4H, ovdlv 6rai dia-

rig EB

1. id] mg. add. A 1. 4. m] corr. ex id B 3

. iioiQccs]

om. D. TO] om. C. A] corr. ex itQ&tov D. 5. Post

TOOOVTCO del. OVTCOI D. 6. IxxeWpov] f'xK D,aadd. D 2

. 8.

Tof] -v$ r&v e corr. A, dmhaGiov SGTCOV C. 9.

corr. ex ins D 2. 6vva.py6xQcci\ ABD,

CD 2. 13. trt, iv raj rjfiLGfi] corr. ex ?rrj b esc D 2

, supra scr.

cl ^n D 2.u in sv rc5 rjfiiGti %ccl ^n D 2. rara^rfij] ~j' B, ijj D, j" D 2

.

14. TOVTEGTLV] supra scr. D 2,

T D, rovA D 2. 15. de] A,

om. BCD, V.DU 810. rovro supra scr. D 4. 16. xfWpov] corr. ex

KSVTQOV D 4. 17. rov] corr. ex TO D 2

. f%K D,"add. D 2

. 19.

v.al on D. 20. lx|< D,'

add. D 2. rovrtGnv] cornp. B, -v del. D 2

.

360

ov rijv 4H rov

rov did [ltd&v rcbv

rb HTJ 7tol rb ZE TtoitiG&ai rr\v

5 avrbv rbv fitixvxhov

avrbv

KAATAIOT nTOAEMAIOT

7tQitpQiav, dMd rv\v

s 3tQiQ%o[ivr]s diet

rov KXvroov, 7tol $ rb

v, naga ds [iovqv r^v tear

iayogccv BK rov 7t-

avêiv alsl rb naga rv\v

avo)[iccA,iav didcpooov % l'6ov Kara rs d(pctiQ6iv xal

avrbv TCQog rfj oîv rats 7toiyiotQais d-faftiiv [iiovog aito-

10

ovdfv {iv ovv 6rai

xadoAov didcpOQov, orav Kara rb A dnoyfiov

KBvrQov rov sitiKvxhov, yivopsvov rov roiovrov

rdg [i6G)s &&Qovii8vas Gvvodovg

15 Kal 3tav6&ijvovs.

av ydo yodô^v itgl rb Arbv MN BTtiKVKkov, b rijg AErrjv AM Aoyog 6 avrbg yiverat,

did rcbv bctefysmv

20 TO d% TtfatGrov 6rai

orav xard rb H rov

Ttfoiyfiorarov 6yiiiov b

jtoiijrai, rqv TtaQodov, fag b

rb

8. TIQO-

1. o^] D (supra est ras.), ov y&q ABC. ^xHsWôv] COIT.

ex ex D 2. 2. TteQisQxopevTis] -s del. C 2

. 3. IxK D,vadd. D 2

.

5. rov] supra scr. D 2. ytvojii^rjv] corr. ex ]P mg. D 2 et

supra scr. D 3. 6. ywoiiEvov] corr. ex fi

N D 2 et D 3

&6iv A. 9. nsQiysIOTBQCCIS] post alt. 9 ras. 1 litt. A.(/

11. Iffrca] corr. ex sanv D 2. naga] nsgi D 2

. 12. ^] seq.ras. 1 litt. D. 15. itav([ D,

"' add. D 2. 16. A] corr. ex

TT^wrovD. 17. TOV] corr. exro C 2. AE~\ EAD. 18. yivtTKi]

tG-tui D, mg. yg. ytVfTatD2

. 20. ffroj B. 23. 7ro^rt] DA 4,

TtOLflTCCl ABC.

MA0HMATIKH2 ZTNTASE&S E'. 361

tp6[ivos did r&v 8) O 6r][iiG)v. OTCEQ 7tdA.iv

fiaivi Kara rag fiftfog ^scoQOvêvccs 8i%or6[iovs'

[iicov y&Q 6 rris &H JCQOS rqv HE AOJ>O yfyvercci,

Ttdvr&v r&v Kara rag ccMag

7tidr^7CQ l'6rj$ del xal rrt

rov KSVXQOV rov 7tiKvxA,ovfjEH x rov XSVTQOV

TtaGcbv rS)v akkczv &tl rov BXXSVTQOV

y'. Il()l rijs TtrjAixotrjTOS Tr} TtctQa rov ijhiov

dva)[iaA.iccs rijg 0krjvrjs. 10

r

'Iva df} frwG&iiz&a, TtrjMxov yivzrai ro

TtccQa rqv avwiLCtkiccv diucpogoV) orav Hard rb

yi6rarov rov MxwrQOv (pegopevog 6 faiMVittog rvy-

}, 7tccQrrj^t]6cc^v rag roiavras r&v agog rov ijfaov

v cci 01 rs 15

ror

yiv&iui rfjs dv&iiaMag' xccl

rov r\kiQv ccvrrls dno%r] titG&g ^.aâvo^vor xal 6 3tixvxAo$ 7tQi rb

eyCvero rov fxxwrQov, xal en iv eels 20

rovrcov v7tccQ%6vrG)v ovds 7taQtj^2.cc00v xi xccrd ^xogrovrcov yag 6v[i(lcci,v6vrG)v xal rr^g cpaivo-

vrift

diQTtrsvGEi, xard ftijxog dito6rd6a)$ rijs

rf] dxQifal ha[ifidvoiro av dtfcpaAcbg xal

3. HE] corr. ex NE B 2 C 2. ytVsrat D. 4.

mg. D 2. 5. cctsi D. 8. eldrrcov D. 9. y'] mg. ABCD.

7tQi 10. fffArjVTjg] mg. inf. D. 10. avcojua^tag] (3" ccvco-

ILcdt'ccs D. 11. drj] corr. ex de D 2. 12. Post to del. ntgi

TO D 2. 13. fxxfWÔ'u] corr. ex x D 2

. 16. xvy%uvov] corr.

ex Tvy%avov A 1. 19. ^yicxa. D. 20. syevero D. ex^" B,

fv add. D 2. 21. nctQijlttCfv D, -v del. D 2

. 24.

-VOL- e corr. D 2(i in ras. 5 litt.).

362 . KAATAIOT IITOAEMAIOT

diucpOQcc Tijg dsvreâs dvcoâîag. x

TOLOVTCOV TOLVVV rrjgiJGs&v noiovpevoi, T^V infaugfyw v-

OTKV Kara TO TtfoiyfioTaTov ?}6 e

diacpooccv rijg av&iictMag ytvopevijv

5 per rfv [ifayv Ttctgodov {loiocbv ual r yyJr,ds rr\v TtQcoryv dv&iiaMctv poiQ&v ft xal r%.

vnodefypottos ?&$ evsxsv, ivct Inl yu&$ r)dvo rrj-

VTC otyiv f][ilv fj TOLKvrrj diccKQiGLg yfV^rat,

tov T ijfaov xal Trjv 6A,rjvr)v tK> ft'

10 ti 'Avr&vivov uccr' Atyujtriovg <&cc[ivcod' xf' [ita

[iv TTJV avaroMjv rrjv TOV fiUov, ngb itVT $ xal d'

G)OG)v ItiriiLBQiv&v Tr\ pfGrjiiftQias. TOV

di07iTvoîvov %aT<x 'Tdgoftoov (.loiQccg vij L'

ovoccvovGrjs TOÔTOV poiQas d'r\ 6A.t]vr] stpcci

15 7t%OV6a 21xOQ7tlOV pOLQCiQ ft F, tCCil CiKOift&S $ T06-

CCVTCCS 7tl%V, ttldrj 7CBQI TCC TtQ&TO, {lQrj TOV

'Ateâvdofia a /_' COQCCV k'yyiGrct ait%ov6TOV ii6rj[iftQt,vov xctTa [ifjxos ov&v a

Kdi i(5nv 6 ano r&v 7to%G)v T&V

20 TO a' TOS Nccftova66KQOv [i%oi Tfjs Tr]QiJ6G)s %oovogTG)V AlyVTCTtCM&V G)7t Xttl fftlfQCdV Ity XKl G)QG)V 1(5^-

2. Supra TrjQiJGemv add. ir6 D 2. 3.

77 ] r\v ABCD, -v

eras. D. 4. yivofuvrjv] -v e corr. D. 5. [IOIQ&V f xal r*]

ft J lo in ras. maiore D. j-*] A 1

,Jo ABC. 6. TCQOOTTIV] ngoi-

renouat. D 2, supra scr. a D 4

. z^~\ rQ BC et in ras. D, tf?A.

8. 1^] supra scr. D 4. 9. TW

j3' Iret] BCD 2,

rco i sret. A,root (seq. ras. 1 litt.) si? D. 11. TINTS'] 8 BD. 12. yap]fort. 8j. 13. /.'] corr. ex V D 2

. 15. i*] FB A 1

,in ras. D 2

,

o ABC, dip mo- -D2

- roaavTK B. 16. pegr] TOV] -i\ r- in

ras. 3 litt. D. 17. a] ? C. /_'] corr. ex b' D 2,ut saepius.

18. iiGT]v$Qivov D. [if]Kos] corr. ex (JUJKOVS C 2. 19. TIKQ-

i^la.G6ti D. 20. tog] corr. ex b' D 4. NKÔVKGO.QOV D,

v supra add. D 2.

MA0HMATIKHS STNTASE&Z! E'. 363

v djthcbg is xccl dxQijS&g Irj /_' d'" ngbg bv %QO-

VOV rbv rifaoV EVQiGXOpBV ^<?<3 {LEV 7t8%OVTCC 'TdpO-

%6ov H,OIQK<$ tg K, dxQip&g de [loioccg Irj v, xcc&ag

xccl v r& atfrpoAa/to diG)7trVEro. xal fj 6^t]vrj ds

v- 5

xvy%vivv rov yMov, dvoâ^LCCQ d' ditb rov ccito-

ysiov rov faixvxAov poiQtts jrg tO1

, TCQL as itdkiv TO

TtfaiGTOV yivfTcci didyoQOV Tr}$ av&naMag. shaGG&v 10

CCQCC fj xpt/3ijg Ttdgodog iytv&tQ tv\

t> r dvrl f T&V Kara i$\v jtQcbrrj

itdkw, iva xal ex rcbv vitb rov(

Iit3tdo%ov

[ivcov roiovr&v naQodcw g)avQOv Îv rb 7tl r&v

didyooov yevyrcu, TtccQa^rjô^â KKL rovrcov 15

cprjtii, rrv]Qr)Xvai rc5 v' rL ri\ rgirris xccrd

Kdfaitnov 7tQi6dov xar' Aiyv7i,rCov$ 'Em,<pl ig' rov

diuoioov rris XQ&rrjs cngag 7taoA.r]hvd'6ros. d()6[io$

[ilv ovv, (prjdiV) r\v GILO,', rov df r\kiov diOTtrfvoîevov

xard Aeovrog {IOIQCCS rj /_' t/3' ^ ^^nvn <pawto it- 20

%ov<5a TO.VQOV poiQccs t/3 7', xccl dxgifl&g ds itEt%ev

fyyiGra rag avrdg. yivsrui aocci] ^.fra^v rov r\kiov xccl

rr}g 6^vrjQ dxQificbs &G)QOV[ievr) did6rcc6is {IOLQ&V 3t$ IE.

uKKu rov r\Mov ovrog itQl ra Tto&ra {ispy rov Adov-

rog vf

Pddco, onov ^ rrfgyGig f'^Wro, ?5T^S rftiEQag 25

3. tg HOIQ<XS\ ins. loco 1 litt. D 2. 7. obs] tuffTe C. 8.

8'] ds D. 12. r(f] i;> ABC, FB renouat. D 2. 13. xov] f A,

om. D, ? supra scr. D 2. 16. v'] v ABCD 2

,v' D, va' Ideler

Hist. Unters. p. 217, "of Halma. 17. KdUinnov D. 'Enitf D,corr. D 2

. 19. GÎCC'} mwc ABCD. 20. r\ /_'] 7/5 D. i$'\

i(3' AC, tJ5' B, ip D. 23. TT)S] r- in ras. D 4

.

<5rlv it, y''

cci ago rr\g ^6rj^ôiccg aocc

y' G)QO,i xaioixal itoiovtiiv i6r]îoivds g g'*

yovwai xr\v riJQrjGiv nob g g' cbp&v farjpSQlv&v rifc

fV rf/ tg' p6r]iipoias [isGovQavovGrjg Tavoov ôioag #'.

5 cvvdysrcci roivvv xal svrav&a 6 anb r&v S7to%6)v eitl

rrjv riJQrjGiv %QOVOS sr&v AiyvjirivM&v %i,& XKL

rid xal G)Q&V i6r][iQivG)v drth&s psv i^lly',

ds ifci^d'' JtQOg ov %Q6vov VQi6xo[iv rbv ijAiov xcttci

ras fjustSQccs vnofteGEiQ, STtsidiJTteQ 6 ccvrog 6tiv [i<5-

10 yfipQivos dia(

P6dov xal 'Atefauvtiqstos,

7t%ovra Atovros {IOIQCCS I x, axQifi&s $

xal T$IV 6kr)vrjv d {ifCi&s xctra itrjxog V&

Tavgov polices d x, cbg lyybs flvai xukiv iv\v

&7to%r}v TEtaQiriiLOQiov, avG)[iKA,ia$ d' ajtb rov a

15 rov 7tixvxA,ov {IOIQCCQ <?v ^^, itgbg ccl$

yivBtai rb nkEitirov dicctpogov trijg nciQo, rbv Inixvxkov

av(Q[iaA,ia$. Gwdyfrcci CCQCC fj dicc6ra6i$ y djcb rfjs

u,6qg 6A.ijvr]s litl rbv ctxQifti] r\kiQv ILOIQ&V 97 v.

rriJQr)ro dfy

ocTtb rfjs dxQiftovg eitl rbv

20 ^g Ts' Ttfaiovccg CCQCC iitslyzv r\ GfAijvr]

yovftdvy rfis 6ftaAiJ? ytagodov poiyac; ndhw g ri dvrl

rcov xard r^v 7tQ(brr]v V7tod'6iv. (pavfpbv df yi-

on xccl r&v dvo rovr&v rrjofafcov 7tal rag

1. zgovtov] %- in ras. A. !<mV] -v del. D 2, comp. B. 5.

TOLVVV~] ovv D. Post v.uf del. o C 2. 9. SGTIV\ comp. B, -v

del. D 2,

ietiv 6 A. 14. rfra^TTjjLio^tov] ante alt. Q ras. 1

litt. D. <T] Ss BD. 15.SyyuK*f*** D, sed corr. 19.

anQifiovg] ccKQipovs celirjvris B; ^ add. mg. A 1

, supra scr. C.

Inl TOV &yiQipfj[] om. D, ([ snlrbv cty.gi$fi $ mg. D 2. &v,Qi,$f)\

av.Qi$fi fyiov B, d supra scr. A X C. 21. ra ] lo ABCD 2,

rj D. 22. F] bis C, sed corr.

cc VQfi"Y] T^S xciTK rr\v Tto&Trjv a

diaxQi6G)s dv0l [loioccis xccl di(ioiQG)) fjds XCCTK TOV

'f

ImtttQ%ov V7tQ(ldMov6cc ratg oLvtai^ liteidfi xal olov

TO itaQtt TJJV avapaMav KK& âs pv acpccigfTixov

hvy%av, Kara ds tbv "InitaQôv TtQOG&STixov. xal 5

f| AAeov df xtei6vcav TOIOVTCOV

QCOV xal r syyitfra VQi6xo[iev TO

ôrccv 6 7tiKvxA.os XKTK TO

TOV

'. UfQl TOV h6yOV TilS XXVTQOTrjTOS VOV 10

V xvxkov.

TOVTOV OVV OVTCOS %OVTOS 6TO) 6 XKVTQO$ T^S

xvxAog o ABP itQi XEVTOOV TO z/ xcd dicc-

JJV A4T, ftp* rjs vitoxC<5&& TO XWTQOV TOV

T&V %G)dtG)V TO E, G)6T TO fiV A yivSti&Kl 15

to catoysioTaTOv TOV ZXXWTQOV GyiifZov, TO $ F TO

. XVT$G) de T& F y^Qatpd-G) 6 frtixvxAos

6 ZJf, XCCi ^-^(D (pCC7tTOllVr] KVTOV q

xal 7t&v%&K) fjr@.

BJtsl TOWVV XCCTK TY)V Cptt7tTO[lV'Y}V TOV fJtlXVXkoV 20

Tils 6A>tfvys ywopdvqs TO

1. svtefaovaa D, corr. D 2. TIVQ^TJ D. 2.

i^ D, TBD 2. 4. ct(pKigTj]Y.6v A. 5. rdv] om. D.

6. knra. poiQ&v] f/ B, [IOIQ&V D. 1. r*] PB D et corr.

ex r-> A, r EC. 9. ^] ^ A, fy D. 10. ^'] mg. ABC,om. D, d KQ mg. D 2

. ntQi 11. xvTdov] hoc loco mg. D 2

et mg. superiore D. 13. KSVTQOV] K' C. 15. cjtfiW

y.vHZov D. ytVfff'9'at] vnoxeiG&cci D. 16. aTroyftorarov] a-in ras. A. r] in ras. D. 17. 6 8-1 in ras. A. 18. Z# ]

Z@ D. 19. E@B] E D.

diK<pooov GwiGTccTcti) TOVTO

liOiQ&v g ri, sirj KV xccl17

vitb FE yavicc nobs r

XSVTQO) OVtiCC TOV

TG)V ,OiOJV

5 plV i6iV Oil d OQ&CCi TJj,

g ft, otov d' at"

|, roiovrcov IK.

xalr\ {lev CCQCC sal r^

F rtSQicpSQSia roiovr&v

10 iGtlv IS JC, OtCOV 6 7T()fc

TO JTJ@ 6^'9-o^coi/toi' xv-

^Ao? T|, 17d' vn avryv

sv&sta F roiovrcov tg

15 V3tOTiVOV6CC OX. Cd6T XCU,

OiG)Vfj [JiV F X TOV

XSVTQOV TOV 7tiXVxA.OV di%&r] T,

TOV XSVTQOV TOV ditt ftfO'COl/T&V %G)diG)V Jtl TO

yLOV TOV XXVTOOV |, TOiOVT&V k'tiTKl XCCijj EF fj

20 anb TOV CCVTOV XSVTQOV lid TO rtfofysiov TOV sxxsv-

XCCi 8A^ {lV CCQCC fjAF diOC[lTQOg TG)V CCVTG)V

3, fj$ dA X TOV XSVTQOV TOV SXXEVTOOV

\,TK%V T&V XVTQG)V TOV T fiiCC {l-

XCCi TOV XXVTOOV I tO1

. XCCi

TOOV

6TCCl

6(QV TG)V

25 rjfitv xccl 6 vrtb Tf]g xxVTQOTr]TO<3

1. $'] 8s D. &vvay6(MVOv] -ov (o) corr. ex r in scrib. A,-tvov supra scr. D 2

. 2. i^] lo ABCD. yeoWa] T&V D.

3. X^VT^OJ] comp. seq. ras. D,w

add. D 2. 4. Post <<5iW

add. Y.M.VY.IOV D, v- del. D 2. 7.

{3] dvo C. 8. ?j]in ras. A.

10. fWv] comp. B, -v del. D 2. 17. E^] ? D. 7) (alt.)]

ins. D 2. 22. Q#] Q_ e corr. D 4

. 24. F t^] corr. ex ^ A 1

,

~i inter duaa ras. D.

MA0HMATIKHS ZTNTABE&2 E'. 367

rrjg 3tQ06vv6&g tov r^g

"EvXv [lev ovv rcbv TCSQL rs rag 6vvyiag xal hi

Ttfol rovg dijôroîovg rijg GsAtjvrjs 6%r)[iari,6[iovg cpai-

vo[iVG)v HXQ 1' voGovr&v ccv Ttg zttifidkoi rcclg rtibv 5

vr^g xvxhaov V7to&6s6iv, x ds

7tQi rag inqvoidelg xal cc^KpixvQTOvg a

6ig &COQOV[IV(QV TtttQodcov^ naff ag ii

yivstui rov t aitoyfiov xal tov TtsgiyMov rov x-

XVTQOV 6 7tlXVXhog, IdiOV XL TCEQl T^V TOV 7tl,XVxA.OV 10

7tl tijg GfAtjvrjg VQfaxo[i

yap v n xal rb avrb xa&ohov r&v

V7toxl6&ai, dfi 6r]iitov, ngbg 6 ndvrors rag T&V v

avrolg xivovyidvGdv a7toxaTa6td6ig dvayxatov tGxiv

ccTtoTffaiGd'ai,) rovro ds xaôvîfv dnoyfiov 6ftAdv, 15

a<p ov xal rag aQ%ag r&v rijg xara rbv

xiv?j<3G)g aQi&yiCbv vcpi6rd[i&a, <bg itl rrjg

vrjg xaraygacpijg rb Z, xal dyoQL&rai, rb roiovro

[itov xara ri\v 7tl r&v aitoysiov xal r&v

rCbv XxevrQG)v rov eTtixvxAov &6iv vnb ri]<s dia ndv- 20

rov rcbv xsvrg&v x/5aAhoiivr]g ev&ffag^ cog rijg

7tl ILSV r&v dhh&v v7to&6G)v TCccG&v ccTtAcbg

1. s'] mg. D 2. 7tQovvGco$ D. 3. re] om. D. 4. 6f-

post -s- ras. 2 litt. A. 5. Post ^S^QI del. r&v D 2.

7rt(JaHotBCD, corr. D 2. 6. syufiiiEvcov D, corr. D 2

. ctvtfjs]

a- et -T- in ras. D 2, supra scr. avrrjs D 4

. KVY.IOV C. vno-

ftiosGi, -i in ras. 2 litt., D 2. 7. [ir]voiSf)s C. 9. yivtrcci]

corr. ex TSLVSTCU D 2. MY.EvtQOv\ -g- supra scr. D 2

. 10. n\corr. ex yu$ D 2

. 12. TI\ corr. ex TO D. iTrixvxôav] corr.

ex vnoKvuloov C 2. 13. fot] corr. ex Seta D 2

. 15. Supra6[icd6v add. âllov D 4

. 17. ccQi&fi&v] corr. ex KQI&ÔV D 2.

v<pi6Ta.iL&ct] mut. in vtficrm^Q'a, D 2. 21. //Er1

] supra //

add. a D, del. D 2.

368 .KAATAIOT UTOAEMAIOT

% TG)V Cpai,VO[lVC3V dvTLJllrtTOV TOO KKl KCHTCC. Tag

rcov 7tiKvxkG)v itaoodovg rrjv dia TOV 7tooxi-

aitoysiov rov 7tixvxA.ov didpfTOOv, TOVTEGTLV rv\v

ZJTH, rr)v avrrjv ftztiiv afel 6vvTr)Otv rr\ TO KSVTQQV

avrov opaAeos TCSQictyovGri fv^fta, cog sv&dds rr^ EF, xal

, OTCSQ av rig xal axohov&ov fiytfticcirO) itdvzote

, zrpog eo nal Iv

iiti d T^S Gshtjvrjs iviGtaxai to. cpctivo-

10 [lVa TG) KCCl V TCilg [IfTCi^V TG)V A KCCl F 7tao6doi$

rov fnixvxAov rr^v ZH dialerQOV ^ Ttgbg TO E Kv-

TQOV rijs TCfQwywyfis VVELV xal rv\v avrv\v rr\ EFftiGiv dia<5d)t

>iv. VQi6xo[iv pao TCQOS fv [iv n xal

TO avrb <5rniiov rcbv itl rijs -dF dia^TQOV rrjv KXi-

15 pivTqv 7to66vv6i,v aid 6vvTrjQov^vrjv^ OVTE pivroi nobs

TO E KSVTQQV TOV diCi [l6K)V TG3V ^G)$L(DV OVT 7CQOS ^6 ^/

rov XXVTQOV) ctkka TCOOS TO ri]v foyv Ty 4E (iTcd~v

rcov xwTotov aiteôv rov E log utgbs TO ttfOiyfiov TOV

MtVTOOV. Xttl On TOV& OVTCOg %t) d&,0[lV Ttd^LV

20 aito Ttteiov&v Tr}ori<j(X)V lK&l[Lvoi dvo Tag pd-

kiGra TO rtQoxi[ivov fpcpavfaai dvîâ^va^ TOVTBGTLV

na& ag o re &exvx3iog rtol ras [i<5ccs tt7to6rd(5t,g

rjv xali] Gfhrivr] ytsol TO aitoyuov rj

TO Ttsgiytiov TOV

1. xca] in ras. D 2,om. C. 2. Supra Ttagodovs scr. coi> D,

del. D 2. 3. TOVTSOTLV] comp. B, -v del. D 2

. 4. ZFjff] corr.

ex Ztf FH A 1,ZKF

f) B, ZHFrj C, Z7} TIT C 2

,-FJf in

ras. D 2. asi ED. 10. Post TW del. ^ %at ^r\ I)

2. 11.

STCMvnliov] s- ins. A. fwj] fw] D', jlrj' D 2. 14. AF] corr.

ex ABF D 2. 15. aft D. 16. E xsWô^] corr. ex 8x-

xfVTôv D 2. 17. z/E] corr. ex z/ E D 2

. 20. M&EIM-VOI]corr. ex K&i[iva)v D 2

. 21. TOVTSGTI B, rovtiGzivnv D, -VTWdel. D 2

. 23. TO (alt.)] om. D.

MA0HMATIKHS STNTAgBSZ E'. 369

)dice to 7tQi rag roiccvrccg itccgodovg rr\v

diCCCpOQCCV ^V^KIVSLV rS)V XXl[lVG)V

VV<3CW.

avccygdcpst, rouvvv 6f

'l7titciQ%og ivf

P6da)

xsvai, dia r&v ogyuvcw rov T ^'/Uov xai rrjv Gshijvrjv 5

r<p 09?' k'rsi anb rijs 'Ate^KvdQov refovTrjg XCCT

ort, rov rjMov di07Ctvo[ivov xara TavQOv [IOIQCCS J

L'd' TO rijs Gshrivris XWTQOV icpaCvBro 7t%ov 'I%d"VK)v

ILOiQCCS KK rB, 1ti%V $ KXQ^&S MC ?''

V\. XCCTK 10

TOV XXl[JiVOV CCQCC %QOVOV &7tl%V fj (XXQl,(}f}

rov KKQiflovs fi^Cov ig ra 7t6[iva {loigccg rt/y

TCBVX

sv rri IK' ftftf??^figices'^CCVTCCL d' Inoiovv iv

f

P6dc3 ror 15

CQQCCS rB fyyidtcc, GwdyErcct, 6 ccitb rrjg

Q6vo$ rcJv Alyvn-XCCi G)QG)V

&v rtdfav1/fj y'9 axQip&g ds

1/ij ftdvcov i$ ov

VQi6xo{iv rov fti> opcchbv jjfaov iitijQvta rov 20

c; [ice, rov d' axQifif} iioiQag t, fZf,

6hrjvr]v xccra ^Kog [iv iitiyjQv^KV

r&v 'I%&vG)v iioiQag xfl ty ? ccv&inaMag d' ditb rov

_ 4. 'Potfw]?

P- e corr. C. 6. 05' hsi\ g^ seq. ras. 1 litt. D,

f f? D 2. 7. $ciQii,ov9l ia'] -I i- corr. ex N A.

{?'] jj D,

add. D 2. 10. r*] corr. ex r A, To BC, PB D, uT D 2

.

inefytv] -v del. D 2. 13. dsw^e]^ B. 14. nsvrs] FED.

15. rff] corr. ex rfj A 4. d'] Ss D. inofovv] int-i ovv C.

16. r*] corr. ex r A, 75 BC, FB corr. ex tp D2

. 18. ~<n&]

in ras. D 2. Post MQ&V ras. 1 litt. C. 19. ^j-V] p D,

D 2. y'] supra scr. D 2

. ^ovcov] mut. in fiovov D 2.

{i6ov anoyeiov TOV litixvxkov iioioag oit A, &6T

xal Tr)v Trjg 6[iaA.ijg 6^tjvrjg drtb TOV dxatfiovg YI^LOV

TOVTC3V OVV V3tOXl,[lV(QV (5TG) 6 XXVTQOg Trj

5 6A,rjvr]g xvxAog 6 ART itoi XWTQOV TO 4 xal

TQOV rr\v A ^/.T1

,

&y ^fS UtitCO tb XV-

TOOV TOV dia ft-

()G)V TS)V ,G)$LG)V

10 xvxhov TO E) xal

XVTQG) T(p B y-'

6 ini-

15

anb TOV B 7tl TO A, YJ$ ti^rjvrj r^v KO.TK TOV ini-

20 xvxkov d)g onto TOV Z iitl TO H xal TO,xai its-

rjT JB xal % E&BZ.

i TOiVVV V TG) [l6O) [irjVLCu'o) %QOVK) dvO 7fQC-

a7toxccTa6Tcc6'ig TOV 7UxvxA,ov xobg TOV xxv-

aTCC d Tr\V XXi^LVrjV &6lV <X7ll%V

25 6hijvri TOV pfaov r\Mov {lOioag rtf A/3, lav

GiaGccvTfg TavTag dq)^co^v xvxAov, '$o[iv Tr\v anb

TOV dnoyuov TOV XXVTQOV ysysvrunEvriv ano%riv TOT

6 ZH, 7tQi-

d' 6 {lev

TTjV ?g

TG)V

a)g

1. ftfdov] corr. ex [itcovs D 2. ^Ttiyiv^ov] Ini- e corr. D 2

.

I] in ras. D. 21. vialrj] BD, Y.CCL AC. 22. iirjviccta) -LK-

corr. ex H in scr. A. 24. iv,v,8iiivr\v^ s- e corr. D.D.

MA0HMATIKH2 STNTASESS E'. 371

rov frtixvxAov stg to. ino^va [loio&v 6oa d' metre

xalj] vjtb AEB yovfa r&v koin&v sis tag 8 OQ&as

farcci HOIQ&V TCTJ vs. $%&& dfj xd&frog <x7tb rov z/

7tl rfa EBii4K. 7td ovv

fj vTtb 4EB ycovici)

oicov [iv i6iv CCL d OQ&al r%) roiovr&v farlvjtrj vg, 5

OL&V d* aC dvo OQ&al T|, toiovr&v QO vfi, sty av

KCilrj llV 7tl TyS /IK 7tQl(pQl,K TOlOVtCOV QO V$,

OLOV stirlv 6 TCSQ! TO 4EK oQ&oycoviov xvxhog rj, ^ d'

sitl rijs EK TCOV AOM&V [Eucl. Ill, 31] etg to $\\LMVK).IQV

ji rj.xccl rcbv vit ccvrag CCQCC ev&eicbv ^ V&v 4K farm 10

roiovrav QI& IA^, di&v farlvfj4E did[iT()o$ QK^

fj$ EK TK)V CCVTG)V ^ id. KCtl Ol&V farlv CCQCC 'Y] [lV

r&v XSVTQ&V 7 t#, ^ ds 4B SK rov

rov McsvrQOv ^0" ^JLCC,roiovrcov xccl

i] [ilv z/Kid1 itakiv fyyicira, rj

$ EK djiofas t/3. 15

xcci fad rb KTCO rijg 4K Aeiy&kv [Eucl. I, 47] vitb

rov attb rrjg z/5 noisl rb aitb rY\$ BK, f1*o[iev xccl

rr\v plv BK rav avr&v ^ Ag, rqv d BE oArjv ^Bitel

r\ plv r^g 64uaAijg ^s^viqg ccTtb rov

1. poiQ&v] D, comp. B, (jiOLQccs AC. <?oa] -o- in ras. 2

litt. A. 3. zf] corr. ex A D 2. 4. EB] EJ A. 5. Icrlv]

comp. B, -v del. D 2. vg~\ corr. ex v nai D 2

. 6. dvo~] fiBD.

toLovTfov 8. r] mg. D. 6.vfi] renouat. D. 8. ofav]

-eov supra scr. D. larfv] om. D. 9. i7juxvx>Uov ] QB D,

o* B D 2. 10. awag] corr. ex avr^g D. 11. z/E] corr. ex

~&s D 2. 12. id] -^ e corr. D 2

. 13. z/E] corr. ex AE D 2.

rt-fr] e corr. D 2. 4B~\ B4 D. 14. HSVTQOV] xfW^ov

ovc?a D. 15. tl^] e corr. D 2. EK] EK ndKiv D. 16.

^TTSI'] corr. ex Tzre^t D 2. dK Aftqo^fV] corr. ex <MlT}yftiv

D 2(-?]- corr. ex SL in scrib.). vwo roi) anb

rfj<s~]vnb rfjg D,

ccnb TOV KTtb tfjs D 2. 17. z/B] B/^ D. Post itoisi del. ro

awo rr^s BJ notst D 2. 18. fAV] om. C. BK] corr. ex

KB D. fo'] bis extr. et init. pag. A. BE] EB D. ^]om. B. 19. fast

?j]corr. ex snl el D 2

.

24*

fjMov diKtiratiis IIOIQ&V r\v rid MJ, rjds rijg

r&v x rijg r^^Êcog IIOIQ&V ny ^Li/3,coGrs

rb TCCCQK rrjv avopccMav avrijs didcpogov

oJLtg, ftscoQBirKi <P % bîcc^ itdgodos rife

till xijs EB EV&EICCS, vjtoxsiGd'G)i\ Gehtjvfy

rtsgl to itBQiytiQv i\v rov SJCLKVKÔV^ Kara rb

H <5rnLloV) xal siti&vx&siG&v T% re EH xai ri\$ BHxd&stos anb rov B iJx&G) enl rr\v EH mfikriftslGuv

fjBA. EJIEL ovv % vjtb BEA y&via rtQi,E%i rb

10 Ttaga r^v av&[iaMav rijs (JfA^V^g didcpogov, fir] civ,

Oiwv \iiv i6iv ccC d og&al r^ 5roiovrov o

jiTg,otcoi>

d' CCL dvo oQ&cil T|, roiovrcov a A/3' &6r xalfj [iV

7tl rye; BA V&EICC$ ytEQHpEQEia roiovr&v EGrlv a A/3,

of

iG)v 6 itZQi rb EBA doftoycoviov xvx&os r%, $ df

15 i)7t avrfjv v&ia<Y\BA roiovr&v a Ag, <HOV 6rlv

j]EB i)7torivov6K (w. &6re KCLL, olcov sGrlv i\ tizv

BE v&la prj Mi % $* BH M rov xwrgov rov iiti-

xvxAov 7f, roLovrcov fGrut, xcclfjBA EV&EICC o A#.

xal or

iov (Srlv CCQK TJBH X rov XEvroov rov iiti-

20 xvxhov ^3c, roiovr&v xaifj Îv BA evfrelcx, zGrai, id

vfi, % d' fV avrijs nsQMpzQEiK roiovrav id td,

3. ctvTfjs] corr. ex avr&v D 2. 4. d'] Ss D. 5. lni\

inl -to C, corr. C 2. 6. &m<?Tj] -rj corr. ex i A 1

. TCSQL-

yto C. 7. rrjs rs] corr. ex T&V D 2. EH v.ai TTJS] in ras. 2

litt. D 2. 8. xd&STos anb TOV] in ras. minore D 2

. B] rjTain ras. D 2

. 9. rj (pr.)] ins. C 2. BA] corr. ex BJ D 2

. BEA]corr. ex BE D 4

. ymvia] om. D lac. 3 litt. relicta. 11.

o jig] corr. ex ojt g D 2. 12. dvo] B B. A{3] corr. ex Af5 A,

e corr. D 8. &GT& 13. BA] in ras. D. 14. E\BA] "TTEA B.

dôycbvtov] corr. ex OQ&WV D 2. ^] ^' D. 16. EB]

BE D. 17. ds B#] d' D. 18. o ;iFj ol^ C. 19. (

SGTIV B. ^ BJf ^x] renouat. D 2. 20. Supra QX ras. D.

BA] corr. ex BA D.

MA0HMATIKHS 2TNTAEE&S E'. 373

sGrlv 6 7tQl TO EHA OQ&O'y&viov xvxAos rjj. &6TS

xalr\ plv vjcb BHA y&vicc TOLOVTCOV faxlv id id,

otrav falv ecujS oo&cci rf, Aowr?? [Eucl. I, 32] ds

f\

into EBH T&V pav CCVT&V t/3 ^3, ofav d' cci d dgfral

T%, TOiovT&v g we' ro&ovrov CCQCC stirai, [IOIQ&V i]H 5

rov sjtixvxAov TtSQHpEQSicc TJjv KJtb rv\ Gshrjvrig 7tl

to uKQifieg TtSQiyeiov ttQt,s%ov6ct diaGraGiv. AA'

fastd^ rov iL<5ov aitoysiov a.7tsi%v fj ^s^tjvrj xccrti rbv

%QOVOV rrjs Trjotftiscos ôi^ccg gas A, dÂov, on, xai TO

TtSQiysiov TO {istfov itgoriysirai tijg Â^V^g, TOVTSGTIV 10

TOV H GruLSiov. s6TG) drj TO M^ xcci dirii&M fj BMN,xal KTtb TOV E xd&Tos 7t avTriv %%&& r\ E&. iti

TOIVVV17 ILV &H 7tQiCpEQl,a $1%^ pOLQ&V g JC^,

rj$ HM V7tOKLTKL T&V CCTtO TOV 7tQLyLOV ÔiQKtV A,

&6TS ohyv Tr^v &M tfwcfyftf-Om yiOiQ&v ~ia va, ir}av 15

xalf}

V7tb EB& 'ycdviK, oi&v yulv i<5iv ai d ogftccl T|,

TOIOVT&V Tec w, oi&v d' ai dvo ogfral r|, TQIQVT&V

ny fi/3.K)6T xal

rj ^lv iitl T^g E& XQi,q)EOicc TOLOV-

TOV 6Tlv ny ft/3, OIGJV 6 7tQi TO BE& oQ&O'y&viov

xvxhog T|, ccvTrj dsr\ E& v&lcc TOLOVT&V xd AO1

,20

ottov 6TivrjBE v7toTivov6a QX. xal ofay itirlv

BE v&Ela ir TOLOVT&V ^TKL xcclr\ E&

2. ytovia] 1^, D, ut saepius. iS (alt.)] corr. ex iu D 2. 3.

~] dvo BC. 4. d'] mut. in d D 2. 5. s] corr. ex I? D.

17] postea ins. A. 9. TO] corr. ex TOV D. 10. TOVTGTW]comp. B, -v del. D 2

. 11. TO] seq. ras. 1 litt. D. 12. E]supra scr. C 2

. xa-9-fTog] Kd&sTo- in ras. minore D 2. 13.

H] supra scr. D, renouat. D 2. nsQicpsQsia] om. D. 14. i]

corr. ex a D 2. 15. CO^TS] 50Tf %at I). ia] -a in ras. D.

17. 8'] Ss D. at] ins. D 2. Svo] p BD. 18.

tptQSLu] fa D, ^ del. et o renouat. D 2. 22. jZrj] om. B.

corr. ex J| D 2, mg. t| D 2

.

I xal %r]xo6TG)v dvo. ita'kiv^ litelv\ plv vnb

AEB ycovtcc roiovtcov f\v po i>/3, oiov cci dvo do&al

r|, f\ds vjtb EBN rcbv ccvr&v wy ft/3, eL'rj

av xai

XoiTtri [Eucl. I, 32] r)VTCO ENB y&vCa rcbv avrobv

5 gvd ~L. &6r xalr\ ILSV enl rijg Eft TteQicpegsicc TOLOV-

rcov i6tlv Qvd 7, o'l&v 6 itspl rb ENE QQ&oy&viov

xvxA.os T|, ccvTrj dsr\ EH sv&sicc roiovrcov QI$ 2/77,

oi&v 6tlv ri EN v7toTtvov6a ^M. xal oi&v 0rlv

CCQK YI [iv EH V&ta 7 xccl Qrjxotircov /8, $ dl

10 iira%v rcov XWTQ&V 7 *#, roiovr&v xalY\EN

TIrj. far^y ago, fyyuSta rfj 4E rrjv EN a

^ dice rov [i6ov 7ieQiyiov rrj$ BM v&tccs Ttl tb N

LVCC xal

15 rOV T XXVTQOV XCtl tOV 7tiXVX&OV TO KVXO

% t&v vnb rovf

V 'Podc) dlO.(Srd6G)V TYJV

xar' Alywitxiovs Uccvvl 1% cngag &' xal

1. f|r]xoffT<5v] || B, | D, || et fl^xoffrcov D 2. dvo] corr.

ex ^ D 2. 2.

v$\ corr. ex MB D 2. Svo] B B. 3. T|] r-

corr. ex c in scrib. A. EBN] -N corr. ex H D 2. 4.

r]]

e corr. D 2. 5.

t~]e corr. D 2

. neQiyeQsia] ^ D,() supra

scr. D 2. 6. QvS] -S corr. ex A D 2

. 7. QIC;] Q- e corr. D 2

9. Eg] corr. ex l| D 2, mg. I| D 2

. s^oor&v] | D, ||/*A /*

BD 2; mg. &UCCYOV OVTCOS f^et is || |3

D 4per r^ hue relatum.

10. |Lifro:|v] ft D, ut saepius; corr. D 2. V.SVTQG)V OVGU D.

F i&] TT- e corr. D. 11. T trj] Tl- e corr. D 2. rr\v\ corr.

. TOV]ex xr\i C 2. 13. 7rpoffvfy0tg] -t- corr. ex o C. 16. TOV] corr.

exroD 2. 17. sv] ins. D 2

. 18. diomtvo^bvriv BD 2,

liivr\v C, 8iomBv[Lvr\v D. 9^^'] -9- corr. ex r1 D (or). ITSt]

corr. ex b D 2. 19. Ilavvt] TIccvvij (-77 e corr. in scrib.) post

lac. 4 litt. D, deinde eras. vvi. t'] *- postea ins. D. agcc D.xai om. D.

MA0HMATIKH2 E'. 375

^ rov fjMov diQitrsvopBvov Kara Kccoxtvov

Ta A.Ei7tov6ccs dExdrcj

3te'%ov6cc rov Asovros x

de xal dxQip&s SXEI%V) eTtsidtJTtSQ EV 'Poda itEgl rd

rsfavrccta rov Aeovtog {istci p,Cciv &QKV eyyitita tov 5

ILSGrnLfiQwov Mara pijxos ovdsv

ditstyev CCQK Kara rov exxsiîsvov %QQVQVrov aKQipovg fjMov [ioiQas sis t& sitopeva

g. AA' end yeyovsv rj riJQrjGis psra y xai y'

xcciQixas rrjs ev rrj 1% rov Uavvl {i6r][ji{i()iasi 10

ccvrcci, d' snoiovv svr

P6da) rore

6 cbro rijs

fl&S d y r* els ov %oovov catiavrcos s&Q rov 15

~Lji, rqv $E oîcc^v GEhijvrjv xccra

v 7t%ov6av Adovrog notices x K, &<5r xcti r

O rov axQi,flov$ fjMov

v ^ /Z, av&[JiaMas d' onto rov petiov 20

dnoysiov rov sjtixvxhov poiyus rky t/3.

rovrcov vjtoxEiêvcov sdro Tta'kiv 6 Exxevroog rrlg

xvxhos 6 ABF Ttsgl XSVTQOV rb /I xccl dtd-

2. D. 4. D. 5.CD.-a supra scr. C 2

. 6. nccQaldcGEi CD. 10.

rfj AC, corr. A 4. rot)] bis A extr. et init. lin. Tlocvvr]

11. d' STIOLOVV] in ras. D 2,deinde del. ovv D 2

. 14. d] corr.

ex I D 4. 15. r*] F ABC, mut. in F8 A, ii D, D 2

, mg.&Uaxov cwQip&g 8s T r D 4

. TOV] corr. ex ro C 2. 20. d']

om. D, 7 supra scr. D 4. 21. tnmuv,l.ov\ Ini- in ras. D.

A, BCD.

H,roov rv\v AAT, iy ^g h'tirco rb uwrgov rov di:

{iGa)v t&v ^(pdicov xvxhov rb E, xal /

y'y()d(pd'a) 7tol

rb B <jrj[ilov

6 ZH m-5 XVX&OS T'YJg 0-

T

E0B Z.

10 STtsl TOIVVV

rov f xal

15 7tQl,%

9 A, av

i(5iv al 6

jVTCO AEB ycovCa, O'LGJV

T|, roiovrcov 9 A, oi&v d' ai dvo

TOIOVT&V gnu. av xf$aA.6vts CCQCC rrjv BE20 Ka&rov 7i ccvryv aycopfv aitb rov 4 x

xalf)

vno dEK ycovia rcov koiit&v ig

000" G)<3T Xttifj [lV 7ll r^g /IK 7t

Qicc roiovr&v s<5rlv oo&, oicov 6 7Col rb 4EKycoviov xvxhos T| ; r\

d' iitl r$\ EK rijs

1. rov] corr. ex TO D 2. 7. ij T8 JB y.al T\ E0BZ] at

z/B E BZ D (s& corr. ex t& D 2). 16. 9 I] corr. ex T& D 2

.

17. xa 7tQor&coQ7i(iEVK] mut. in TO TCQort&fcoQriiJisv* D 2. 18.

T] e corr. D. dvo] B B. 19. s^dUovrss D, corr. D 2.

BE] corr. ex B D 2. 20. ayeopfv] ABC, aydyco[iev A 4 C 2

D,

bene, sed cfr. p. 381, 2. z/A] corr. ex AK D 2. 21. zlEK]

A- e corr. in scrib. C. 22. dvo] B B. TTf^iqpgpgta] Q D,

9 in ras. D 2. 23. 6] ras. 1 litt. B. 24.

rj]corr. ex e D 2

.

MA0HMATIKH2 STNTASE&S E'. 377

[Eucl. Ill, 31] sis tb fiiiMvxA.iov iioigag a. xal r&v

vn avrag agcc sv&si&vr\ Îv 4K 6rcci, roiovr&v

QI& v&, of

ia)v 6rlv f]4E vitorivov6a. QX, f\

de EKr&v ccvr&v a y. &6r xai, o

r

iov <5rlvr\ psv 4E

liTa,v r&v y.dvrQ&v It-9", f]

ds B4 x rov XEVTQOV 5

rov sxxsvTQov [id /la, notr\ yihv /IK v&ia <5ra,i I tO*

, r\df EK Quotas o f. xcci iitd ro TTO rrjs

L^ccv [Eucl. I, 47] TO Kitb rijs '<4K itoii ro

ccjcb rye; BK, eôpw ncti oAyv [iv trjv BK v&iav

prj As1

, Aotjri)v ds rr^v EB r&v ccvt&v^Trj Aa. Tta'kiv^ 10

I plv rr\<s oficcAijg GfAijvrjs aito rov

diK6Ta6i$ [IOIQ&V rjv jilg jit, fjd rij

TO

ttQL TO O.7t6'yiOV f]V rOV JtlXVX&OV) XKT& TO H 6rj- 15

HftoV) xal tti&vx&fid&v rijg re EH nccl rijg BHxd&Tos cbro rov B ri%&G3 iitl rrjv EH r\ BA.

itd ovv % V7tb BEA y&vicc, ot&v piv eltiiv ai

~d OQ&cci T, roiovr&v ftirlv a xg, otcov d' ai dvo OQ-

&al T|, roiovrovft vfi, fft? civ xccl ^ f^v 7tl r^g BA 20

TCQl(pQl,CC TOLOVTCOV /3 V/5, OtOV <5rlv 6 7tQl TO BEAdf

i\BA v&lcc roiov-

1. 7}piY.v'AUov] Q D. Tc5i>] corr. ex r<5 D 2. 2.

corr. ex uvxfig C 2. 3. v&] in ras. D. z/E] in ras. D. Post

EK del. * D 2. 4. a y] D 2

, Sy ABCD. 5. (isrcc^v] ^ D,corr. mg. D 2

. Ez/] /Ê B. 6. rov sMevxQov] corr. ex &i

rov %VTQOV C 2. 7. o] corr. ex & D. 8. Ittyctv] corr. ex

D 2, supra add. TO$. Supra pr. TO add. v D 2

. 12.

-ctaraGis in ras. D. 15. G^^LOV] c D, GTJ D 2.

16. ini&v%&siG&v] -G- postea ins. A. 19. Svo] p BD. 21.

3 D, ut saepe.

f$ v-9*, ol&v etfrlvj]EB vrtOTivov6cc px. xccl

famv CXQCC % plv EB v&icc p? Aa, i\da BH

IK TOV XVTQOV TOV 7tixvxA.ov Is, TOLOVT&V stirai

xccl-YIBA sv&sta a

t/3.KKJTS xai, oiav fatly

r\BH

5 v7toTsCvov6a ^jc,roiovrwv uai

v\ [ilv BA eGrat, v^ Ad,

^ d' iit a,vri\g 7tQi<peQEia roiovx&v % A(J7ot&

d itSQl TO BHA OQ&oycbviov xvxhos r%. xccl

vitb BHA aQtt ycoviK roiovr&v stirlv x$ Ad, oicov

stalv at dvo 6pwi_r|, % d' vnb ZBHoty [Eucl. I, 32]

10 t&v [isv avrcbv x& xg, oicav d' aC d 6Q&al T|, -rotov-

id ]vy. toGovTcov aga edrlv poiQCbv fjHZ rov

tV CCTtO TfS (fSJivi 7tl TO

ditel TOV (i&fov cirtoysiov a%Z% XCCTK rbv %QOVOV

15 Tils Tr]QrJ6G)g [lotgccg Thy i/3, lav vjto&G)[id'ci TO ILB&OV

aitti'yzLov KKTa TO M xal fjti&vt.avTfs Tr\v MBN xdd'-

STOV 7t avTfjv d f

yd<

y(o^,v ditb TOV E T^V E&, 6Tat,

17 {llv HZM 8A^ 7tOL(pQiK T&V

XVX&OV [IOIQ&V X$ JU^ ? AotJTl) df ^ ZM20 &6T xal

r\ (iv vnb MB Z y&VLCc, TOVTSGTLV [Eucl. 1, 15]

^ vrtb EB&, OICDV [lev dtiiv at d 600m rj, TOLOVTCOV

i(5r\vifi ,

oicdv d' ecu dvo ooftal r|, TOIOVT&V xd 7,

XCcIf] [lV 7tl Tils E^ 7tQi(pQlCC TOLOVTOV 6TiV X$ 7,

olov o ytol TO BE& ogd'oychviov xvxhos r|, avTrj df

4. a] postea ins. D. 5. &>rca] (>a D. 6. iari D. 7.

-A in ras. D. 8. 1^] -tf_inras. D.

_9. dvo] tJ3D.

ZBH] corr. ex ZB D 2. 10.

<?] A, corr. ex 7<? D, dvo BC.

11. ^y] corr. ex nid D. SGTLV'] comp. B, -v del. D 2. 14.

D, corr. D 2. 18. HZM] H- corr. ex E in scrib. C.

21. EBB] EBZ BC, corr. C 2. 22. icziv] comp. B, -v

del. D 2. r] ins. D 2

. 23. E] E^ c^a D. (>rt D,comp. B.

MA0HMATIKHS STNTAEE&S E'. 379

ES sv&slcc roiovr&v %,oiW stirlv ^ BE vno-

w. xal OL&V 6rlv aaafj plv BE ev&eta

Aa, f]ds /IE fisrcc^v r&v xwroov i iO1

,roiovr&v

VTtb AEB y&vfa vnoxsirai, roiovr&v QICCC,OL&V 5

sitilv KI dvo OQ&al dj, ^ ds vito EBN Idefyftri nd 7,

nccl koi7ti]v [Eucl. I7 32J rr^v VTtb ENB XUTCC^SL-

Tcbv CCVT&V QVZ v, yivsTcct, xccl rj [iEv iitl rfls

7tQi<pSQeia TOLOVT&V QV$ v, oi&v itixiv 6 Ttegl ro

ENS OQ&o'y&viov xvxhos r|, avrfj dsv\ ES toiovrcov 10

Qit, Ay, otcov s6rlv ^ EN vitorsivovGcc ^x. xal o'i&v

i&rlv CCQCC YI plv ES sv&sta I xal stflKoGx&v ^, 17ds

AE [JiSTcd-V TCOV XSVTQCOV i-0",

TOtOVt&V Xttli\EN

~i K. xal sx TOVTCOV aga i'Grjv syyiGra rf/ 4ET&V KBVXQ&V rrjv EN nu.'kiv uTtsttricpsv fj

dice 15

rov M fifWu aitoysfov rijs MB sv&SLas iitl ro N

xccl $ aAAcov ds Ttksiov&v TrjQt]6csv tovg avrovg

va /

yo[ivovs fVQfaxopw , co<s x rov-

rb ns^l r^v VTCQ&SGLV rijg 0^t]v^s 20

XCCTCC r^v rov 7tiKVKkov 3tQo6vv6iv I'diov TTJjg ftfv rov

xsvroov rov iniKv^Qv 7tQiayK>yri$ Ttzol rb E xsvraov

rov dice {isGcov r&v ^codicw aTtorfôvîsvrjs^ rij$ ds rb

ccvrb noil rb xccra rb [i6ov uTtoyeiov rov 7tixv%A,ov 6rj-

1. ES] in ras. D. 2. 97 [itv] infra add^D. 3. ilF] ~^

e corr. D 2. 4. ES] corr. ex E D. T

?j] i| ?j D, rf^D 2.

6. ^^] S' D. Edei%dr]] -%- corr. ex -A in scrib. C. 8. yi-

vsraL] mg. D 2,P D, F% D 2

. 12. l^xoarcov] comp. BD. ^f]

renouat. D 2. 13. T&V] corr. ex TW A 4

. 14. iar\v\ A 1

, foij|v A.21. TtQOGvsvGLV 22. imY.vv.'kov] bis A, corr. A 1

. 23. (ie-

ccov] -ceo- e corr. D 2. 24. TO (pr.)] om. D; mg. allaôv ovrco

tr}<S 8s Kara TO (itcov anoyeiov TOV m crrj^. acpogifcova' avra>

<r-o D 2.


[istov atpoQi&vGYjs avrov diaîsrôv {i^xeri, agog to EKBvrQOv ri\g bîa^g TtEQiaycayrig ri\v itQoGvzvGiv tittey

inl r&v akl&v yiotov^vrjg^ a/Ua Ttdvrors agog rb NKara rr\v faqv id ra stSQa didtiratiiv rye; 4E

5 T&V KVTQG)V

diet t&v yQaîî&v CCTCQ r&v

fj KXQiflJis rijs 6A.rjvr]s

Tovrcov ds OVTOS djtodsdsi'y^svcov dxoA.ovd'Ov rs

10 ovrog Gvvdtyat,, ruva av tQ63tov xccl snl x&v narcc

rfjs Gshtfvrjs itagodcov rag T&V peGcov KIV^SOV

ipw dno r rov r^ ccito-

dQi&[iov xal aitb rov Kara rbv iitinvKkov rijs

rrjv ywofidvifv itQfa&stiiv ty dcpai()6iv rrj Kara

15 ftijxo? {i6r] 7Cag6d(p rov TCCCQCC rv\v av&iiakiav diacpoQov^

robv yQamL&v fj roiavrr\ Karaâ^,^dvrai 8id-

aTto rGbv 6ftotc3i/ rols 6tt&i[ivoi ^(DQ^îdrcov.

VXv iiti rijs v6TQas rcov

rdg avrdg v7to&G)[id'a iCOio-

20 dixag xiwJGfic; dito%ijs nal dva)[iaMaS) rovrltirw dito-

v rag IK rov SmkaGiuGpov Gvvyyiisva

A, av&paMag S1

dno rov pfaov uTtoydov rov

1. diaiisxQOv] -STQOV in ras. D. 2. TIQOGVSVGIV] -i- corr.

ex r) A. 4. fisra^v'] corr. ex ft D 2. 6. s'] om. C, mg. D 2

.

jroog 7. JLa^dvsrca] mg. superiore D 2fol. 109V

,eadem mg.

sup. fol. 109r(i] axptfiife] diaKQipsi, TtdgoSoi iK^dvovxai) D,

del. D 2. 9. 8s] Stf U. 10. 6Vro?] e corr. D 2

. 12. WQIGKO-IIEV B. 13. Supra rov add. O.QI&IIOV D 3

. Kara] x- corr.

ex y in scrib. D. TOV~\ corr. ex TO D. 14. yivopivj]v] corr.

ex P D 2. 16. fie'v] del. D 2

. 21. (isv rets s* TOV] in ras.

post ras. 1 litt. D. 22. f] e corr. A 4, mg. 9!' A 4

. d'] 8s D.


xvxkov

rqv NSr&v avr&v

t/3,xal avrl plv rrjg E& xa&srov

,avrl dl rijs BA rrjv HA, dice per

x rov Mtfaftai rag nobg rep E

xocl rag z/E 5

xal EN VTCO-

r&v 4Kxal NB sv- 10

rov

(Srai t i,

HyyiGra ,oiov

H 6rlv ^ [iv 15

% rov

rov

exxevroov pft fia, ^ df BH BK rov xvroov rov

zitLXvx&ov tf, xaroa d rcov EK xal E& r&v

avrcbv o f, xal dia rovror\ {ilv BK 6'A^ f'tfrtu, 20

xa&a7tQ di,a[iv [i7fQo6d'v ,rcbv avr&v

fi/ij Ag,

i\$ BE bpoi&g pr] Aa, ^ ^ -^S T^V AoiTt&v

JJi/rj w;. GUST' 7ti xal ra anb B& xal &N 6vvr-

itoiEl TO ajtb rqg BN [Eucl. I, 47], xal ravr^v

[iijx[, roiovrov [i& Aa, o'i&v i]v i\ N$ v&ia 25

xal oltov 6rlv aoaj]BN v ijtorivov6a ^x,

2. N&] N- obscurum, vt- supra scr. D. aydyoopsv D. 3.

supra scr. D 4. 8. OVGCCS] faces B. 18. KWTQOV] x-

corr. ex a in scrib. C. 20. o ?] g D. 21. ldsLJ-a(iev~\ posta ras. 1 litt. A. 22. Post ftrj del. xg D. 23. onto] anbr&v D. xat (alt.)] supra scr. D. 25. ofeoi>] orco C. TJV]

supra scr. D 2. 26. T L&] TT- corr. ex JV" D.

TOLOVTCOV k'tirai xal % plv N& svfatcc x gyyiGra., 17

6' en avTils 7tQL<pQia TOLOVTC3V xd y, oicov <5rlv

6 7tQi rb BN& tiQ&o'yaviov xvxôg T%. &6rs xal ^VTtb NB& ynvia, TOVT&TLV [Eucl. I, 15] r\

VTCO ZBM,5 O'ICDV \iiv L0iv ai dvo OQ&al T%, roiomcov serai, xd y,

OLCDV d* ccC d oQ&al rj, roiovrov t/3a syyititcc. roGov-

TC3V 0rlv CCQK f]ZM TOV BttlMJKhoV 7CQitpQlK.

7C\ rb H 6rj{itov rr\<s 0^vrjg a7t%t, TOV Manoyfiov tag Aowrag ig rbv sva xvxkov

10 xg jiti/,xal komriv fôîfv rrjv HZ 7tQi<pQeiav

td ftg' &6T xalfj VTtb HBZ yovia^ oicov piv eltiiv

ai d ogftccl t$, TOiovr&v 6rlv id fi, otcoi/ d' ai dvo

oo&ai T$) roiovt&v xd1

Ad, xal ^ (dv fal tijs HA TCSQL-

<pQLCC rOlOVTCQV 6xlv X& Ad, OIWV 6 7tQ\ TO HEA15 OQftoy&viov xvx&os T(J, ^ d' &tl Tfjs AB T&V koin&v

[Eucl. III7 31] etg TO fmixvxfaov ~QV xg. xal T&V vit

KVTag aga V&IK>Vr\ ply HA Z<5xai TOIOVT&V A Af,

OLCOV 6rlvf)BH vitOTBivovtia QK, q ds AB T&V avTcav

QL /f. K)6T XKl, OIG3V 6TLVJ] [lV BH X TOV XVTQOV

20 fov *TCixvxA,ov f t, f} df BE di%&r] ^trj Act, TOLOVTCOV

xcclfj [ilv HA 6Tai, cc 3c, 17

df AB oftotog . xal

4. rovxiGTiv] corr. ex T-/. D 2. 5. I'ffrat] SGTIV seq. ras. 1

litt. D. 6. i'yYL6TU D. 7.

17]xal

17D. 8. 67](ji8tov] <?* D,

D 2. aTr^Fi] corr. ex &nsi% D 2

. 11. xai'] bis 'C extr.

et initio pag. HBZ] HZB C, HBZ supra scr. C 2,corr. ex

BZ D 2. 12. rotoimoi; 13. TOLOVTCQV] mg. D 4

. 12. f'crrtV]

comp. BD. d'] de comp. D. 13. T|"] BD, supra add.A 4

,om. AC. TOIOVTCOV] etiam in textu D. HA] HA

&QK D. nfQLcpSQficc TOiOVTcov] mg. A 1. 14. HB A] BH D,

ERA D 2. 15. <T] 8s C. 18. Post BH del. if D 2

. VTTO-

TSivovGa] -v- corr. ex o in scrib. C. 19. Mg. rotovrcov soriv

ice [ig oi'cov ds CCL dvo OQ&al T D. 20. jitr]]corr. ex fTnr D 2

.

21. a x] ax AC, ut saepe. ylB] -E e corr. B 3.

MA0HMATIKHS 2TNTAEE&S E'. 383

KQK rjEBA TOIOVT&V EGTLV vj> A, otcof xal

fj

AH r\v a %. Km, ETCEI Tta.'kiv TK VLTI avrcbv GVVTE&EVTCC

TtoiEi rb CMQ Trig EH TETQccyovov [Eucl. I, 47], EÔ^LEV

xccl rr\v EH ^KEL T&V CCVTCOV wy A HyyuFta. &6TE

XCCl) OICOV <3tlvfjEH V710TIVOV6CC ^K, TOlOVr&V XCil

ij [ilv HA 0rcaft v&, r\

d' ETC

roiovr&v ^ v/3, oi&v fatly 6 itEQl rb EHAVLOV xvxhos T$. xal

fj vjtb HEA CCQCC y&vtcc rov

Ttccga ri)v KVcopaMav diccyoQov, olW fidv EI<?LV at dvo

OQ&ccl T%, roLovrov 6rlvft vft, OL&V d' cci d OQ&al T|, 10

TOlOVt&V a 3CS" OTtEQ ItQOEXELXO

Kavovog TCQcc'yârEia rijs xafrohov

r'Iva ds Tt&Kiv xccl dia rijg xccvovixrig

E% ETOipov didxQiGiv r&v Kara [iQog 15

) TtQOGavsjtArjQ&GaiiEv TO HUTU T^VV V7t6&6lV 7tQOXT&ElllVOV r^LlV XKVOVIOV TOtg

xal Tijv di7tki\v ccv&iiaMav TtQOÊLQ

dvvcc[ivot,g GEfadfoig dice T&V avT&v

%Qr]6d{ivoi, Tcclg Ecpodoig. ÎETK plv y<xQ T<X TCQ&TK 20

dvo 6E&idi,cc TCC 7tQi%ovTcc Tovg

TQLTOV GsMdiov 7tQi%ov Tag

1. EBA] corr. ex EBA D 2. tGiiv\ comp. B, -v del. D 2

.

^,5] corr. ex vg C 2,

corr. ex Js D. 3. EH~\ corr. exEN D. 4. EH] corr. ex EN D. injyiti, fyytcra] in

ras. D. 6. HA] EA B. 9. dvo] B B. 10. r|(pr.)] corr. ex

T in scrib. D. tariv] forat B, om. D, comp. ins. D 2.

j? v]|3jv

D. 12.']

om. A, mg. D. KKVOVOS 13. ccvcoficcli'a?] mg.superiore D. 15. pt&odfvuiifv] -co- corr. ex o in scrib. C.

16. TtQoo&acpcaQfGiwc; D, corr. D 2. 17. TtQOwrs&Eiiitvajv C.

21. Supra rovg add. KOIVOVS D 2. ccQi&\[iovs A, <xQi\ft(iovg A 1

.

384 KAATAIOT IITOAJEMAJOT

rep Trjg *fl>fH&U$ apfifytcS jrôg TO TOV aitb TOV

a7toyiov, rovrfan rov M, GwayopEvov ex T&V

Ttaaod&v iistafpeQSG&ai nobg TO axaif&g K

TOVTStiTlV TO Z. OVTtEQ yttQ TQ07COV ETtl Tijg XXl[JiEVr]g

5 dito%ijg T&V 9 A [loiocbv sds^ccîsv TJJV ZM itSQicpSQeiKV

H,OIQG*V ovGav i$ a, IVa, sxsidrjitSQ TOV M [isGov dno-

ysiov K7tei%sv r) ê^vri poiyus thy tj3, rv\v axb TOV

Z axaiflovs ajtoyetov dictGtaGiv avTfis SVQCD^LSV 6vva-

yopwriv [loia&v dyhovoTi, r^s Iy, nobs as ^ ^^ rov

10 &tt#wdov rtQoG&cKpaiQStiis T^g xaTa ^xog ufayg KLVT^-

<5EG)g ocpzCksi, AaiLpdvsG&ai, , ovT&g xal iiti T&V

Tag yivoîevccg

foxoTrjTag dia rCbv KVT&V â^dvovTeg^ LVK{if}

15 sxcctiTov iiaxaokoycbijisv, Jtaas&rjxaiizv oixefag

T&V KOid'^&V V T& TQiTG) GshldtG). T&V d'

GEXidlWV TO [IEV T8TCCQTOV 7tQLE$l, TCCg

ETtl TOV a xcivovCov diatpooag Tijg naoa TOV 7tixvxkov

ccva)[iccMccg cog Tijg ^yL6Trjg 7tQo6&a<paiQ6'EG)g ^%^^20 T&V a poiQcdv yyi,6Tcc cp&ccvovtfrjg XKTK TOV Tcbv f

ytobg TCC Te Adyoz/, TO df

Tag v7tQo%ag T&V yivs-

lLvcov diacpooav x Trjg dfVTaag

1. KQiftpiov D, sed corr. 2. TOV] corr. ex TO C 2. avv-

corr. ex Gvvayco(ivcov D. 4. rowceGZi D, comp. B.

6. 9 I] 9a A, cfr. p. 380, 22. 6. [IOLQCCV C.^1. "rly] -y

corr. ex f C. 8. owccyo^vriv} corr. ex ovvccyofisvcnv D 2. 11.

dqpftAet] corr. ex dyetti] D 2. OVTCOS] -TO? supra scr. D 4

.

13. 7iQOK8i[ivr}$] corr. ex ^yKftfievrje D 2. itQOG&ctcpcuQSGsoos]

-&- ins. D 2, -ECOS in ras. D 2

,deinde eras. cog. 14. lapovtss D,

-t- supra ras. D 2. 15. Ixadroj] mut. in fxacrTov D 2

,00 supra

add. D 2. 16. aetfyt<Bi>] Oft D, renouat. D 2

^.T^tTw] f BD.

17. 7r900fy.Tf-9-7jjti.fVag D, sed corr. 20. a] om. D.' jtemf]-m supra scr. D 2

. 22. didyoQOv B.

MA0HMATIKH2 STNTASESE E'. 385

cog xccl svrccv&cc rrjg {leyfarrjg jtao6d'a(pcciQ6a)g

ri xata rov r&v | xobg rarj

,LVCC rb {iv d' GeMdiov

rj trig xara to

rov xxvroov 7tQi rag 6vwytag ytvo^V^rov 7tMvxkov, rb ds e' r&v evvcfyonEvov v7tQO%G>v tx 5

rrjg Kara rb TtsQfyfiov rov sxxevrQov Ttsgl rccg di%o-

t6[iovg denoteA,ov[i8vr}g avoâîKg.f'vsxsv d rov xccl xara rag [ira%v rcov dvo rov-

rcov &6O)v TtccQodovg rov fjtixvxkov roc Zitifi&Movrcc

rCbv jtaaaxfiiiw&v vitQO%G)v ava^'ycog Aajipcivf- 10'

<5Mdiov itQid%ov ra QyxoGra,KK6rov rijg a7to%ijg doi&iibv rov TCCCQK-

diacpoaov A,K[i($ccv6[iva 7CQo6ti&6&aL rr\

7tQK>rr]v av&piccMccv KXiîvr] xccra rb d'

. xccl rccvrcc d fj[iiv 6vvrtaKrai rbv 15

rooitov rovrov.

6rG) yap itdfav 6 XXvtoog ri^g tiMpi^g xvxkog 6

ABT TtQL KBVtQOV tb Z/ XCii did^tQOV X^V A Z/ F,

&P ^ff vrtoxffad'G) rb %vtoov rov dice [ifacov r&v

t,<pdiG)v rb E, xal aito&rjyid'ffayg rrjg AB 7tQHpOiag 20

yocc(pvrog r 7tol rb B rov ZH&K 7Cixvxl

^ EBZ. dd6<5&a)6ccv df Aoyov VXv ditoxijg

|, cj<jr dia ra ccvra rolg itQOttitoddiyn,tvoi$ tlvai

rr]v vnb AEB y&viav rcbv diTtkatiiovczv rrjg

2. p] Io BC et in ras. A, t(3 D, FB D 2.

^

3. csh'diov ]]

corr. ex aeMdtov D 2,-ov in ras. A. 4. yti/ofif'vrjg] -ij- eras. A.

5. e'] nsiinrov B. 8. jjvswx D. xat] om. CD. 10. &VK-

loyov D, v supra scr. D 2. 11. |rjxo(7ra] |" D. 13. Supra

-ueilLsvov add. ^ rat s' cekiSlq) D 2. âfi^dvofjisv C, corr. C 2

.

14. 7tQmrr]v] om. D. 15. nQOGccyctiQSGsi D, corr. D 2. 20.

7ro/,Tjqp'9'ft<77]g] D, ano\EiyQ'Ei6ir}g ABC. 21. re] supra scr. D.23. TO. amd] corr. ex ravrd D 2

.


xal

BE $ TOV 4 A,

OCTtb TOV

5 E XWTQOV 7il rrjv

sv&sicc fp-

^isvrj rov iiti-

)

r

iva TO

10 TtteldTOv didcpo-

QOV

EMN,TS { BM.

15 ensl TOLVVV vivitb AEB ycovCa ,

oi&v \iiv sltiiv

ai d oQ&al T|, TOIOVT&V vnoxsiTai, ^sc, otov ds ai

dvo OQ&al T, TOLOVTCOV ~6JL, i7i av xccl i] vrtb AEAT&V Aoirt&v is T&g dvo oo&ag ^x. KHST xal rj [lev

Bill TfjS dA V&ia$ 7tOL(pQlCt TOIOVTG)V 6TiV ~QK^

20 Oicov 6 7tQl TO 4EA oQ&o'y&viov xvxAos r|, fide

7tl TYl$ EA TG)V koiTt&V [Elicl. I1I? 31] 1$ TO

nkiQV 5- xal T&V V7t CCVTKS aocc sv&zicbv r} {l

TOIOVTCW 6TKl, J, Ol&VJ]/IE V7tOTlVOV6tt ^3C

z/A T&V avT&v ^y v. KKI otcov aoa i6x\v

EA

1. fioLQ&v] D, ft AC, B. 2. irfljiQ-SLOcx. B. 4A] e

corr. D 2,6 AA B. dt^oo ^ xat rj REKA\ om. BC. 3.

ex HEX^ D 2. 4. ?)] om. BC.

T.^v&sfaom. A, -cpccm- in ras. maiore D 2

. 16. df] d5

D.

17. dvo] B B. Ante ~GJL del. r?D 2

. 18. Svo] ~jlBD. 19.

~

corr. ex ^yt D 2. fcrtV] comp. BC. 20. JEA] corr.

ex yfE^ D 2. 7)] corr. ex st D. d^] d

j

D. 23. fWi]fdTtV D. z/E] seq. ras. 1 litt. D. 24. zM] //- corr. exA D a

.

MAGHMATIKHS STNTAgES E'. 387

sv&sta ~i ift, rjds 4B dpot&s lift jZa, TOLOVTOV

6Tai, xcclf} fttv EA sv&sZa I eyyitira, fj

ds dAo^ioicog rj vg. xal fasl TO anb rijg B4 fatyccv TO

CMO TfjS dA TtOiSt TO CC7CO TJJS BA [Eucl. I, 47], ^KSi

aga sGrau xal okri [isv ^ BEA ev&eiayi/rj vy, koiitii 5

8s fjEB TOiOVTOv ^vy jily,

otcov 6rlvfyMB BK TOV

KSVTQOV TOV 7tt,XVxA,OV i. XCcl OIG)V CCQK Itftlvi\

EB vTtoTetvovGK ^3c, Toiovf&v sGTcci, xccl % {ilv BMid x, f)

d' m KVT^Q TCSQL^SQSLCC TOIOVT&V 1/y

otcov stiTlv 6 TtBQi TO BEM OQ&oytiviov Kvuhog 10

xalr\

vnb BEM agcc ^covta^ r^xig itSQifysi, xv\v

diacpoQccv T^g fawafuxfoisct, of

icov piv sfaiv ecu

T|, TQIOVT&V BGTlv 1/y fl^, OIG)V 6' Cti d OQ&alTOIOVT&V g v8. diijvs'yxEv agcc KKTK TCCVT^V T^V

aito%ils ait60Ta6i,v TO ytccoa tv\v av&paUav did- 15

Tcbv XCCTK TO cutoysiov yivonsv&v HOLQ&V a

oiQa noil ^rjxotiToig vy. <5Tiv $ TO okov TO

TOV TCSQiySlOV dlCC<pOQOV yLQlQ&V ftAt)" KCil O

f

iG)V

CCQCC 6TLV TO [ifylGTOV dlCCtyOQOV |, TOlOVTCdV <5TCCl, TO

Tys pices ILOIQKS xccl T&V vy QrjxoGTcbv ft/3 A^ ?a xal 20

1. z/E] corr. ex AE D 2,AE A. T i&] T T- corr. ex H A,

e corr. D. 4B] corr. ex AE D 2. 2. %ca] v.- in rae. A.

F] seq. ras. 1 litt. D, Is C. 3. jBz/] corr._exBA C 2

. teZil)Kv~]

"k- in ras. 2 litt. D 2, supra -ft- ras. 6. ]Ty (alt.)] infra add. Dr

supra scr. D 2. MB] "BM' B. 9. <T] ds D. V] corr.

ex tin' D 2. ccvtrj?] corr. ex avr^v D 2

. 11. ^'rigj corr. ex

f ris D 2. 13. f] dvo C. IGXIV\ comp. B, -v del. D 2

. d]14. SirivGyv.$vo C. 14. SirivGyv.tv] mut. in dnjvtyxs 8' D 2

. %ara] corr.

ex KUT' D 2. TTJV] supra scr. D 2

. 15. &no%fig] a- et -TJS e

corr. D. &#OfUfi&t* A. 17. pi&i (lOiQca ABD, jtttat ^oiga C._ d _

i-r]H06toi$ ry] -TJ- e corr. in scrib. C, vy D, vy. B,comp. B, -v eras. D. TO (pr.)] om. D. TO (alt.)]

corr. ex TW D 2. 19. SGTIV] comp. B, -v del. D 2

. roiovrcav]corr. ex TOLOVTOV C 2

. 20. f^xocrcov] comp. D, ut saepe.

25*

388 KAATAIOT nXOAEMAIOT

OO TG)V

ooGavrcog df xal 7tl roov koijtcbv rîrjîdroov

itdhv dice roov avroov ra ovroog ha[ifiav6-5 [iva [iQr] trig roov dvo dvooîaîoov vitoo%fig TiaQe&rj-

rotg oixuoig doi&noig ra sxiflciMovTcc exccGTG)

x^S QrjxoGra r&v oh&v \ dr\-

Kt diTtkccGiovi r&v

w, os 6nv Kara rag QX rov

10 ysiov rov exxsvrQOv.xccl

'

ds 7CQO<3&tfxa[iv GfMdiov TIBQIBÔV rag%ara ttkdrog yivo^vccg TtaQodovg rr\g Gfhtjvrjg iyKccrQcc ra pfyrj rov dt,a [ifacov r&v tydiwr cog iitl

rov dia rcbv Ttoh&v avrov xvxhov, rovr6nv rag ayto-

15 A,a{i{lavon,vag rovrov rov xvxhov noi,(pQiag iira,vrov re dia u,6G)v r&v ôodi&v xal rov 7tol rb avrb

%vroov Ao|oi) r^g 6htfvr]g xvxhov xa&' xd6rqv roov

xara [iQog 7tl rov Aojov jtaoodcov. %%otfn&a d

xal Ttabg rovro di'%i, rr\ avrrj, di rjg xal rag [ira%v20 rov r i6rj[iQivov xal rov dia [i6'G)v r&v

7tQi<pQLag rov dia r&v itoAeov rov farjiifoivov

yiGapzfta, Ivftade âdvroL cog ri\g {ira%v rov dia

roov %G)diG)v xal rov POQLOV t)voriov 7toarog rov

Ao|oi) xvxhov 7tQicpQiag rov di a[i(porQcov roov

25 jtohoov avroov yQacpo^vov {nsyiGrov MJKÔV 7tvr ftot-

QOOV vitaQXOvGrjg, 7tidijitQ xal rîiVc, xa&dtto xal roo

'IitTtdoxq)., dia roov 7tol rag /3oQiordrag xal voncordrag

itaoodovg cpaivo{ivoov

1. TW (pr.)] corr. ex TO C 2. aQi&po)] corr. ex CCQL&P&V D.

5. ccvopaHiaiV C. 6. fxaffrcu] -w e corr. D. 8. Q] ins. D 2.

9. api^ju-w] corr. ex KQL&Î&V D. og] corr. ex o D 2. ZGTIV]

comp. B, -v eras. D. 11. '] sfidopov B. 12. ywoutvas] corr.

ex yivoptvovg D. 13. TO] om. D. 14. MKlov] om. C. TOVT-

iati'v] comp. B, -v eras. D. 16. nsgl TO] TCSQL post ras. 2 3

litt. C. 18. ;ioio] loôv KVK).OV D. ds] om. B. 23.?)|

VOTIOV A 4, 5) v\oviov A. 24. Aoôv] inc. fol. 106r B. 25. no-

Acov] corr. ex Ttollcov D. 27. (Sopftorarag] -a.- in ras. D.

VOTIOTKTKS C.

MA0HMATIKHS STNTAEE&2 E'. 389

TOV c)dia%ovr\ ttfafarri ndgodog

xaTaAa[ifldvTai,, xai ndvrcc 6%sdbv ra

rag tygijtieig avrrjg Tag rs JtQog Tovg a6TQagTag did Tcbv ogydvov dscaQovpevag

Talg TrjAtxavTaig xaTa

fag xal dia T&V (pe%ijg

Tai. KCLI iGriv TO Ti^g xa&oAovxavoviov TOLOVTOV

1. fqp'] i] sop' D. 17] om. D. TtctQodos] corr. ex TVKQ-080) D 2

. 2. KccTahccfificivETai] mut. in xatfAajLtâvfTO D2

. 7.

taxi D, comp. B. TO] in ras. D. 8. roiovrov] des. fol. 136rA,

fol. 136 V uacat. Post VOLOVTOV add. fol. 106r B:TO rfjs v-aftfaov G&Jiviwfis tivapcdias V.O.VQVIQV n^dî Iv

\L\V TOtff 71QWTOIS $VO GSildlOlS tOVg KOLVOVS KQL&ÎOVS T?Jg Tf TOV

anb TOV ccTtoyslov TOV y.y,vrqov V.LV^G(OS KKI KVTTJS

Gf^vrjs &rtb TOV axptjSovg dtnoytiov TOV nmvy.l,ov nol txi

sni TOV Koôv uvxris ngbg xbv 810, (IGCQV xa>v ^codiatv :r^>

V 8 TO) y GSfodlCp XK<S 8lCCGpOQCtg XOV [18GOV KTCOySLOV XOV

TtQog xb axQtfisg anoysiov : Iv 8s xoj 8 xag SiacpoQag

xfjg nciQa xbv 7tinwx.lov avooiiaMag xov 7tiKVKl.ov nuxct xb ano-

ysioxctxov xov iv,y.vxQQv xvy%dvovxog, xijg 8s G^VT]g inl xov

slg xa. nQoriyov^svci (pfQO^vrig :

iv 8s xoi f" vnsQOiag (comp.) x&v yivofitvav avwâZiagiv. xfjg V.UXCL xb itSQiyEiov xov SKKSVXQOV fttGscog ngbg

xbv KCLXO, xb anoytiov ctvxov &SGLV xov snwuv.l.ov xfjg Gehrjvrig

xag Kvxug sv SY.CCXSQK &Gi anb xov KKQifiovg anoysiov ini-

Y.V-AÔV ft ccfpiGxap* : iv 8s TW s xag v7tQO%ag x&v naxa xag

[Ltxu^v xov anoysLOv %ai nsQiyefov xov SKKS'VXQOV nagoSovg xovimy.vY.lov yivo[ivcov {isyiGxav nccga XTJV inl xov iniv.vY.ôv

luscrjv xrjg Gs^vrig ft^Giv SiacpOQav nQog xr\v inl xov anoytlovxov SKKSVXQOV &ZGLV xov iniY.vY.lov yivo^svr\v (iyiGxrtv avcoâ-

Mav <ng tf]g iiyLGxrt g vnEQO%i]g xrjg nctga. xi]v B avcoâ2.iav nQogxr

tv a ijxoi xi]g naqa xr\v inl xov negiysiov xov iv,Y,vxQOv ftscecog

xov inwvy.'kov vnSQO xfjg yivo^vr]s ^yiGxr\g av(0[iahLag ngbg xr\v

inl xov anoysiov xov SKKSVTQOV &GIV xov iniY,vy,1ov

avcoiLaMav x&v B A<9 ft (isxa^cp&tiGi^g ttg s^rôoxd.

iv 8s xoj xag anolaîâvo^svag negicpSQslag Itp'

xov <xt8iaY,ov (jisxa^v xov 8ia ^GOJV x&v aj8i(ov Y.VY.IOV v,al xov

koôv xfjg 6lr\vr]g Y,vv,lov xa-91'

Y.a6xr]v x&v Y.axa ^Qog inl xov

l.o,ov Y.VY.IOV xfjg GBlrjvr^g nagodaiv xov SLU x&v nohcov xov 8ia

piGiov x&v o3Sicov Y.VY.IOV :


'Y]'.Kccvoviov rfjg xad'ohov

'

IT

MA0HMATIKHS STNTASE&S E'. 391

QY.&

<wgle

QP*

QV&

Q&P

QOK

ffxrj

GV.B

6*$Gift

tfiy

Gi

G8

GCt

Q7t

IK

ICC

v8

o

rf

LCC

io

xy

XT]

ty

X

&V?

He

IT]

LCC

P

~v'p

(17}

V

vcc

^Lv8

v8

vs

vr\

vy

ir\

[IS

v&

Ifis

vs

IE

8

xg

35

vy

y 40

IK

X

18

V

v8

V?

45

vrj 50

O votiov

1.7]'] mg. B, om. ACD.

fol. 113 VD, totam tabulam fol. 106V B, coll. d om. C.

coll. cc 8 fol. 113r, reliquas

4.

t; corr. ex aTroyft'ov D 2. nlccTovs ncci (iôvs] corr. ex

v D 2. 5. itQOG&acpKiQEGELS (pr.)] TtQOG&aycuQilGsojg B C,

D, -âqp- in ras.; TtQOG&ctcpcciQeG^? D 2.

(alt.)] TTô^'d'aqDa^sfffcos B, 7tQOG&cc<paLQGg D. 6.

add. D 2. dbroyft'ov] om. D. fjnxvjtôt;] om. D. 8. (36-

A, om. BCD. 9. i>#] vrj B. 10.ITJ] trjt D. x]

11. v?] v D. 12. %<?] xa D. 13. a] corr. ex J int^, A.scrib. D. y] et reliqua pars columnae ad lin. 43 in ras. D.

rfiS D, et similiter deinceps in hac co*l. (w=

c). 20.

18.

31. ^f] ^D. 32.

^xs] ?tg D. 35. pxtf] ^t-9- D.

43. Zij] corr. ex te in scrib. C.

45. vg] corr. ex (^g in scrib. C.

50. l\l seq. ras. 1 litt. D. 51.

in ras. D. voxiov TIEQCCS] A,TO.

la. D. 33. xe] v.8 D. 34.

tf ] y D. 36. t? (pr.)] g D.

^; (alt.)] t D. 44. ttf] tf B.

tg D. 48. 8 (sec.)] t<? D.52. o (sept.)]

Infra add. A:

slclv ovta)$

]

pfr\ in ras. Dom. BCD

tf.

Gvvta&i8V TW F

A /I /I Xl

J Z i;

f

O6axis ovv eav jtQOcuQcbiis&K T^V did

TOV xavoviov iprjcpoyoQiav Trig G

7tonq6a6&ai , ka(l6vTs ra XKTK TOV vnoxijLvov v

5 'AksâvSQsCa IQQVOV [isGcc M,vij[iccTa xi\<s

xovs rs xal aito%fis xal avoîccîas xccl

xbv vitodedsiynevov rgonov rbv 6vva%ftvra

xilS dito%iis aQi&iibv SntKuGiaGuwtts itdvxoTS xccl dcps-

k6vT, lav %K>yiV, KVKkoV ffawsyXOVTSS T tg TO T^g

10 civcopaMccs XKVOVLOV Tag yfaQccKiîvas CCVTG) [loiQccg V

X& y' 6kldiG) TOV {liV CCQi&lLOV TOV

COg ^t ILOLQ&V OVTOg

an avT&v, nal TOV yv6^vov15 aQi&yibv i00L6oîv lg TO ai)TO xccvoviov xal xr\v

vr]v CCVTG) 3iQo6&acpcciQ6iv v

Xttl Ti TO 7taQaKlllVOV V TG) 7t{JL7CTG)

o^^cc %&$. [iTK df TCCVTCC xccl

TOV ddi3tha6i,a6tivov T^S u>

20 Vyx6vT$ ig TO, avTa ^fAtdt9

otia av

Ct VT(JJ

XTG) ^fAtdtOJ, TO, TOGKVTCC

ov

1. -91

'

i/>rjqpog?o()tae] om. D. 2. ECCV] s- in ras. D 2.

om. C. 3. ffffojvtajtTfc] -t- in ras. 2 litt. D. 4. TO] om. D.

8. Supra aq>l.6vTt$ add. avfô^t D 2. 9. xvxAov iccv f'^co-

ptv D. Tf] supra scr. D 2. 10. {LOLQCCS iv] corr. ex ph D 2

.

11. ajH-ttyiotJ] -<&- in ras. D 2. 14. ywoptvov D. 16. rs-

taQTO)] 4 BC. 17. jrf'fiTTTw] f^BCD. 18. ctTtoyQaitxaufd'a D,sed corr. 20. a.v\ tdv D. na^d-Ativxcn D. 21. 'HTCO] zBD. TO] corr. ex TO C 2

,om. D. 22. anfyQai^d^.ed'd] a-

niut. in I- B 8. 7tQoc&rjCo^tv\ A 4

, Ttôc^r'jOo^lv A.

MA0HMATIKH2 2TNTASE&S E'. 393

Gopsv ccisl ry xr$&6ipfrfl rov d' Gskidiov JtQ00&a(p-

aiQG(, xai rag 6vva%&i0Kg ^LOLQCCQ^ lav [iV 6 rfjg

dnb rObv rov ntfxovg xal r&v rov

OIQ&V, sav d5

VJISQ rag oft, 7too6d'^&o^,V ccv- 5

rats. x<*l rGbv ysvoîevcov CCOI&[IGJV rov jilv rov [itj-

xovs Ixfiahovrss ano rijg xara rr\v jto%rjv

oitov av Karakrferi, Xt rqv 6Atjvr]

s, rov $ rov ithdrovs rov Kitb rov fiogziov

L6oi60[iv LQ rb avrb xavoviov, xai, otiai 10

av <b6iv a 7iaoaxi[jivai avrco iiotoai, v rd5' 6-

Atdto) rov jthdrovs-) rodavrag ay^su rov did ii6ovr&v ^(pdi&v rb Kevrgov ri\g 6eA.ijvr]$ 7tl rov did r&v

xoAcov avrov yoacpo^vov iisyitirov Kvxkov^ xal fdv

[ilv 6 d6tvrp>y\LivQ dQt,&[ibg v rolg ng&roLs f T 15

(m'%ot, &g nobs rag aoxrovg, av d' v rotg V7t

avrovg, cog Jtobg ô'rjôiav^ rov plv itgarov r&v

idiov 7iQi%ovrog rr\v dit aoxr&v 7tgbg

iav avrijg itdoodov, rov dl dvroov rr\v ccnb

iag Ttobg rag ccoxrovg. 20

1. &tt D. d'] TtraQTov C. 2. 6] r\v 6 D. 3. [ioi-

(corr. ex 9v D 2) D.

rf\om. D. 5. Q7t\ -n e corr. D 2

.

r. D 2.BC. 7. ly.dM.ovT$ D, corr. D 2. Post

del. TO D 2. 11. ^'] corr. ex D 2

. 14. %ca] comp. ins. D 2.

15. ^] j] AC, om. B. Is] in ras. D. 16. Post Gfi%oigadd. OTL pr]dv aîokoyov if

1

Iv xcci$ Gvvyiaig tbv tv.%- xf]g 6t-

l-r}vr\s v.vD, del. D 2

. 17. KVTOVS] corr. ex aviots D 2. 19.

tr\v] om. D.

394 KAATAIOT IJTOAEMAIOT

i. "On, ntjdlv dîohoyov yivsrui diayogov sv

ralg 6vwyiai,g itaga rov exxevrgov rijg

xvxkov.

dxoA.ovd'ov i6uv ditiTaGai Tivdg,

5 xal Ttsgl rag Gvvodovg xal rag jtavGehrjvovg xal Tag

v ravraig fafotyetg a%Moy6$ XL$ diayoQK TtccQaxo-

xal dia rbv SKXSVTQOV rijs GsAtjvrjs nvxkov

TtavTore xal xdvros &v avratg lit avrov rov

TO xwrgov rov STtMvxAov rvy%aviv,10 AAa xal acpsGxavai, avrov 7teQi<pBQeiav Cxavrjv dvva-

tiftai dice rb rag [isv xar' avrb rb dndysiov &6is sv

rats [i6G)$ &a)QOviLvais 6vvytai,s aitorzhBiG&ai, tag

<f axQifais Gvvodovg xal 7tav6htfvov$ psta rijs xar-

QOV rcbv qxhtcw dv&iiaMas â^dv^âi15 7taga6Tij6at, rr^v roiavrriv diacpogav [ir]d[iiav

auaQtiav itZQl ra yaivopEva xara rag 6vvyiag dvva-

\nivr\v a7tQ'yd6a6d'ai, xav py 6vv7ti2.o'y%r]Tai, rb Ttaga

rr\v xxvrQorrira rov xvxhov diacpoQOv.

6rc3 yap 6 XXVTQog T^g 6&nvn$ xvxhog b ABT20 7CQl X8VTQOV TO Z/ Xal did^lTQOV TJJV A AT, (p ^g

i

C3 TO {lev rov dia indtiwv r&v tydicov XSVTQOV

1. t'] BC, mg. A 4, rj mg. D. on 3. XVKÔV] mg.

superiore et mg. exteriore D 2. 4. 7m'] corr. ex inl C 2

.

SGTIV~] comp. B, -v del. D 2. 5. tag (sec.)] om. CD. nav-

nccv(['

D, ut saepius. 6. cc^Loloyos] corr. ex &io-C 2

. nccQd'nolovd'iJGei C. 7. Supra did scr. TT" D 2.

8. sv\ A 1

, f|v A. 9. ccTcoysiovraTov D, sed corr. 10.

8i8oG&ai C,radd. D 2 et mg.

v^'dodât. 16. v-

s

D. 20. y.tvrQoiv D, corr. D 2. dtafUTôv] dta D, *Q

add. D 2. Jz/FJ mut. in AEP D 2

. 21. stlriiiy&co D,corr. D 2

.

MA0HMATIKHS STNTASESiH E'. 395

TO E 0r)lltOV, TO <f (XVTlXl'lLVOV T& Z/ Tijg

xoo<5vv0G)g 6r]ptov xaTa TO Z, xal en

^ CCTtO TOV A K1tOyLOV

AB 1tQKpQLCt

[iw 7tgl TO B o H0KA 5

ds ^ T B4 xul1}HBKE

Kdl tinrjBAZ.

itd rouvvv Kara dvo

rQOTtovg dvvarcct, diacpQi,v 10

TO TtCCQK TfjV KVG)ILCtMaV

KKTCC TO ATOV 1tlXVXOV i T TO

CCVTOV yivopsvov ps^ova. Ttgbg rc5 E ywvCav a

ncci dia TO tv\v itQ6<5vv<5i,v Tijg XCCTK TO {i6ov 15

Kttl TtBQiyeiOV dlCC[lTQO

XSVTQOV, odha Ttgbg TO Z 6rj[itov yi

$ 6VVl6TaTCU TO [lV TtCCQCi TYJV 7CQG)Tr]V CCiTLKV SlK-

,OTCCV Kcd TO TtccQcc T^V civo^a^Cav T^g 6Avjvr}g

TO d XCCTa Ti]V dVTQKV) OTCCV 7tQl TO 20

aitoyuov i) TO TtegCyMOv rj ffs^vrj $ TOV STtMvxkov,

drjAov, OTL, OTav plv TO naga xty it^x^v afaiav did-

(pogov nfalGTOv GvyLfiaivri, TOTS TO ply nccQa TYJV

dVTQccv avfitaiG&rjTov b'GTai itavTfh&g dice TO Tyv61tl T&V (CCltTOlVG)V Vd"L(X)V OVGCtV TOV 25

1. atyittfav] c D, ut saepius. rc5 //] root Cj D. 2. ccno-

,-tC- e corr., D; ft del. D 2

. 3. A] supra scr. D 2.

5. H&KA} H&KA D, ut uidetur. 6. la&tncW] om. C.

8. ^rt] -i postea ins. A, corr. ex ianv D. 14. TW] TO D.

16. itQCysiov\ -v e corr. D. E] corr. ex IH D. 20. 77]

corr. ex r\v D 2. 21. TO] om. D. rj] T\V TJ D, j TJ

D 2.

om. D. 22. Supra alriccv add. ccvcapKMccv D 2. 23.

D, corr. D 2. 25. OVGCCV] corr. ex OVGK C a

.


ddidtpooov

dvvarbv d'

isvsyxetv 6vvcc[iq)OTQoi,s rots ftccoa rr\v uvw-

dicccpooois excctsQov r&v tpcorov rov (ikv nark

5 TCQOti&SGLV OVTQg) TOV df KO.X CCCpKiQEGlV, OTKV ds rb

xccza rr\v dsvTQccv rb

TtteiGTov (Svâivri^ tore TO plv naga xi]v

ndhiv dveTtafad'rjTOv ittiv dia rb xal o'Aov rb

rr\v dvoâh'ccv ^ ^dfv 7} ^K%V TtavrdxaGt,

10 rr\g 6ehtjvr]$ Ttegi rb anoyeiov T)rb Ttsyfysiov rov

xvxhov rvy%avov6r] ,diofasi d'

r\

rfjs [isG&s &G)aov[ivr]g {IOVGJ TK> itaoa rqv

drj 6 yikv ijAiog TTJV

15 7tot,oviivos T&V ^ wy yioiQ&v, f)ds 0^tjvrj na&rov

xal avrri rrjv ntefarrjv dcpaiQtfw itoiov[ivr] r&v cc

v, Iva xalYJvnb AEB y&vi'a rag 6vva[i(porQK>v

d IIOLQ&V dinka.6iova$ itai%r] idjiZ??,

xccl u.%-

ditb rov E g)K7Cro^vrjs rov rtixvxkov rijg

20 E 7t&v%&G) riB0 xdfaros [Eucl. III

7 18], xal hi

dxb rov d 7il rr^v BE xd&rog %%&(*) v\4M.

iti ovv r\VTtb AEB ycovi'cc, OLWV psv zltiiv ai

d oa&al r^ rowvr&v 6rlv id ft^, otcov $' ai /3

roiovr&v x-91 Ag civ xal i

1. adidcpoQov] supra scr. D, corr. ex SidrpoQov C 2. 5. XT']

mut. in y.ctxa D 2. 6. TO] om. D. 7. av/ji^ccLVfL D, corr. D 2

.

TO] supra scr. D 2. 8. Ttdliv] -iv in ras. D. IGXIV\ comp. B,

i'cTKi D, ~ supra scr. D 2. 9. nuvrdnaaiv BC. 10. ccnoytwv] -e-

e corr. in scrib. A. nsQiysiov] -I- postea ins. A. 11. d']ds D. 12. T&5] TO C. 18. TtfQiî C. 21. JM] post ^ras1 l litt. D. 23. amV] comp. B, -v del. D 2

._ttd] D 2

,

T| 8 D. d'] tf D, ^g D 2. p] 8vo C, corr. ex Zp' D. 24.

itrj p. 397, 1. icxiv] supra scr. D 2. 24. i/Jg]

?supra scr. D.

MA0HMATIKH2 STNTASE&S E'. 397

AM itSQiysQSLK roiovr&v x& Ag, o"ic3v stirlv 6

rb A'EM oQ&oy&viov xvxhog r, 17d* art r?\

TWV Aowr&v [Eucl. Ill, 31] sis rb f)(it>xvxfaov ~QV nd'

xal rbv vx avrag agcc sv&ei&vi\ psv AM roiovrwv

ftircti A Ad, oicov ztirlvfj4E vttorstvovGa ^%, ^ ds 5

EM robv avrobv (>tg a. w^rf xat, ot'ov l<5rlvi\ per 4E

pera^v tcbv XSVVQ&V I 1%-, i\ds B/l sx rov xevrgov

rov sxxevrQov fid1

jiia,roiovrcov xal

17 pav AM Utitai

ft A??, r\ds EM &(iota)g & v&. xal iicel rb aitb rijg

jBz/ ksfyccv rb cbro rijs AM jtoiei rb aitb rrjs BM 10

[Eucl. 1,47], yivsrai, xalr\ plv EM sv&sicc p& A?, fj

3s BME oA^ roiovrcov v& Ag, oi&v 0rlv xal y B@IK rov xs'vrQov rov STtixvxkov i Te. nol OICQV stirlv

CCQK ^ EB VTtoretvovGtt QX, roiovrcov xcclrj psv B@

sGrcci I A(J, 17d' at' avrij? XSQUpfysut roiov- 15

xt |^XO<?TWV g, otcov ^tfrlv 6 jrfpl rb BExvxhog r%. xal

f]vnb BE CCOK ycovia

rov ttfaitirov diatpogov rrjs avcoiiaMas, oiov [LBV sltiiv

CCL drfo oQ&al r, roiovrczv 6rai I xcd sfyxoGrcov g,

OLCQV (f ai d OQ&ccl r|, rowvrcw f y avrl f a rcbv 20

1. 6 2. T] supra scr. in ras. D 2. 2. z^EM] ^M D.

ot'oov fffrlv KQK onfQ (coir, in 6 nsQL D 2) TO z/EM dpO'o-

ycovtov xvxZog T| TOIOVTCOV Grlv rj snl tfjs dM v.& kz r] D.3. koinwv] civraiv B. ^fUKViAtov] r\- corr. ex JV in scrib. A.

QV V. 5. I] e corr. D 2. 6. EM] ME B. 7.

i|

A 1, > A. 8. W>r0ov] - in ras. 2

litt.^D. z/M] e

corr. D 2. 9. inti to] supra scr. D 2

. 11. per BM EV&SIO]in ras. D. 12. BME] -M- corr. ex E in scrib. D. <mV]comp. B. V.KL] om. D. 14. B0] corr. ex X@ A 4

. 16.

neu] comp. supra scr. in ras. D 2. s^v.oGrmv'] comp. e corr. D.

?] corr. ex xat D 2. 19. dvo] BD. T] 5e>ta corr. ex

%at D 2,T supra scr. ncti s^-noar&v] e corr. D 2

. 5] corr.

ex y.cti D 2.

Kara rb A aitoysiov fivrog rov

dir)V'yKv aoa naoa ravryv rv\v alriav rb icaoa rfjv

didcpogov %r]Ko6rots dvtilv

$ dvvarai [nag cooa

5 Ttdfav vTtoxefa&G) xara rb A psdov 7tQi /

yt,ovf

iva drikovon ^ vno AEB yovia rag

d w,10 Kal fai&vx&eforjs nl

rfjs biotas Karayga-

(pi]<S rfjs EA v&iasKd&roi, rjx&coGav ITCI

rrjv BE ano [iv rov A15 ^ AN, aifb d% rov z/

^ z/M, JTO $ rov Z7il rqv BE K^^d-l-

<5av f)Z &. Kara ravra

dJJ rOLS H>7tQ06&V , 7tldlJ7tQ fj 7COOS t& E20 oiav [iv ffaiv ai d oo&al T|, roiovr&v 6rlv d jig,

oiwv d' at dvo uQ&al r$, roiovrcov & A/3, iv av

Kal ai [iv (p' xaroas [Eucl. I, 15] rcbv 4M Kal

Z& 7tQi,(pQi,ai, roiovr&v -O1

A/3, OLOJV sfalv OL 7tol

ra E4M KOI EZS oa&ovavLa KVK^OL r- ai d' la?

1. A] supra scr. D 2. 3.. Svci B, (3

D. 4. tg'] TABC. 5. A\ supra scr. D 2

. 7. nsQis^si D. 11.

seq. ras. C, -x- corr. ex i D 2. 13. Inl rijv BE

D. 14. BE] B BC, corr. C 2. 15. anb ds rov 4

z/M] A, om. BCD. 17. sni rrtv BE] A, om. BCD. Ix-

ri&ttou. B. 18. ra CCVTK D. 20. iorlv\ comp. B, om. D.22. MCCTCCTSQUS C. xt (alt.)] om. D. 24_>tat

/

]om. D.

xvxioi] *v D. ^|] ^" AIA TO ICHN 6INAI THN A TH Z D,corr. D 2

.

MA0HMATIKHS ZTNTASE&S E'. 399

xarQccg r&v EM xal E& r&v hoLit&v [Eucl. Ill, 31]

SIS ttt yilMVXA.LCC O MJ. XCCL T&V V7t aVTCCQ CCOCC

v&i,G)V xaroa [iv r&v AM. xal Z& roiovrcov

& vrj, oi&v 0rlv xarQcc r&v AE xal EZvovti&v QX, xccrQa de r&v ME xal EH v&i&v r&v 5

avt&v QI& Af tiers xai, oi&v <5rlv XCCTQCC [ilv

xal EZ v&iG)v I i&, 17db dR x rov

JLt^, 0TCCL Xttl XarQtt [lV TG)V

O va, XKTQCC ^ TGJV ME XCil

T&V avrcbv I t. xal 7td rb aito rifc BJ tetyav rb 10

onto rijs AM 7toil rb dnb rij? BM [Eucl. I, 47], 0rca

xcclrjBM ^YIKBL rcbv ccvr&v fyyiGtcc ft-9

1

f

xalfj iilv BE V&IK forai v& vrj, r\ de B&

roiovrov o tf, otov ncclrj Z3 f)v o we. dt,a ta avrcc

$ xcclfjBZ v7tOTivov6cc t&v facw fyyitircc ztirai, o 15

l. XCCi 6tl,V, fog fjBZ 7CQOS XCtTQKV tG)V Z& Xttl

jB^, ovt&s f)BA agog xccrQccv rcov AN xal BN

[Eucl. VI, 4]* &Gre xcci, OL&V 6rlv r\ (ilv BA X rov

XWTQOV rov 7tixvxA,ov ^ If, fjd% BE Idffy&vj v& vri,

roiovrov xccl ^ [isv AN h'Grai o d, ^ d BN r&v 20

syyutira tf, Aot^T) dfjNE roiovrcov vd jZj>?

1. >tat] om. D. 3. %ai Z&~] coir, ex xca S'Z C, corr.

ex Z D 2. 4. z/E xat'] Ez/ D. 5. ^] seq. ras. 1 litt. D.

ME %ai\ EM D. E#] -S e corr. A. vv&si&v 7. ev-

&EiG)v] mg. D 2,

in textu TOLOVTCOV QL& P. v,ai ol'cov KQCC SGTLV

SKKTSQCC r&v 4E, EZ sv&sicav D. 7. T t-91

]in ras. D, i i& C.

~

corr. ex JA D. 8. I'ffrai] seq. ras. 1 litt. D. 9. xat (pr.)]

comp. supra scr. D 2. o] o D, o D 2

. 13. tv&sictG C, corr. C 2.

14. o] o AC. Z3] SZ D, 3- renouat. D 2. j\v\ corr.

ex T\D. 15. o] o A, 6 C. 16. rcbv 17. BN] mg. D 2

,

in textu r&v AM, END. 17. ?] -S in ras. A 1. ovrat

CD. AN] post ras. 2 litt. D. 18. BA] corr. ex BJ D\20. r] (alt.)] in ras. D. Hyyicra r&v avr&v D. 21. NE]EN B.

olcw y AN i]v o d. eitsl df dice ra TCQOXSL^SVK xccl

y] EA VTtOTivov6a ccdicccpogsl T&V KVTOJV vd\t,y,

<5vvKyTa.i, on xa^ oi&v sGrlvf\EA vTtorsi'vovGK QX,

TOIOVTOV xali] [lev AN ev&etct <STCU o

77 lyyiGru, i\

5 ^' iit avrijg 2teQiq)Qia TOIOVT&V oTJ TCCC^LV^ di&v

6rlv 6 Jtspl TO EAN oo&o'ycbviov XVKÔS r%. xali\

vitb BEA &QK y&vici, ^v dnqvyKv ^ Gs^vri naga

rrjv 7il ro Z TtQo6vv<5iv, o'icnv [iv zlo'iv ai dvo

ooftal r|, roiovrcov o ^, ol&v d' ai d oofral r|, TOIOV-

10 TCDV o d. S)0r xal v&dd TO TCCCQK rrjv avcoiiaMav

trig 6&rivr]s ditjvf'yxw %r]xo6tois d, artQ ovd' avra

7tOl,L TIVK CCîOÔyOV K^KQTiCCV 7lQl TO, KKTK Tag 0V-

vyias (pcuvopfva [iqd' oydoov fyyitira dvvct[iV(x, i

COQKS, o6ov xal 7tK() ccvtas rag rrjQr}(3is ov

15 6ta,i, itfaovccxis dia7t<5iv.

TCCVTCC [IWTOi 7CKQ^^^CC OV% G)$ [IT} OVTOg

rov xal xgbg rag r&v Gv^wyi&v m6xilji,

xal ctvTas ravras rag dicccpOQas, xav

20 dirjiiagrrjiiwov xara rag dice r&v &utG&Si\rfvayv

VLKX&V X&fy(DV aTtodfi&ig TtttQa TO p

Tri SIK rijg xxVTQ6rr]Tog avanii^riQG)^vri dice T&V

1. AN~\ corr. ex AN D 2. xat] comp. supra scr. D 2

. 2.

tLvovGcc] -a supra scr. D 2. adicccp^QSi D, corr. D 2

. 3. 9%4. lyytara] mg. D 2

,in textu diccysQfi r&v avrwv seq. spatio

14 litt. (del. D 2) et deinde ei>9sfa %6rcci o

T\ fyyutra D. 5.

TttQupsQfia] comp. ins. D 2. n&kiv] om. D. 9. o] icrlv o D.

d'~\ Ss D. J] dvo C. TOLOVTCOV] -v ins. D 2. 10. ^]

oj A; o d D, ut saepe. 11. d] corr. ex A D 2. 14. OGOV]

D, OGOV mg. D 2. 22. avaTtsn^Qcofisv^g D, corr. D 2

.

MA0HMATIKH2 STNTAEE&S E'. 401

IK'. IIsQl r&v rr\g Gshrfvyg jt

Ta plv ovv agog rag xarahtjfaig r&v axQifl&v rrjg

tfelyvris nagodcov 7taQaha[i(lav6iiva 6%sdov ravra av

l'rj. Gvpfiaivovrog d' rti r^g Gshrfvyg xal rov ^defa&rjGiv rr\v avrr^v yivsGftui r^v (pcuvoiievyv 5

TtccQodov rr} KXQL^SL dua TO ^ 6r)[iiov Adyov

G)g (pa(isv, trpj yrp> JtQog rb KJto6rrjîK xr\g

avrqg uvayKctiov av sty xccl axohovdov rcbv

rS aM.G)V (pKLVOHSVCOV SVSXSV KCCl llttfaGTtt t&V TtSQi

rag rov r\Mov txtefyfig ftscogoviisvcov rbv jtsgl rcbv 10

av avrilg 7toit]6a6âc hoyov, f| cov dvvarbv

dice t&v agog rb XBVTQOV ri]g yv\ nai rov dia

r&V ^G)dlG)V KVX&OV VOOV[lVG)V CMQlfi&V TCaQO-

dov ncd rag aitb rr^g ofa&g r&v 6ôavrcov 9rovrstinv

an6 rivog smyavsiag ri\g y^g, &G)QOV[ivag diaxgivfiv 15

xal itakiv rb wavriov ajtb r&v cpaivo[iva)v rag axgi,-

felg, TtaQaxokovftovvrog d rft rouavrri 7tt,0xî rov

Wrs rag xara ftfôg 7tr}fax6rr]Tag r&v TtaQaMd&ovavv rov do^vai rbv rov aito^rrnnarog koyov dvva-

6&ai iiQtt'yiiarsv&rivtti, ^r avrbv rbv rov aytoGrrj- 20

parog koyov avv rov So&i]vai nva

LIV r&v

1. m'] C, oi B, om. AD, # mg. D 2. TISQL

Ifojv] mg. superiors D 2,in textu

(j) OCQ supra scr. D 2. 4.

gt'rj]

supra scr. D 2. sTtt-Gvûivovrog D. 6. T^] corr. ex xv\v D.

Aoyoi/] I- corr. ex z/ A. 10. TOV] corr. ex t&v D 2. 16.

ax(H|3erg] KKQifisig rtKQo8ov$ D. 18. TraâHaleoc^] -a|f- in

ras. C. 20. Ante prize add. rets t&v TtctQcdld&GJv StdoG&cuKVSV TOV &fivai rbv rov ccnoGrrJiiccros Myov D, del. D 2

. ccvrov]

supra scr. D 2. 21. rivet] rrfv D. 22. nccQcdacGovrcov C.

rovricriv} comp. B, -v del. D 2.


afj yfj 6yiLiov Aoyov %i) ovds TOV TOV

koyov drjkovori, dvvaTOv av ydvoiTO

T&V 7ictQcckktt6<56vT(av , CQGXEQ

av [lov&g TO did TWOS

BGyg TOV rov ajto6Trj[iaTog Aoyov SVQELV dia

TO TOiavTrjv \LV TLVK TtaoaMaxTMrjv fYigrfiiv xal xatf

dvvaGdau âtal^^vai^ Tqv ds TOV

TtrikiKorrita iiydapcbs. 6 [isv

CCTtO TOV fjkiOV lldkilSTCC TTJV TOICCVTYJV S^TttGlV

10 rpai' itidri yap 0,716 TIVCOV akk&v 7tgl TOV ijhiov

v[i{3Epr]x6Ta)V) VJIEQ (bv v Toig %ijs

TOV Adyoi/, aKokov&si TO TOV KKTO, TO

ZTEQOV T&V (p&T&v K7to6Tâ.TO<s SO&EVTOS Ktti TO xctTa

TO ETEQOV dtdotf'lhu, TteiQaTCU TO TOV Y}MOV XClTCl6TO%a-

15 6[lVOS OVTC3 XCCl TO Tijg 0^tjVl^S CCTtodEMVVElV TO [lev

ttQ&TOV VJtOTl&EHSVOS TOV ijklOV TO EA(JC%l,6TOV Ccl<5d"1]TQV

liovov itctQttkkaGGEiv, Iva xal TO ajt6c>Tr][ia avTOv

[lTtt d TCCVTCC Xttl filtt T^g VlC* OVTOV

fjfattXilS K^L1^C3g^ TtOTS [lV G)S [lYjdfV ai6&r)TOV, 7tOT

20 ds xul &g ixuvbv TOV r\kiov 7taQcchkcc66ovTOs ,E'V&EV

&VTG) XKI OL koyoi TOV Tr\g 6^vrjg ccrtoGTruiaTog did-

(fOQOl, XK&' Xtt6Tr)V T&V XT^L^VCOV VnO&6K)V XCCTE-

fpCHLVOVTO di^TCCÔ^VOV ItCCVTCCItClGlV TOV XCCTCC TOV ijhlOV

ov povov v TW TtoGov, aM.cc Hal si oAeog Ti

1. a] av C, S av C 2. 2. Post ttyov del. a D 2

. 8f]lov-

OTL] -j]- e corr. D. 3. TtKQakccGcovrcov A et -QK- supra scr. D.7. ncctcdriiicpd'iivai D, corr. D 2

. 10. nvcav] -i- corr. ex ft D 2.

rbv ijkiov] xr\v aelipnp D. 11. ri]v Gel.ijvr]v] xbv ijhov D.15. OVTO> D. 16. TO] supra scr. C. 17. na^ccl \

GSLV A,a.66tw D. ccvrov~\ corr. ex uvrri D. 18. itccQated'si-

D. 20. ttca] om. D. naQccid66ovTO$ D. 22. MCC-

C. 23. itu.vta.itciGiv\ -v del. D 2, comp. B. 24. 6'Acog]

ins. in lac. 3 litt. D 2. ri\ supra scr. D. TtaQcciccGGai D.

MA0HMATIKH2 STNTAEE&S E'. 403

f',ivcc [irjdsv T&V ddrjAwv slg TYJV

i ov dvvrj&ir]Hv av <bs svi [idfoGra dxoL^&g Trjorr

ai, itoGov xal KTCO 7Cr}Mxv]s rov Kara xoQvyfjv &TIO- 5

7tl Tov dia rCbv

TOV oQi&vTog xccl wvx^ *yQcc(po[ivov usyfarov

xvxkov.

7fOi^cc^v yaQ xavovag dvo TfrQccTttevgovs TO plyovx J.dG6ovas T66aQG)v 7tt]X G}V XQ<>S ^6 TKS 10

xv\v de

dia TO

K7COTTd(yd'cci Gcpodaa dxQifi&s xccl lit

xd0Tr]V T&V JCAfV()WV, JtlTa TCCCQd'yod-

zv&siug yQamias ftp' BXCCTBQOV xccTa ^0r^g Tys 15

TG) TQC3 TKtV XCC-

VOVCOV 7tl TG)V CCXQCOV d[KpOTQG)V OO&

TTQdya)vtt. 7Col [i6r]v xv\v yQK^riv i'6a T xal

kriktt OTtYjV %OV XaTQOV XttTtt TO [1<30V YIXQl,($(D[lV'Y]V

TO [lV TfQOg TTl OfySl 60[lVOV ^7CTtjVyTO $ JtQOS Tfj 20

6^VT] ll%OVCC, OVT&S &6T "JtKQKTL^S^BVOV TOV

TG)V OCpd'CC^flCOV T& TrjV ttaTTOVCC OTtfjV %O

TLG) did TYjS TOV T$OV XCil Sit* V&iaS Oltfjs Tr\V 6-

1. t/S'] mg. AC, Bt B, om. D, i ing. D 2. 7iuQal.ciy.riY.ov D.

4. ax^tpcog] -co? euan. C. 5. trotf] corr. ex Tjjg D 2. 6.

6t D. 7. TroAcov] corr. ex noMcov D, "wdicov C.

10. nri%(Qv D. 11. ftg] ins. D 2. ylvscftui D, corr. D 2

.

13. aW D. ccKQifi&s] supra scr. D 2. sit' v&si<xs~\ sv

sv&sla D, mg. xal 7t' EV&SICCS D 2. 14. ZTCEIXU] -8- corr. ex i

in scrib. A. 15. isGs corr. ex iscov D 2. 17. x&v

corr. ex TO UKQOV C. 18. nuQccllri^u} supra scr. D 2. 19.

v D, corr. D 2. 22. sldcaovu D.

26*

OVV f| L'6OV ExdTQOV TG)V XKVOVGJV XCCTCC

rov ETEQOV r&v itEgdrov itgbg T& rv\v

e%ovn JtQt,6[iaTiG) xal VCCQîo6Kvrg dt'

5 [i(poTEQa)v aoviov, &6r 6vvdE&i]Vtti n\v vrt' avrov

rciQ KQOS tats 'yQaâlg rcov xavov&v

VTtb xVTQOv, itSQKx.yzG&aL de dvvaG&ai, TOV ra

fyovta, 7tccvtcc%fi noil ddiaGTQoy&g, di,cc6g)rjVG)(3KVts rs

^K0i rOV TQOV TG)V XCCVOVCQV tQV[IT] %OVTCC TK

10 TtQl^lldtLK &dpo[lV 7tl Trjg XdT()OV {ifarjS y^^^S<5rj[iid nva agog rotg yfaQcc ty fiaGEi itfyaeiv TO faov

xcd on 7tA,L6rov aito rov xara rb cfeoviov

K<pe6rrix6ra xal ditto[iv rrjv acp&Q

rov rriv (Id6iv fyovrog xavovog ig [ifyrj \ xccl rovr&v

15 n fuaGroV) stg o6cc fdvvd^d'cc r^îrov avrov xavovog TCQOQ rolg

rag inl rd avra [lEgy xtevodg itgog rf]

^ 7t v&iag dMtjhaig fyovra xccl rb faov

7tttvra%6&Ev rijg avriig xal pforj

20 itgbg rb di avr&v xa&sriov XQi,iivci[ivov

rov XKVOVCC dg&bv xal drtciofyxki-Tov nobg rb rov bgi-

v

2. sxat^cov D, corr. D 2. 3. STQOV C. 4. omjv] corr.

ex olnriv A 4. $t'] ins. D 2

. 5. dftqporf'^cov] -fiin ras. D.

6. tag] rd B. rate?] corr. ex rdg D 2. KUVOVIGW D. coffTrsp]

corr. ex eb? D 2. 7. M] om. C. 9. rd] om. D. 10.

itf,\

corr. ex TI(SQL) D 2. 11. niqccsiv] -v del. D 2

. 12. xara] xa D.

13. diskopev\ -I- in ras. D 2. dqpo^to/Lt^rjv C. 14. ft^rj]

ftf- in ras. A. 15. oca idvvd^8&a] -a s- e corr. D. 17.

TtQiGfiKTiu] ante -a ras. D. 18. TO] rov C. 19. navraôO'sv]corr. ex navraôrs D 2

. 23. TtQo8iK^lj]^vr\v C. 710:9-*

in ras. D, ^ D 2,corr. mg. D a

.

MA0HMATIKH2 STNTABESS E'. 405

rco rov OQiôvrog iiti nvog avfrtiGxoTrJTOv %COQIOV

LGTapfv TO ooyavov OQ&OV, &6T rag ntevQag rcbv

xavov&v, xa& ag yvcovrai, aMrjhoig vitb rov aJoWbu,

TtQog [LftirjiipQfav TSTQatp&ai xaaaMtfAovg yivo[ivag

rf] 7taaaxi[ivr] nsGrjppawfi yQa^firj xal rov psv tv\v 5

ficcGiv %ovra xavova OQ&OV axAiv&s

k'n T adyaA&g 6rdvat,, rov d

i TO a%6viov v T& rov

"IJKa[lV $ Xai TQOVVd"V 7tQ00rj0^06^VOV ^,V VXV 10

rov xal avTo X&QMyetfd'at nQOVicp figu%Z xara rov

rfi (Id6i nfyaTog T^g di^rj^v^g yâ^îjg,

Ti}g 7tA.i6Tr)g TtagacpOQag rov rb

i'Gov atp0TG)Tog 7toaTog r^g rov TQOV xavovog

^&6T dvvaGd-ai 6viiitQia'y6[ivov avrm TO 15

v TCOV dvo MQCCTCOV yivQptvQv 7t

3toiov[i&a dq TOVTOV rov Tg6itov Tag rijg

Tr]Qjj<)i,g Kara rag in avTov rov ^rjôivov xal

7tol ra TQOXixa Gy^ta rov Sia [isGcov r&v fydi&v 20

xvxhov ywoiiwag ytaoodovg^ itidr] xara rag roiavrag

6%6ig oi T dia T&V jrdAov rov bgiôvrog xal rov

xVToov rr\g 6hijvr]g ygafpo^voi yLzyiGroi xvxhoi oi

avrol fyyiGra yivovrai rolg dia r&v itd&cov rov dia

1. TW] in ras. D 2. 3. CCÔVLOV] pr. o corr. ex i in scrib. C.

4. tTQd<pQ-<xL] corr. ex tfzdx&cci D 2. 5. iieGrmpQivy] -vy e

corr. D. 6. &v.ki,v&s] corr. ex aKQifi&s D a. 7. ST<] mut. in

iitt D 2,tni C. ri\ mut. in TO D 2

. 8. Gvîrgmg T^] -? t-

e corr. D 2. 13. itfoiGTrig] corr. ex nfavgas t^s D. rov TO

LGOV] corr. ex TOVTOIS/OV D^. 15. avvjieQiuyo^vov AC. 18.

dry] de D. 20. peGov D. gtodiov D, sed corr. 22. rooi>]

corr. ex TOV D. 24. yivovTuC] corr. ex 1^ D 2.

rcbv ^codC&v ypaqpoâVotg, nobg ovg ai Kara

TtccQodot, r^g ^^tjvrjg ftsoaQOVvrai, KOIi\

axoi-

g atto%Yi rov Kara xoovcpfjv Gr^LSiov dia rovrov av-

5 oovTfg ovv rbv TK TtQiGyiKritt fyovru xavova Ttgbg rrjv

KKT avrag rag itl rov Î^^QLVOV'

aiig)OTQeov rcov bncov Kara TO

rb XBVTQOV avrrlg dtOTCrfv-O'/J, Kal

7tl rov fanrov KavovCov rr\v

10 rcbv aKgcov rcbv v rolg KavoGw v%~icbi

Tfj dir]Qr]HV'fl ig ra | t[iri-

rov OQ&OV xccvovog fvofaxo^v,0rlv r^^jLccrov % -rijg itQOi,Qr][isvris dicc6rcc(5a)S v-

^fta, oi&v 0rlvf)

x rov xvroov rov vitb rijg ttQicc-

15 yoyijg yoa<po[ivov iv TG) rov î6ri^Qi,vo

|, KKI Aafiovrfg r^v VTCO rife

vjtorfivopwrjv 7tQi(pQi,av rccvryv

aitl%v r6r rov Kara xoovtprjv (5rîiov

rb (paiv6[ivov nevrgov r^g G^tjvrjs ^l fov dt,a rcbv

20 sroAcoi/ rov boftovros nai avrov yaatpoiisvov

xvxhov, og 6 avrbg yivro ror xal TK> dia rcbv

rov T l<5riyiQivov xccl rov dice [isticov rcbv ^c

VXV [lV OVV TOV TJjV yiVO^VTJV KaTtt

25 Tttefarrjv TtaQodov Tijg Grjktfvrjg axQiflcog

1. (itocov] seq. ras. C, corr. ex ptaov D 2. yQcc<po[ie\ D,

corr. D 2. 3. tovrov] corr. ex TOVTO D 2

. 6. Ttccgodovc;] e

corr. D. 7. OTC&V] -n- e corr. D 2. 10. r&v (alt.)] -co- corr.

ex 01 in scrib. C. 11. Sieigrwevr) CD, corr. D 2. 13. sori D,

comp. B. 18. ani%v~] -v del. D 2. 21. og] corr. ex cos

C 2D 2. noUcov D, -II- eras., mg. I D a

. 22. re] om. D.

peoov D, corr. D 2. 25. STuyivcaGnsiv D.

K T?j dlO7tTV6l, ItSQl T TO &Ql,vbv TQO-

rtixv 6r][iiov

CCVTO TO TOV Ao|ov avTr\$ xvxkov POQSIOTCCTOV

did TS TO 7tQi TCCVTCC TO. 6r][ita <JD'Lxavbv did<5Tr][itt

Tqv avTrjv Ttgbg afadyffiv XKTCC 7t2.dTos Jtdgodov cupOQi- 5

&6&ai, xal dia TO itgbg KVTG) TK> KCCTK xoQvcprjV

TOT Tr\v 0^vrjv ywopwrjv v1'

ov 7toiov[i&cc rag rt^^tfftg, rv\v

xaT2.ct[i(ldvTo df TCEQI Tag TOICCVTCCS TtaQodovg 10

KSl TO XVTQOV T^S <5kv\V1]S TOV XCCTa XOQVyrjV

xal 17' fyyitiTK ^OLQK^ &s xal X T^S TOLDCV-

pOlQ&V K7todlXVV6&at, T^V Jt&l6Tr}V

XCCTK itk&Tog f'g?' xdTQK TOV did [izG&v T&V

Ttdgodov, oGcus 6%dbv vJtQ%ov6(,v ecu ditb TOV 15

XCCTK KOQV(pi]V 6r][llOV 3tl TOV fat)pQLVOV V'

8iyiidvKi potQcct, I vij tefaovdccL TCC

ditoGTdtff&s [lotQas j$xccl rf T&V dab TOV

V Jtl TO &OIVOV TQOVtiKQV 6r][ltOV dfdMy-

3CJ/VCC. 20

VXV d TOV Hal TTJV TtQOg TCC 7tCCQCcA,A.d%l,S 7tL-

7taQTr]QOV[lV Jtd&lV XCCTd TOV CCVTOV

TQOJtOV Ti]V 0^Vr\V 7tQ\ {lV TO ^i^lQivbv TQOTtMOV

2. hi 7CQi~\ -n ittQi in ras. A. 3. ccvTfjs] om. B, suprascr. D 2

. 4. TK] ins. D 2. 6. ro5] rots rm D. 7. tors]

om. D. 10. 'AK-ctlKiLfiuvopE&ci D. 11. atei D. 12. <*rj-

A. v.a.1 (alt.)] comp. mg. D 2. rfjg TOiavrj]?} corr. ex

ocvTfjs avTfjs D. 14. ptcov D, corr. D 2. 15 OGCCL D,

corr. D 2. 17. dEdiypsvai, A, sed corr. 20. (JLOIQ&V] ft seq.

ras. 1 litt. D, ft D 2. 21. rov] supra scr. C 2

. xai xj\v\ suprascr. D 2

,corr. ex v.a.1 rov C.

408 KAATAIOT HTOAEMAIOar

6rj^lov rvy%avov6av did re ra 7tQOiQr][iva xal

rb TtkeiGrov rors avrqv aystircbGav fag litl rijs

Kara rbv {isGrjiiflQivbv Jtaoodov rov Kara K

6rj[iiov KOI rqv rtccQccMci&v [istôvcc xccl v6r][iavror-

5 QCCV 1taQ%lV. KTtO TtfolOVCDV dq T&V XCCTK TCCg TOl-

avzccs jtaQodovg rrrjQ^f

vcov vâtv JtaQaMd&cov pCav

TtKîv %&rj6oiid'a) di ^g rov T TOV

VQOTIOV CC[IK 7taQCC^TtJ60^V KOI t^

.

10 ly '. 'Artodfiîg r&v rys 6kijvr]s'

Aiyvx-

rov r^Mov xccradvviv

Jtl rov ii6r}iif$Divov yEyfvrjiiwrjv, xal cpciiVro

15 fftilv dux rov ooydvov rb %vroov avrils and%ov rov

Kara xoQvcprjv 6rj[iiov [IOLOCCS v /.' y' ifi'' rj yciQ iiti

rov fanrov xavoviov dicc6rcc6is roiovrcov r^v we /_' ifi ,

slg ola diyorjro ^ x rov xwroov rov rilg TttQiuywyvis

KVKlov 1, YI81 ryhixavrr] v&ia vnorsivzi rtQi,q)Qiav

20 roiovr&v v L' y' tf' ,OLCOV <5rlv 6 xvxhos r%. ccMa 6

dnb r&v v r& a' r

rov Kara r^v xxi,[ivrjv

KOI râQC3v o/3 xal coocov

5. Y.axcc.~\ not corr. in Y.CC A. 10. ty'] yt B, om. ACD,mg. A 4

,t mg. D 2

. 11. ydg] 8s B. x'] xl D, -e in ras.;% supra scr. D 2

. IVft] e corr. D 2. 13. n&ovtos C.

14.' Post SKI del. TO D 2. m^svrifuvi^ D. 18. rj] ins. D 2

.

20. TOIOVTCOV] om. D. ccU' D. 6] corr. ex oi D 2. 21.

a'] r& ici A. ?tft] e corr. D 2. NccfiovaOGov C, Nccfio-

D. %QOVO<S\ corr. ex ^90^01 D 2. 22. %*i[ivr)v A.

corr. ex slew mg. D 2.

MA0HMATIKHS STNTA5E&S E'. 409

// y\ axoificbg ds y'' ^g ov

TOV jw-fv VI^LOV svofaxopsv [is6cog fisv its%ovra

r&v Xyhcbv pOLoag A, axo^cbg ds so?, T^V (? 6s-

A.ijvyv ti6G)g 7t%ov6av To%6rov potoag xs ftd, xl

rr\v [iev ccTtoyfiv poiQcbv otj ty, rag d5

ocTtb rov petiov 5

anoyeiov rov JuxvxA.ov [lotQccg 6%p ac, rag d' ccitb rov

POQSIOV TtSQarog rov nhdrovg {loioag rvdjl. itgoGs-

ri&si ds dice ravra, xal rb TCKQCC rqv &vmptt&fav dicc-

yoQOV navraxo&ev BK rov ofastov navovog diaxgiftsv

[loioag g jcg, &g xal r^v axgiflrj rijg dehtfvrjg &S61V 10

KKr sxetvrjv r^v &QKV iitiîv xarct fisv rb [tijxog

AlyoKSQG) iioiQccg y 7, xccra ds rb nhdrog STtl [isv rov

Ao|oi) xvxôv ccitb rov fioostov Ttsoarog

ejtl ds rov dia rcbv nohow rov dia [is6cov rcbv

og 6 ccvrbg syyitircc i]v rors r& (L0rjpfiQivfa cforo rov 15

dia iis6G)v r&v fydiov xgbg rag aoxrovg [toiaag d v&.

ds xal KI psv rov ^[fyoxsoco [loloai y I rov

itobg (isff^fipQtav STtl rov avrov

potoag xy p& 96 ds faij(iQtvb$ rov sv

xara xoQvyrjv 6rj[isiov ngbg [isorjôiav opoiog [loioag 20

A vij' rb aoa xsvrgov rqg 6shr}vyg a7tst%sv

aito rov xara xoov^v tiqjisiov poioag [i& JS

vsro ds attfyov noioag v ve' TtaorfMa^sv aoa % 6s-

1. /.'] corr. ex K D 2,

ut saepe. 3. Xeil&v D. Ice] e

corr. D 2. s"] ft F D, p ? D 8

. 4. Post p&fo>g ins. (iv D 2.

^] renouat. D 2. 5. d'] dt D. 6. rov (pr.)] renouat. C.

STtwvnlov] SKI- e corr. D 2. 7. rvd] -v- e corr. D 2

. 8.

diet ravrcx] mg. D 2. 9. TtKvra%6Q'sv^ supra scr. D 2

, ^_ add. A.

sx] dtoc ravra EH D. 11. ans^siv D. 13. %VHA,OV anb rov]mg. A 1

. 15. 6] om. C. 17. ctn%ov6iv'\ -v del. D 2. 20.

ojiotcog] bis D extr. et init. pag. 21. nevrgov] *.- corr. ex ain scrib. D.


rb 7tol xr\v xxst,[ievr)v ndoodov c

potoav a xal $)pto0cd g exl rov di avryg xal r&v

tto&cov rov OQLôvrog yoag)o^vov {isyititov xvxhov

dit%ov6a dxQifi&g rov Kara Koovcpfjv

rovrov dÂoO'fVro? ysyQacpftcaGav sv T&

rov dia r&v nolcov rov oQ%ovrog xal rijg

[ifyiGroi, xvxhot, itQi

rb avrb xevraov 6

10 plv rijg yijs pfyiGros

6 ^5, 6 ds

ce rov Kara ryv

XEvroov

6 JTz/, Jtabg

15 ov dsr\

xal xsvroov [isv s

xowbv ndvr&v rb K,f ds 8ia r&v xara

20

dsr\

sv&staf} KATE, V

6y[iiov anfyovGa axoip&g rov xara xoovcprjv

rov P rag 7tQoxi[isvag {LOioag [1& /n^, xal

Kara r

1. V.KTO] corr. ex nccQa, D 2. corr. ex %ara D 2

. 2.

a, 3 |g D, || D 2. tov nolov D, corr. D 2

. 6. dr)Hca-

mut. in 8r] do&svzos D 2,sed rursus corr., sacpcd supra

scr. D 2. 7. xca TTJS os^vr]s] supra scr. D 2

. 8. ft^ytcrrot]

yQcerpofjitvov {i&yiGTOv D, sed [isyioTov corr. in [ityiGroi. %vxiot]corr. ex xvxZov D. Deinde rep. CCTCÔVGK lin. 4 Y.VY.IOI D (utin textu, 5 /Zrj eras., 6 TOVTOV, add. D 2

,7 TrdHoov, corr. D 2

).

16. EZH0] -Z- e corr. D. 21. rj (pr.)] corr. ex N in

scrib. A. ds~\ om. C. //] corr. ex A A4.

MA0HMATIKHS ZTNTASE&S E'. 411

tfTS K4H xccl y Ad, xal ti aitb tov A,

o ywstau oiîg t&v QQ&VXMV, xcc&ftog psv TJX&G) sitl

tyv KB r)A A, TtaQaUôg dl trj KH ij

AZ.on [iv ovv trjv H TtSQicpEQSiav tolg cbro rov A

Vr\ Gshrjvr}, tpavsQOV ci)6t sty av 5

xal e^rjxoGrcbv f rcbv sx rijs rrjQiJGs&s

7ti dl ttdiayOQO) î^G)V <3TIV fjZ

itQicpQt,a rrls H dux to rrjv yv\v oAyv Gqufiov Ad-

yov %iv Jtgbs tbv EZH xvxAov, elti av xal ^

ZH@ 7tQl,(pQl,CC TG)V ttVT&V SyyitiTO, K f. CO0TS Xal 10

^ vjcb ZA& y&viK dice TO it&Kiv adicccpoQtv to Atov xwtQov XQOS tbv Z@ xvxkov, oi&v pw

cci d oQ&ccl r|, toiovt&v 6tlv a ^, olov d3

cd

toiovtwv/3 id. tcov d* avt&v 6tiv xccl

rj fay [Eucl. I, 29] avtf] ycovia ^ vnb AdA ftid' xul 15

fj jlV 7tl tils -dd P^ VÎCCS 7COl(pOlCC XOlOVtOV

6tlV ^ td, OLCW 3lQl tb A /IA OQ&O'ycbviOV XVX&OS

TJj, KVtrj drj AA V&ICC tOlOVtOV ft HOC, OIG)V <3tlv

$1Azl vitotivov6a [Eucl. III

? 31] ^K. tcivtr^g d ddicc-

<pOQG) Ad660)V 6tlVfjAd" KCU, OIG3V &QO, SGtlv

f} 20

AA v&ta sea toiovtcov 6tlv j Ad v%-i<x, X

3. TraâHrjôg] oc D, HOG D 2. 6. [ioiQag] ft supra

scr. D, jJ D 2. efrnoGtav f] |J D, if ^ D 2

. 7. ccduxcpoqa)]

a- e corr. D 2. êL^cov] mg. D 2

,M. D. 8. rfjs] corr. ex 1% D 2

.

10. ZH0] Z D. eyyiotu] -a. postea ins. A. a} p a D.11. ZA@] corr. ex AZ D 2

. 12. Z] mut. in ZH D 2.

13. roiovrcov 14. rf] supra scr. D 2. 13. $'] Se D. 14.

(pr.)] dvo C. <T] de D. IGTW] comp^B,^ -v del. D 2.

15. rj (pr.)] ins. C 2. AzJA

~\corr. ex ^ 1$ D 2

. 16.

&QK\ comp. supra scr. D. 17. fartV] comp. B, -v del. D 2.

19. Jz/] corr. ex AA D 2. 20. iorlv ilaGccov D, deinde

supra add. 7? D 2. ylzf] AA D. xat 21. ^1^] supra scr. D 2

.

21. ^ ^yl D. AJ AA D.

lift jit??, el'rjav not

rjvnb TKA y&via agog TG> XWTQGJ

ovtia TOV xvxhov, otW pv efaiv ai d oa&al T|, roiov-

TCW ftO1

/Lt??,oi&v d' CCL dvo ood'al T|, TOLOVT&V 9^ Ag

5 &6te xcclfj [isv ETtl rils AA sv&stag jtsgicpeQeiK roiov-

rcov 0tiv 90- AST, oicov 6 Ttegi rb AAK OQ&o'yKtviov xvx-

Aoff r, % & sal rife AK r&v tout&v [Eucl. Ill, 31] etg

TO YllLMVKklOV ft xd. XCcl TG)V VTtOTSlVOVGcbV CCQCt KVTCCQ

SV&SLtyV fj [lV AA k'tiXtti TOIOVT&V 9 A-91

,OLC3V 0TLV

10fjAK vitorswovda ^x, ^ df AK T&V CCVT&V o x' foGts

XKI, OLOV vos itinv17AK x TOV KWTQOV r^g yi}s, roi-

ovrcov nalv\ [iv AA k'tixai o ^tg, ^ df KA Oftotog o A-9-.

QX' XCCL OLCOV CCQCC <5rlv flAA V&iCC O ^tSj TOIQV-

15 tov 6tca xali]A/I v&la k& g. r&v d' avr&v i\v xal

KA v&ta o A#, fjd KA x TOV XVTOOV

svos' xal OLOV aoa 6tlvf)KA x TOV xw-

TOOV Ti}s yrls fii/dg, TOWVT&V etirai xalfjKAd oAiy,

7tQi%ov<5a df TO xaTa T^V TtforjGiv rijjg 6^vri$ an6-

20 ^T^fta, A-9- p~.

TOVTOV dfdfiyilWOV 6TCO 6 TijS 6&tjVr]S XXVTOOSo ABF itol xdvTQOv TO z/ xal dtdfiToov Tr\v

TO iv TOV dt

4. dvo] JJBD. 6. 6 Tif^t] corr. ex OTT^ D.

AAK D.'

11. ^4X] -K e corr. D. Supra .KSVZQOV add.

o^ffa D 2. 13. 7]v] ins. D 2

. J^i] corr. ex AA D 2. Ante

rj (alt.) del. fa D 2. ^^stxro] add. D 2

. 14. o] o D, o D 2.

16. efoeC D, tt&tl D 2. o] corr. ex o D 2

. KA] -Arenouat. D 2

. 17. xat] corr. ex gat D 2. a^a] comp. reno-

uat. D 2. SGTL'V] & D, i-

D 2, mg. icri D 2

. 18. xat] x? corr.

ex % D 8. 61?]] corr. ex o D 2

. 19. TT)S] T- corr. ex rjin

scrib. C. 21. ta mg. D. eMfvtQos] ZKHSV- in ras. D.

MA0HMATIKHS STNTABESiS E'. 413

xvxkov XWTQOV TO E, TO

tov eitwvxhov Grjiieiov rb Z, xal ygcupevtog

B 6rtov TOV HKA

HB@E xccl xcclj\ BKZ, v

XCCTCC TO AV Oil AE KCll

7ti TYJV BE aito ply TOV

4M, catb dl TOV Z % ZN.7Ci TOiVVV XCCTtt. TOV %QOVOV

- 10

rj [ilv vyfb AEB y&via, of

icov ffalv ai d ogftcci

T%, TOLOVT&V QV$ X$, XCCTQCC [Eucl. I? 15] $ T&V VltO

ZEN KKI AEM T&V nlv kont&v si<s TK$ dvo OQ&ag ny

3. &uxvx;iov] s 'tf D,*

supra add. D 2. 4. EA\ JB B,

-z/ corr. ex ^f D 2. xca (alt.)] corr. ex v. D 2

. 6. d' ij^co-

GCCV] 8iij%Q'a)6Kv C, corr. ex S' &%&a)6ctv D 2. 7. xM,7j'9'M>av]

corr. ex iv.fiKrift'EiGK C 2, eMp/Lrj^frcra B, ante djrd coll. Halma;

puto delendum esse. 8. ZN] -N e corr. D 2. 10. rd] supra

scr. D 2. 13. dvo] mut. in J A 4

,D.

Ad, oi&v d' efalv ai dvo dgftal T, TOIOVT&V

G)6T xalfj {lev (p' xaTQag T&V AM xal ZN

<pQia TOLOVT&V h'tiTai[i 77, oi&v sfalv OL Jtsgl tec

xxiyiva QQ&o'y&via xvxkoi T, dice TO ttivfv slvai TV\V

5 AE TT} EZ, ^ d' scp' exareQccs rcbv EM KOI EN rcbv

avrcbv ghp vfi [Eucl. Ill, 31]. xal r&v viC ccvrccg CCQCC

sv&si&v fxaTSQa plv r&v AM xal ZN toiovx&v 6rlv

[l V-0", ol&V BKttrtQK TK)V AE XCti EZ V7tOTlVOV6&V

QX, xarQa df t&v EM xal EN rwv ocvr&v ^7 o-

10 G)<5t Kcti, oicov iGxiv xarQcc [iv rcjv AExcel EZ fv&fi&v

I #, ^ dl AB x rov xevrgov rov XXVTQOV n& jita,

Toiovr&v xccl exarfyct plv r&v AM xal ZN 6rai dy,

xccrQK df r&v EM xal EN t&v avr&v & x%. xccl

7tl to ccTtb rijg B^J fafyav TO cbro r^g AM 7toii

15 TO artb rijs BM TfTQcc'ycavov [Eucl. I, 47], |o ku.i/ xccl

tr\v pev BM ohrjv ^xi toov avr&v [ifr Aa, rrjv $

BE 0[ioiG)g fi d, Aotjr^v $ rfjv BN roiovrav A A^,

xcclfjZN ^v d

rj.xal itd ra ait avr&v 6vv-

TtOLSi TO (XTtb Ti]S BZ [Eucl. I, 47], %0[1V20 xal Trjv BZ tiitoTfivovtiav ^njxft, T&V avToov A vd~

&6TS xaC, OLCOV tirlvY}BZ vitOTeivovtia QX, TOLOVT&V

xal $ plv ZN k'tiTai 7g ^, YJd' it avrr\<s itQi,(pQi,a

TOLOVTCOV l XCC, OLOV 0rlv 6 7C()l TO BZN OQ&O-

xvxhos T%. xalrj

vitb ZBN aga yMvia^ OLCOV

1. dvo] BE.TJ] ins. D 2

. 3. mu] A D, ^ D 2. 4. T|]

corr. ex rov D 2. 5. tf'] Ss D. 7. eWv] comp. B, -v del. D 2

.

8. z/E] corr. ex AE D 2. 9. o] 6 ABCD 2

,& D, o mg. D 2

.

11. T i&] corr. ex ~H& D 2. 12. piv 13. exar^a] supra

scr. D. 12. ML(alt.)]_ins.

D 2. n;cu] ^_D. 16. ^ let]

in ras. D. 17. ji <?] ^ AD, corr. D 2, ^' A 4

. 18. ZN]NZ D.

22.^1D 2

, |f D. 23. Is] corr. ex ? B 3C 2,

-f ecorr. D 2

. xor] corr. ex v.1 D 2. 24. ZBN] -B- e corr. D.

ftfV eltiiv ecu dvo QQ&al rj, roiovr&v ttfrlv i xa, oi&v

d' aC d oo&al T, roLovrcov p, syyttfra. roGovr&v

aocc [loio&v <5nvf)@K rov faixvxAov

jra/Uv, 7tidrj xccra rov %govov r

yzv v\ GeAtjvr] rov {lev [i86ov anoyeiov rov sjuxvxhov 5

[loioccg tf/3 x, rov ds K rov ptGov 7tQiyiov rag

Aoiitas driôvori [ira rb fyuarthilUov [loigag 7t{$ x,

6X0.1 Kal % plv KA 7tQl(pQLK [LOlQGbV Ttfi X, V]$

KA o/l^ iioiQ&v 9 o- dofrrj aoa <5rlvi\

vnb @BAyCDVlCC. KH5r fast, OIG)V 0riV

f} plv 4B X rOV XV- 10

roov rov MCvroov n& fta, ^ d BA in rov xvroov

rov 7tMvxA.ov f t, roiovrov xali\EB ddixro ji

xal %r]xo6rG)v d, ra d' ait avrwv Gvvr&zvra 7toit rb

aitQ rr\$ EA rfrodycovov [Eucl. I7 47], sô^v xal rr\v

EA \IV\KBI r&v avr&v jl M-. rb ccoa xarcc rrp> njorjGiv 15

rijjg 6kijvy$ rouovrov 6rlv ^L x, olcov xal

BA x rov xvr()ov rov faiKVKôv vitoxeirai

f]df EA

i] ccTtb rov xwroov rijg yv\ iiti rb

rov %%vroov |, r\d EF

i\ccitb rov xvroov

n*< to ^^Cyôv rov fxxwroov h& xft. tiMa 20

rb xarcc rqv nrJQrjGiv rijg 6&ijvysrovrdtinv r EA v^ta rouovr&v A-9

1

t oiov

1. dvo~] B B. f'orrtV] comp. B, -v del. D 2. 4.

corr. ex fast D 2. 5. Supra unoysiov add. tag loncds D 2

,

sed del. 6. op] corr. ex 5^" D. rov (alt.)] om. D. 8.

IWca] & D, \ D 2,

sarca mg. D 2. 9. &EA] supra scr. C 2

,

AB C. 10. &GT' D.rj] e corr. post ras. 2

litt^D 2

. 11.

TOV iv.v.ivTQOv\ mg. D 2. 13. ^Tjxotfroov] || BD 2

, |"7D. 16.

iavtv] comp. B, -v del. D 2. 17. rov v.^rpov] mg. D a

. 18. E^4

^] C 2D, fa?] AC, EJ seq. ras. 1 litt. B. 19. fcxeVifOv]

D 2, mg. sxxg'D*. xôv] D 2

, comp. D. 20.

ax- D, Ix-x- D 2.

vbg f)x rov xvroov rf}g y^S' xal dicsv ago. 6rlv

YI [lev EA v&ta rov xard rqv rtjorjaiv ty

a7to6rrjârog A-91

ji, ^ (f x rov xwraov rfjg

roiovrov h'tirou xal % [isv EA sv&slK rov xara rag

5 GvZwyiccs psGov anoGrrjiiaros vO1

o, ^ df EF rov xara

rag di%or6{iovs [istiov uTtoGriJiiccros Ay fty, ^ ^' tx

rov xsvroov rov 7UxvxAov r&v avr&v i'

d' fip.lv Kara rov sxre&siiis'vov raonov

10 r&v rils GsAijvys ditoGrrjiidr&v axoAov&ov avel'rj

xal

rb rov i\Mov Gvvartodstt.ai, Jtao%iaov xal rov roiov-

rov yivopdvov dia rcbv 'yQa^&v^ i TtaoGdo&ffev rolg

xara rag 6v%wyia rijg GfAtjvrjs d7to6rtjâ6i,v ai

Koryrs r&v v avralg GvviGraiiw&v ytobg rf}

15 y&vicov vito r rcbv dia^ra&v Âtov xal 6^tjvrjg xal

6xi ag.

id'. Ilfol ryg nyhixoriqrog r&v ev ratg Gv^vytaigxal GsA.vr xal

20 T&v drj Jtobg rrjv roiavrrjv i7ti6Xfyiv Zcpodcov rag

kufv aAAag, o6ai di vdQop,rQiG)v r)

r&v xard rag l<5r\-

u,aivag avarohag %a6vcov doxovGi, rrjv r&v gx&rcov

xarajiErorjO'iV) 7tao^rrj6a^d'a dia rb pr} vying

dia r&v roiovrcov rb itQoxipvov Aapfldvs-

2. Gkri\GeJ(.rjv7]s A. 3. rov xaVrôv] corr. ex TO * D 2. 4.

Kara] x| C, xa C 2,

V.K D. 5. Gvvgvyiccs D, corr. D 2. i"9-]

corr. ex vo D 2. o] o^ D, supra scr. D 2

. 7. K&VTQOV TOV\om. D. 11. JiUov] fyiov v.uC D, xat del. D 2

. 15. re] om. D.

17. id'] mg. AC, ~jl B, om. D. nsgl 19. ffxiag] mg.superiore D. 21. Supra ?'f

add. xcct? D 2.

MA0HMATIKHS STNTAEE&S E'. 417

, xara6xvd6avrg ds xal avrol rr\v v

vitb rovr

ljt7tdo%ov did rov rroanri%ovg xavovog

roav xal did ravrr^g itoiov[iVOi rag ytaoarrjot]6ig rrjv

plv rov yMov didîroov VTCO rijg avr^g k'yyiGra yovtag

sx rcav ditoGrrjiidrcav ccvrov

ds rijg Gshrjvrjg rore povov xcd ccvrqv vytb ri\g avrijg

r<n Y\MG) y&viccg 2tSQi,%oiievr]v ,orav v rccig TCKVÊ^-

voig rb nfyiGrov Kito^rrâa rrjg y^g uiifyri xara rb

ov6a rov emxvxkov,xal ov% orav rb 10

dxohovd'cog ratg rcbv itgorsgcov VTto&sGsGw.

itgbg dl rovrois xccl rag y&viag avrdg at>iok6'ycp nvl

shdrrovg xttrKAaiifiavops&cc rcbv xaQadsdopsvcoV) ovxsri,

pivxoi dia rijg iv r& xavovi xara^r^0G)g tTuAo'yt,-

6[ivoi, rb roiovrov, dMa did nvoov Gfkrjviccxcbv %- 15

rb pv yaQ 7tor farjv VTtorWi, y&viccv

r&v diaperQG>V 7tQo%iQov x ryg rov xavovog

ridvvaro yivEGftai did rb iinidspiav znaxo-

7tl rov roiovrov xara^ror]6iv^ rb $ xal

Jtdvv vmlv Karcpaivero diGrd&iiov rqg v 20

ralg Hitifiohaig rov TCi'jtQo6Q"^6avrog nhdrovg 7tl rb

^xog rov xav6vog rb dnb ri\g otyf&g jcl rb TtQiGpa-

nov Ttteforyg ovGqg ytaoaîrori6C3g diaifjv6d"?ivai, rqg

dvva[ivr]g. Inel d' a7ca% i] 6ktjvr] Kara rb

2. Tsrccm]%ovs C, Q supra scr. C 3. 5. Ttavxa.fj\\ -t- corr.

ex n in scrib. C. îrjdsî&g] corr. ex {.i7]df(iiav C 2. 8. raig\

tots C. TtavoeJirivoLs] -OL- in ras. D. 10. rov] r- corr. ex

S in scrib. C. 11. anolovd-ojg A, corr. A 4. vno&sGSGi. D.

13. tkdfovs D. 14. (LtfVroi] corr. ex [itv n D 2seq. ras. 2

litt. TT?S] corr. ex r? in scrib. D. 15. Post tnUfyeav del.

*a| D. 18. ytVfdât] corr. ex / D 2. 20. rfjs] corr. ex

rafg D. 22. ft^xog] p- corr. ex x A 4. TO (pr.)] TOV D. 23.

nteiGTccis ofaccLs D, corr. D 2. 24. <f ] 8e D.

\kiyi6tQv avri]g aitoGrrjiia xrp i'Gyv rcn v\kito Ttobg rrj

otyei y&viav syaCvsro noiovGa, dia r&v 7tol rovro rb

a7totfrr][icc rrrjQr]îV(ov <jA.r)viaxa)v sxAsfyecov rr\g vito-

TWO[ivr]g VTC avrijg y&viag rb fis'yf&og iTtikoyiCf>\LVQi

5 xal rqv rov j]Mov GvvaTCodsdsi'yuzvrjv sfyopev avro&sv.

rbv ds rgortov rr^g Toiavrrjs snifiohijc; dia dvo

rcov vitoTerccyiLEVGiv sxfofye&v evxaravoyrovT& yap e' srst NafloitoM.a66K()ov ,

o i<

erog KTCQ NafiovutiGaQOv ,Kar' AiyvTtxiQv 'A&vQ xt,'

10 sis iv\v K'YI coQcig IK A.rjyovGrjg iv Baflvk&vi, ^^|rof] 6^Vrj xA.L3tl,V

,XCCi S^zkeiltSV tO JtA.l6TOV CCJtO

vorov TO $' rrs diKpeTgov. 7td ovv fj yilv <XQ%JI rij?

V [lTa CDQCCg TOV 1100VVXTIOV XCCl-

6 df [i6os %Q6vo H,T<X % fyyiGtcc, aC i]6av iv

15 Bafivkcbvi r6r farmEQival f /.' y' dia rb rbv v\kiQv

ccxQificbg iitiîv KQLOV poiyus K xal %r]xo6ra y, 8r\kov,

on yiyovtv 6 pfaos %QOVO<S r^g x2.fy(DS<) or rb

Gxiav ^7t7tr(DXL rijg dia^rQov^ v

[ira~

[1 y' (ogccg i<jr][iQivag rov

20 [i6ovvxr{ov, v $ 'Afaâvdofta Tt&'kiv iisra f povccg.

xal GwdyM 6 onto rr}g fcTropJg %oovog rq Aiyvitriaxa,

xal VHLSQKS Tig xal cooag frgjpqpiircfcg aitkag

1. avtfis D. 2. ycovLKV\ corr. ex ycovia A 4, y^ D. TO]

e corr. D 2. 4. uvTfjs] -rf)<s e corr. D 2

. yooWas] y^ D, y D 2.

5. 6vvu7iodiKW[Lvr]v D, Sedeiyfievrjv mg. D 2. sfyofiev] s

supra scr. D 2,

sed del. 7. vxccravor]Tov~] pr. t in ras. A.

8. f'] BD et postea ins. C, is corr. ex xf A. Irft] comp. D,corr. D 2

. NccônccUccaaQOv BC; alt. I add., alt. G del. D 2.

9. s'trog] om. D. Nccovcc6a.QOv D. 'A&VQ\ 'A- ins. D 2. 10.

tfe] corr. ex ss A. rtjv^ supra scr. D 2. Bafivk&vri C.

11. Qitemsv} -v del. D 2. 12. TO] om. A. 13.

-v del. D 2. 16. dx(>t|3c6ff] -Qifi&s in ras. minore A 1

.

B, tf D. 19. [iev] om. D. 22. ws] renouat. D 2.

MA0HMATIKHS STNTABE&S E'. 419

ds rd oftcda vv%ftrm,Qa 7g /_' d'm &6te xal

j) psv iifarj xccra iiyxog itdgodog rr)g 6^v^XyJi&v noioag x A/3, ^ #' axQifirig poiQag xt,

?r6 roi) axoyeiov rov faixvxhov poiQas T\L xccl

f, q d' anb rov (loQeiov rtfyatos sitl rov Aojov xvxhov 5

JTjil.

xal cpavsgov, ort, orav O1 xal y poiQag dtp-

rcbv Gwdstipcov rb xsvrgov rijs G&v\vv\ Jtl

rov Ao|oi) xvxhov nsgl rb pdyitirov ovGrjg

xal % ejtl rov yQa(poîvov di' ccvrov agog

Ao|c5 iisyfarov xvxhov rb XBVTQOV rf\ Gxias, xa&' TJV 10

at iLs'yitirai yivovrcu, zrtiGxorriGsis, rb reragrov

eig rr^v GXLKV sîjCLTCrsi, rr}g diaperQOV.

r& % b'rsi Kccpftvôv^ o i&nv 6xs' erog

xar Alyvnriovs <&cc[iVG)d' i% slg

rqv ir{ XQO piccg &Qag rov peGovvxrCov iv Baflvh&vi 15

QsteiTtsv % 6e^vri ait aoxrcov rb rftiitiv rf\$ diapsrQov.

ysyovsv ago, xal avrTj fy sxfoiijug v 'Ak,avdQia itgb

a i' y ftgag i6ri^QLvi^g fyyitira rov prtovvxriov.

xal Gvvaysi 6 cforo ri}g iiCQyi\g %govog fry Alyvxriaxaxal j}[iQag Q$g xal cbgag farjjifQivag aTth&g [iv 7 20

xal g', axQificdg d O1

/.' y', did rb rbv ijhiov

1. i' 8'] U' 4 D, U" A" D 2. 2. yiura] xeu a D, xaor D 2

.

3. Xr]l&v] corr. ex Xsil&v D 2. 4. ^Trtxvxôi;] corr. ex ano-

KVK%.OV D 2. fljT^xoffTcT] B, |" D. 6. aqpforrryxst D. 9.

17]

corr. iex r)v seq. ras. D. 81' avrov] mg. D 2,

dia TOV suprascr. D. 11. ywovTKi] corr. ex I'

1 D* XBXUQTOV] ~j' B, <J- D,<? D 2

. 13. TOJ] r<St C, t eras. ^'] corr. ex t' D 2.

^TTFI]

corr. ex h D 2. ^<rrtv] comp. B, -v del. D 2

. 14. Nufiova-

Ga.gov D, .AT del. D 2. Atyvm

l

ov<$ D. 16. |^/lf(,7ri'] -st-

corr. ex i D. %uat>] U* D. 17. SKJ.en})'' D, &tfoti/>? D 2

. 18.

^(TTjju-f^w'^ff] corr. exiGr}{iEQt,v''rjt; D 2

. ^yyiotra] pr. y e corr. A 1.

20. <7x<?] ffx- e corr. D 2.

27*

Kaoxwov poiQag ^*j ifi' co6t xalr\ (Ss^vrj Kara

H6G)g \lV 1tl%V Afy6xQG) {LOiQag X X/

1/rjid. aq)i6rrixi $ xal dab [iv rov aitoysiov rov

frtixvxAov iiOLQag xr] ,aitb $ rov ($ooiov 7toarog

5 rov Ao|ov xvxAov VLOIQKS 6%f$ tfl.xal vrv&v aoa

v, on, oravt, notgas Kal 8 nfyrtra rcbv 6vvd-

TtS'm rb xvrgov rr\g GfAijvrjg 7tl rov Ao|oi)

jtol rb avrb [isyio'Tov ovtiyg ccTto^rrîa rov

xwroov rils Gxiag ri\v tor][ivr]v %ovros Ttobg avrb

10 frfaiv, rb r^LLGv ptgog dg fr\v Gxiav ipitiTtisi rqs 6-

K, sav {Lev 0" y' poioac; aTcfyr) r&v

litl rov Aooi> xvxAov rb KEvrgov ri\g <?At?V>?, ^ /.'

^xo6ra {nag [lOioag ontiî rov dia {ifacov sal rov

15 nabs oQ&as r<p Ao|w di? avrov

xvxAov, orav d g (loioas xal r66aoa

rcbv 6vvd6[ia)v 7tl rov Ao|oi) xvxhov, jlxal ri %q-

a rov dia î6csv anfyfi fuag poioas 7tl rov nobg

Ao|w dC avrov yoa(poîvov [ifyfarov xvx-

20 Aov. sstel ovv rj ^lev rCbv dvo &ctefy$tov vjtao%ri rb

2. 7ti%v] -av e corr. D 2. 3. id] corr. ex m D 2

. cctp-

D 2, acpiavrjusi, ABCD. xca] comp. supra scr. D.

7. &itexij] D, cLni%Ki ABC. 8. yiiyiGTov] corr. ex M9. KKVTQOV] H- D, Tt-p D 2

. 10. rjîGv] /_'

corr. ex 0eb}i7<ftt* D 2. 12. all' CD. y'] 7 A, xal y BCD.

ftotpag] corr. ex jitoD 2

. 13. loôti] I- corr. ex /7 A. 14.

rov (alt.)] rbr A. 15. Si' avrov'] dice rov CD, corr. D 2.

16. fe'] comp. ins. C 2. riccaga ni^nra^ J fV B, J E D.

17. r*~\ r ABCD. sôora] g B, | D, H D 2. 19. Si*

avrov] dia rov CD. 21. d'l supra est ras. A, 4 D, A' D 2.

-lrr supra scr. D.

rov xevroov avrijs dvo diaGraGecov ebro rov dia

r&v Jcodtcav, rovretinv anb xevroov rijs Gxiag,

e%r}xo6ra pices [lotgas /.' ?>', yavegov^ on xal oky rj

rijs 6eA.tfvrjg vnoreuvei peyCtirov xvxhov

efyxodrcbv [lias ponces Aa y'.

6i>xarav6r}Tov d' ccvto&sV) on, xccl % ex rov XEVTQOV

Tys 6xt,as rils XCCTK rb avrb ineyiGrov dnoGtrjiia rr\ 6^-wrjg vitotsivsi, (iv [lias [IOLQCCS ^xo6ra ji

xccl ri,

3tQ, ore ra ro6avrcc e^rjxodra rb xsvroov rrjs

rov xsvrgov rijs Gxias <XTtt%v, tqnfar&eo rov xvxAov rrjs 10

& rb rb rjpidv rijs teArjviccxijs dccc^froov fxfoAoi-

diacpoQco d\ &drra)v 6rlv ^ diitAcc6iG)v xccl srt,

rots y 3t[i7irois [iitov rijs & 'Pov xdvrQov rijs 6A.rjvr]s

xal dia itfaiov&v d roiovr&v

rcc ra$ xxi[ivas Jtrjhxo- 15

rrjrccs xaraA.a[i(lciv6[jivot, 7tg6$ rs ra aM.a ra Ttfyl ras

&G)Qoviiva 6vyx%Qijii&a avrals xal vvv ye

t$\v dei&v rov fjhiaxov aito6rrj[iaros xara ra

avrd etioiievriv , ftxal 6

r

'l7trtaQ%os r}xoAov&r]6v ,xal

cos f&v iteQihaiifiavoiievcov vitb r&v x&v&v xvxh&v 20

fjMov xal Gehrivris xal yijs adiayooG) elarrov&v ovr&v

3. ||7j%o<rra] comp. BD, ut saepius. rj]e corr. A. 4.

-si corr. ex i in scrib. D. 5. UK] I- e corr. in

scrib. D. 6. EvnaraVOTJTOV ] fu- corr. ex a- D. xiV-

TQOV~\ comp. ins. D, corr. D 2. 8.

ftj corr. ex (iD 2

. r'*]

lo ABC, Fs D. 9. ore] supra scr. D 2. 11. TO] om. CD.

jjfpurv] /.' B. cshriviuy.fis'] corr. ex cs^vrjs D 2.

dimid. eras. B. 13. 7] TQLGL in ras. minore D 2.

tsuntois] corr. ex I seq. lac. D 2. 14. r*] r ABC,

D, Pa D 2. roLovtcov] -i- corr. ex v D 2

. 16.

-KV- renouat. D 2. rs\ corr. ex TO D 2

. TO. (alt.)]

om. D. 17. ZMsiipis D, sed corr. 0v*Mg$ifaie4ta D, corr. D 2.

19. i]y.olovQ'r}6v~\ -v eras. D. 21. y^g] corr. ex T?)g D.

D.

TWV v reels GgxtiQcus avTcbv yQKtpo[iVG)v

KVT&V TS xal T&V di,a[iTQG)v.

if

. IlQl TOV fjAiaxov anoGTiJiiaros xal T&V

5 TOVTOV TOIVVV dedopsv&v, xal OTL TO xaTa ras

tivtvyuag neyiGTOv cbrdtf-n^a rrjs 6kijvr]$ TOLOVT&V

6T\v |d T, OLOV <5xlv vbs r\x rov XWTQOV rr}s y^j,

dia rb TO fitv yi6ov ddt%ftai TCOV KVT&V i/O1

, TTJV d'

K TOV KSVTQOV TOV 7tlXVXA.OV 7, l'd(Q[lV)

10 6vv(x,yTai xal TO TOV i\KCov aitoGTrjpa.

6Tco6ccv yaQ oi piyiGroi xal iv T<p avTcfr

vxhoi rfjg [iv fjhaxfis 6 ABPTO ^/, TtJ df 6A.r}VlKXiiS XCCTK TO

<xtto6Tr)[jiK 6 EZH 7tol XWTQOV TO, Trig ds

15 XKTCC r^v yi\v 6 KAM itsgl XWTQOV TO N^ T&V $ diu

TG)V XSVTQCOV 7ti7Cd(OV TO [lV TTJV y^V XCCl TOV ijAlOV

TO ABF, TO dl TOV ijfaov xccl TJJV 6-TO ANT, xal a%cov pv xoivbs 6 4N&, ccC

de dia T&V 7tcc(pa)v v&ia,t, TtaQcckkrihoi,

20 yi,yv6^vciL xul Tcclg dtK^TQOts facet, nobs

TOV plv yhaxov xvxhov3} A4F, TOV ds

fj E@H, TOV $ Tils yn$ n KNM, TOV ds rijg

1. GcpaiQuis] ^9' D, -QUI$ add. D 2. 2. tf] om. BC. 3.

te'l mg. AC, B, om. D. 5. TO] ins. C 2. xara] corr. ex

v.K\A 4

. 6. Gvvytas] GV- ins. D, supra -as add. rd, sed del.

8. TO ftsV] ins. C 2, ptv B. 9. ?] post ras. 1 litt. D. 11.

lisyiGToi] corr. ex M D 2; supra add. rgsig, sed del., mg. oi

(ifyiGTOi D 2. tntiTtsdq} C, sed corr. 12. GcpatQ&v Kvyikoi]

corr. ex op v,v D 2

, mg. cycciQ&v. ABF] corr. ex ART D 2.

19. incttp&v A4, S7ta(p&\v A. 20. yivopsvai D. diccpe-

T^otg] corr. ex ^ D 2, mg. OTO D 2

- 21. A4F~] corr. exAAT D 2

. 22. rov (alt.)] in ras. D.

MA0HMATIKHS STNTABE&2 E'. 423

M

o

ig 7Ji> ipitCTtrsi Kara TO

(5TOV aTCoGTrjiia v\ Gektjvrj, r\ OJZP,&6T farjv elvai xr\v N TVJ Nilxal exarsQav TOIOVTCW %d 7,

OlOV 0TLVfjNA X TOV XV- 5

TQOV vfjs yij svog.

dst drj evQsiv, bv %SL Aoyov

TOV fjfaaxov ano-

agog Tyv NA sx TOV

XEVTQOV Trjs y^g. 10

sxpsp^ci&G) ToCvvv riEHS.

xal eitfidJi edsfi-apeV) on ^ rfs

di^d^iSTgog xaTa TO ex-

v Tats 6vtvyiai$ [i-

66Trj[ia vitoriVi TCSQI- 15

tpQiav TOV xaT avTyv yga-

CpO[lVOV 3tQl TO XVTQOV T1JS

yf\S xvxkov TOLOVXOV o Aa ~%,

oiW 6Tlv 6 xvxlos T%, sir} av

VTtb ENH ycwta TOL- 20

1. els] e corr. D 2, supra scr. C 3

.

crsi] -Imsi renouat. D 2. 2.

rj OnP] -f]O- e corr. A 1

,O- reno-

uat. D 2. 3. were] a>6t8 Y.ul C, yidC

supra add. D 2. rf?] xj\i corr. ex

rr\ A 2. 5. oiov~\ -i- supra scr. C.

NA] corr. ex NJ A. yie TQOV D,corr. D 2

. 8. N4~\ corr. ex NA D 2.

9. NA] corr. ex NJ D 2. 13.

$ D, OTO mg. D 2. Jx-

-i- corr. ex v in scrib. A.

14. [isyiGTOv] corr. ex M D 2. 18.

xvx^ov] corr. ex HV D 2. x] corr.

ex x- D 2. 20. ptv] corr. ex (i\ D 2

.

ENH] -H e corr. D 2.

OVT&V o Aa x, oi&v at d ooftctl r? ^ df fj[ifai,K ccvrfis

VTCO 0NH roiovr&v ncttiv o Aa x, otW sfalv aC

r* (btfte Kttli\ [iev sitl r^g H itQi(pQi,a roiovn

6rlv o Aa x, ol'cov 6 jrspt TO NH@ dgftoy

5 xAos r|, ^ d5

Sri rr^_@N r&v tont&v [Eucl. III731

els to fiiiwvKkiov QO& m} ft. xcu t&v viC avn

KQK V&l,G)V1} [LV H 6tai, rOlOVHCOV O

/ fl, OLG)V

6rlvriNH SiapsrQOS ^x, fj

$ N rcbv KVT&V

fyyitfrct' &6t Ko,i, OLCOV edrlv ^ ^ v&ia %d

10 roiovr&v xccli\@H k'tircu o tj A^. rov d' avrov

xalYINM ax rov xsVrpou rij? yi}g fVdg. AA'

Myoc; 0rlv rijg UP nobs rr\v ff, ov fyst, rcc

/3 Ag i

yi

yiGra xobg rb V, yivtxai ncclf]

IIP rcbv

avt&v oî &rj. 6vvayi(p6tQKt, aga ij

r H xccl

15 IIP TOiovt&v i&lv a y Ta, olov 6rlv 17NM

AA 6vvtt[i(p6TOcci, ijT IIP xal fj

027 6'A^ rcov

avrcbv ffaiv ^ dice rb faces avrag dvai dval rcctg

rjhoi r yda, cos scpa^m, i&lv Jt

Nil rri N' xal Aot^ aoai]HZ

1. at] ttalv at D. rjpfafHx] mg. D 2, t' D. ^ vno\

v- e corr. D 2. 2. (3]

^vo CD. 3. &r] -TT- corr. ex c

scrib. A. 4. 6] ^riv 6 D. 6. ^tHvxAtov]-^

D, a D 2,

mg. îxy_D2

. 7. H] 9H D. Supra oreov add. *r]

$s

&N QI& v& /A7JD 2

, supra I'yytffta lin. 9 adp. D 2. 9. F]

corr. D 2. 10. roiovrov] T- e corr. C. OH] H& corr. 62

IV D 2. Jly] corr. ex It D 2

. 11. I-GXIV\ comp. B, -v del. D 2.

xca] om. C. JVM] -AT e corr. D 2. <iUa D. 12. &

comp. B, -v eras. D. oV] corr. ex o D 2. 13. ^ Is] ^ AC.

TO] corr. ex TOV C 2. ytvsxai] y

+D,

*supra add. D 2

, rx D 2.

15. flciv} ins. D 2. 16. ccUa] om. C. 17. fîv] comp. B,

-v del. D 2. dvaiv D, corr. D 2

. ratg] corr. ex xoig in

scrib. C. 18. tlaiv] comp. B, -v eras. D.

MA0HMATIKHS 2TNTASE&2 E'. 425

roiovrcov o vq fi-fr,ol'ov stirlv

r\NM sv&sla vog.

xaC tGrw, fog % NM agog ri\v H, ovrcog ^ ftev NT3t$bg rqv HF, j]

de N4 ngbg ryv 4' oiov KQCC tiriv

og, roiovr&v xctli\ pm 4 stirou o vg ^9-,

dsf]

N r&v avr&v o y la. (Dd-ts xcct, oi&v

fj ply N@ sv&Sicc |d 7, j] de NM fVdg, roiov-

t&v foiv xal trv N4 rov

d' msi, olov farlvi\NM sv&sicc

Toiovt&vv\IIP dsiy%"Yi o

^JTs A^, cog ds ^ NM agog 10

ryv TIP, ovr&s y NB XQOS rrjv ^77 [Eucl. VI, 1],

Kttl OLOV ago, rj N& sv&slu svog-, rotovzcov ^ [isv ^776rca o

fie Arj, Aomri ds % IIN tcov ccvr&v o id x/3.

Kal otcov farlv aoa 17 plv TIN sv&sta p 7, r\ds NM

sx rov XSVTQOV rye; 'yijg evdg, roiovrcw KOIv\ plv &TL 15

v fyyiGrcc, 17ds &N (ttrj 6%r].

i\iitv agu^ on, oiov 6rlvfj

IK rov xilv-

rgov ryg yrjs fvog, roiovr&v stirlv rb [isv ryg GsA.rjvqs

sv rccig 6vvyais [i0ov ccTto^ry^a v&, rb d rov j]Mov

jutfi,rb d' anb rov nevrgov ri}g yv\ ^X9 i tijs XOQV- 20

rov Ktovov r

1. o] o D, ut saepe. i6xtv\ comp. supra scr. D 2. 2.

7) (pr.)] supra scr. D 2. NM] renouat. D 2

. vrjv] supra scr. D 2.

H2] corr. ex Hr_D2

. 6. N@] N- in ras. D. 7. N4]JN, N e corr., D; 8v mg. D 2

. 8. OGL] corr. ex fif D 2. 9.

OLOV] corr. ex ov C 8. evos] post ras'. 1 litt. A. 10. i] (alt.)]

seq. ras. 1 litt. D. w^dp] ^ D. 11. nqog 12. N8] suprascr. D 2

. 12. #77] mg. D 2,IT D. 13. &?']

<?e' V- D. 16. cy]

6y D. c|7]] -T] corr. ex N C 2. 17. &$a J^LLV D. 18. lariV]

om. D, comp. JBD 2. cslrivri?] 6f- add. D 2

. 20. OGL\ &6t D,

fai D 2,act mg. D 2

. 21. 0|rJ] corr. ex |ij D 2.

tg'. Ilfol [isye&cbv rjMov xal Gfkijvrjg xal yijg.

Evxaravorjrog d' avr6&v yivzrui xal 6 r&v 6rQa)v

[iy&G)v AOJ>O ano rov rCbv diapdroav r\^Cov r xal

6hrjvr)g xal yfjg.

5 sjtsl yao dsdewtui piv, ort, OLOV vog eGtivijNM

lx rov xevrgov r^s yijg, roiovrcov BGrlv y [ifv &Hsx rov XZVXQOV rrlg af^vrjg o tf Ay, ^ $ N@ v&ta

%d t, l6nv ds uai, (bg r\N nobg H, ovr&g ^

itobg x^v 4F [Eucl. YI, 1], xcbv ccvr&v xal ri^g

10 $$i,'yiivr]g ya<?t l~o[iv xal rqv z/JT % rov XWTQOV

rov riUov r&v avr&v /.

r

fyyiGra' xal rcbv dift-

^ 01 avrol 6ovrai koyoi. &6T xai, OLOV 6xlv

lg 6krjvr]g didpfraog fVdg, roiovr&v xalf\ plv rr^g

fGrai, y xccl dvo TtsiiTtrcw fyyiGra,, 17df rov r\Mov

15 vq xal d TtepTtrov. r\ [iv rrjg yrlg aoa didîfroog rrjg

6A,r]viccxrlg XQiTtkaGittv 6rlv xal k'n rotg dv0l niyat-

roig [i%G)V) i\$ rov Y\ÎOV rrjg [lev tifhyviaxrlg oxrco-

xal h'ri rolg d Jtfyjtroig [iicov, rr]g

1. tg'] mg. AC, si B, om. D. nsQi yjfe] add. D 2. 2.

6 T&V] 6 t- absumpsit lac. pergam. D, xal 6 T&V OTSQZWVmg. D 2

. 4. %at] ins. D 2. y?)g] e corr. D 2

. 5. ot'ov] corr.

ex ov C 3,ex OGOV D. 7. Mg. o ^ 5t >ty D 2

- 8. r] corr. ex

p D, mg. l-tft' D 2. fWiv] comp. B; s- e corr., -v del. D 2

.

tif\v D. 9. TTJV] supra scr. D 2. 10. JKGI] /act B,

corr. ex &ort D 2. 12. orov] post -t- ras. 1 litt. A, -ov e

corr. D. 13. xca] om. B. 14. <Wo] B B. itepnTcov] E' B,

supra scr. D 2. 15.

<?]A D, corr. ex ij ABC. nîiTcov]

s' s B, e D, s" D 8. 16. T^tTrâorteov] corr. ex . TQinldcio] D 2

.

lartV] comp. B, -v eras. D. #rt] corr. ex fjrt D 2.

it- e corr. D, t-' s B. 18. d] mut. in TSTQGI D 2.

s's B, D, f' D 2. pe#o>v] A B, M D 2

.

itsvrankatii&v xccl ETI, rc5

xard ravrd d\ sjtsl xal 6 {lev djtb rov vbg xvfiog rov

ccvrov 6nv VO, 6 <T dnb r&v y tealft XSÎTCTCOV

avr&v k'yyiGra A-9*<?',

6 d' KTCO rcbv Irjxccl d

pofas ,$%y>d (1 zyytftcC) GvvijxTai, [Eucl. 5

XII7 18] JifitVi on xai) otov ev6g i<5tiv rb rife

6rQsbv iifysd-os, roioritcov sd-dv TO pv rye;

dr

,rb df rov r\Mov ,<5%[i8 {!

rccitA,tt6i,ov aQa, fyyiGra rb rov oÂtov rijg

it,'. TlEQi T&V xccra pEoog xccQaM.dt.E&v Âtov 10

xccl

Tovrcov roivvv ovr&g vTCOKEipsvcdv axokov&ov civ

stv\ itQOGcatodEiâi itukw 8ia j}Qct%Ea)v ,riva ccv rig

TQOitov EX rqg rCbv aTto^rrniccr&v itrjfaxorrjrog yMovT xccl GEktjvrjg xccl rag xccra [tEQog ccvr&v yivoiiEvccg 15

itccQCcMd&i'g sitikoytfôiro xccl xa&rov rag EJtl rov did

rov xard xoavcprjv 6r}[iEiov xal avr&v

6rc3<5av di v rc5 rov ftriEvov Efarov xvxhov

1. srt] corr. ex litl D 2. TW] corr. ex to C 2

.

-s- e corr. in scrib. A, r](ii6i {LSQSI D. [ii(av] M D, et

similiter saepius. 2. ravtd] mut. in ru ccvrd C 2,

rcc ccvtd D.

8'] Ss wi D, di D 2. xat] om. D. , 3. d'] 8s D, -g e

corr. D 2. ntpnimv'] is B, f" D, ut lin. 5. 5. ^zftd] ,s-

e corr. D 2. 6. ort xat] %ai ort D. SGTLV] comp. B, -v

del. D 2. 7. JffrtV] comp. B, -v eras. D. 8. g^ D, corr. D 2

.

O.QCC] corr. ex SKCcrovtaytcci,-' D 2

. 10. t'] mg. AC, t B, om. D.

14. TCOV] corr. ex r D 2. 15. avrwv] avr corr. ex ccvt D 2

.

16. dta TOV] om. D. 18. pvyfatov uMov] corr. ex ft KVD,

et similiter saepius.


6 [iV rrjs yijjs ndkiv [ifyitiTOS xvxhos o

o $ xaTa TOV ijAiov $ xv\v 68A,tjvrjv 6 -Tz/, Jt^bs ov

$ fj yr] 6r][itov koyov %i>) o EZH, xal x

Jtdvt&v TO K) fjds dia rcbv Kara xoQvcprjv

xal

TOV F Kara

trig T/i

cro

fav

10 VXV V7tOXi,[lVr]S &>

oicav 6Tlv 6 JTz/ xvxkog

'av {iv Jtd-

KJH xal %

$ TOV A15 JtaQdA.krjA.os plv ij^cs

TTJ KH i\ AZ,, xd&Tog d5

iit avTTjV 07A A.

TOiVVVILY] [18VOVTOS dfl TOV aVTOV

tl XaTQOV TG)V (fG)TG)V r\ [lV TtS^l TOV

60[ivrj dia TOVTO T&V naQaA.hd&cov

20 JtavTaitaGi, xal dvitai6&rjTog 6Tai rc5 xal Tr\v XXv-

TOV xvxAov avTov yuxQav dvai xal TO dno-

\iiyd, TJde Ttfgl Tr\v GfA.ijv'qv xal Ttdvv av

ysvoiTO aitiftviTri xal T^S XKTK TOV zitixvxkov xivrJ6G)s

avTi]is VXv xal Tilg avTov TOV fiuxvxkov xaTa TOV

25 XXVTQOV OV ^HlXQCiV TtOLOV^g 7CQtl Tag dtt06Td6l,g

diacpoyav xaTQas, Tag [ilv TOV VI^LOV

4. K] renouat. D 2. 5. KATE] A, corr. ex KFE D 2

,

xa r F BC. 8. FJ] corr. ex A D. 9. zoiovtmv] -i- corr.

ex o in scrib. C. 11. 6] add. A 1. 17. ale D. 19. TOVTO]

corr. ex TOV D, TtKQcdu&otv D. 25. iiiv.Qav~] -i- corr.

exTJ

A.

MAOHMATIKHS 2TNTASE&S E'. 429

l \JLQVQV TOV vbg hoyov dei%o[ieV) Afyco ds TOV

^i Ttgbg TO v, Tag $ rv\$

dfao'Ta fig tag f|^g (podovg

vcw. lhriq)a[iv 6s TK>V T6<5aQG)v TOVTGJV

{LKTCOV TtO&TCC [lV SvO TCC 'yiVO^lSVCC TOV 7tMVXkoV 5

MCCTCC TO CtTtOySlOTCCTOV TOV XXVTQOV TVy%aVOVTO KCil

TOVTCW 7tQOTQOV [lV TO p%Ql> TOV KltOyeiOV TOV B7U-

KVKkoV, O GwrplTKl 8iCC T&V JtQOCi1toddl,'y[lVG)V [p. 422, 7]

TOIOVTC3V |d 7, OI'OV 0Tlvfj

K TOV XVTQOV TJ]$ yf\

l/dg, $VTQOV d TO fl>%QI> TOV TCfQiyflOV TOV 7tl- 10

xvxhov (Swccyo^ifvov xal TOVTO T&V ccvT&v vy v

[p. 416, 5], TK dl koma dvo ywopwa TOV

XCCTK TO Tteoi'yfioTaTov TOV xxVTQovXCll TOVT&V df TtttklV 7tOOTOOV [lV TO [l^Ql TOV UTIO-

yLOV TOV 7tlXVK&OV GWCCyO^VOV dlK TK TtQOaTtodf- 15

deiyyilva [p. 416? 6] TOIOVTMV ]ny vy, oiov 6tlv ^

x TOV xwTQov T^g y^s fVo, dVToov de TO pfyQi

TOV TtQifyLOV TOV 7tMVXA.OV 0VVK'y6^lVOV KCtl CiVTO

T&V avT&v ty Ay.

Jtfl TOIVVV fjTA 7tQl(pat,Ct VTtOXMTCCl, [IOIQ&V A, 20

sli] av noil $1 VTtb FK4 yewtec,

oicov \iiv eltiw ai d

daftcd rj, TOIOVT&V A, oicw d' KI dvo oa&al T|, TOI-

OVTG)V f. &6TG KK\1] [lV 1tl T^g AA 3tQl,(pQia

TOIOVTG)V 6TLV,

OLG)V 6 7t()l TO AKA

1. S\ corr. ex <fy' D 2. 2. KGL] ac i A, &GL D, fai D

2.

sv\ BC^D, sv AC. 6. xara] post ras. 1 litt. D, infra %-

add. ^ A. 7. Mg. a BCD 2. itQo-cv A. 10. Mg. u

BCD 2. rov (alt.) 18. negtyfiov] bis D. 12. dvo] 3vo rd D

utroque loco. 14. y mg. D 2. rov] corr. ex ro C 2

. 15.

TiQodsdfLyntvcc B. 16. ol'ov] -i- in ras. C. 17. d mg. D 2.

dsv\

dfvreQOV D priore loco. 22. roiovroav ri-] supra

scr. D 2. $'] 8s D 8

. dvo] p BD 2.

KVKlog r\, ijd' iitl t% KA rav Aout&v [Eucl. Ill, 31]

sis t<> flpiKVKkiov ~QK. Kal TGJV vit avrag aga v-

r\ [ilv AA roiovr&v 6rai f, OLCOV 6rlvr\AK

QOs ptt, fjd K4 r v ccvrcbv ~gy v. KOI oiov

5 CCQCC 6rlvi\AK vos, toiovtcov xal

fj pv AA sGtat,

o A, i5$ KA evftsia, o

vfi. rcbv d' avrcbv 6Tiv xal

f\KA4 V&tCC iltl [lV tOV fjAlCiXOV

/ o^Z, ml $ rcbv tifhyviaxcbv teara [iv rbv

OQOV |d 7, xccra $ TOV dvtQov vy v, Kara dl tbv

10 rgitov ^/y vy, Kara $ rbv rdragrov ty ky xal homyccpa i] Ad, rovrstiriv ^ Ad, jtd adiayoQcp i6iv

avitioi, iitl [ilv rov fjfaaxov aTto^rtjâros k'tirat, a6&

^, 7tl de r&v 6^vLccx&v Kara [iv rbv nocbrov OQOV

fy Z^, Kara dl rbv vrQOv vfi vvj, Kara d rbv TQITOV15 jHy a, Kara dl rbv rtragrov A/3 pa. &6r Kai, oi&v

6rlv r\AA vitoreCvovGa OK, roiovr&v 6rai ^ AA

vnaxovo^vr}s^ iva ^ ravroôycb^v, rijg avrils

o/3v& Kal o vg v($ Kal a VTJ xal a ivy îa

Kal a v &' Kalrj pv 7t* avrri$ aga 7tQi,(pQi,a roi-

20 ovrcov k'Grai o/3 v Kal o vd Ij] Kal a d vd Kal a K

Kal aji fyyitira, OLCOV itirlv 6 7t$l rb dAA OQ&O-

yaviov KVK&OS T|, 17d' bitb A4B ywvia, TOVT&TIV

2. rîiY.vv.'kiov^ comp. macula obscur. D, corr. D 2,o n

mg. D 2.

5. A A} corr. ex Ad D. 6.J] seq. ras. 1 litt. D. d']

supra scr. D. 8. CCGI\ &ci D, t&ai D 2

,ut saepius. litl~\

-i

in ras. A. 9. de (pr.)] ins. D. 'Tor(pr.)] supra scr. D. vy]

corr. ex fiy D 2. 10. r^raprov] j seq. 1 litt. deleta D.

Ay (alt.)] e corr. D 2

^11. slew] ft- ins. D 2

. 12. aviaoi]-ot in ras. A. 13. OQCOV C. 17. TawcoHoy&iLfv] -o- pr. in

ras. C. 18. xca'(pr.)] om. BC. o (alt.)] o seq. ras; 2 litt. A.

xy] mut. in xa D 2,sed rursus corr.; xy mg. D 2

. 19. v -91

]

corr. ex v& A, ex vri& D 2. TtSQiytatia] comp. postea ins. D.

22. d"\ $t D.

v\vjtb ZA [Eucl. I, 29], OLCOV piv d6iv ai dvo OQ-

&al r|, roiovrov oft

v xal o vd TTJ xal a d vd xal

a x xal a |it, OLCOV d' ai d oo&al T|, roiovrcov o a x

xal o xt, -9- xccl o A/3 x xctl oji

o xai o vfi L &6r

sjtsl xal TO [isv A Grjiistov adiacpogst rov K XSVTQOV, 5

% de ZH& TteQiysQsicc adiucpoQG) [i%a)v 6rlv rijs Hdice rb rr}v yijv okqv 6r)[Liov Aoyov %sw TCQOS TOV

EZH& xvxkov, xccl % H rijg TtccQccMd&cog TtEQicpz-

oicov 6rlv 6 EZH xvxhog T|, rotovT&v enl

rov f}A.i,ccxov ayto^r^ccros Ititai o a x, iit\ dl 10

6A,r)VLCCXG)V XCCTK [lV TOV TtQ&XOV OQOV O X% ^,

xara d TOV devrsQov o A/3 xg, xccra $ rov rgurov o

ft o, xccra d$ rov rtragrov o vfi ~K' aitey 3tQOXi,To

rov avrbv d rgonov xal iiti r&v koiTt&v anoGra- 15

rov xara xogv(pr}v (ftftisfov rag yivoîdv

Zxatirov OQOV 3taQaMd,i,s ^Lôy^d^voi, dta

g ti%Qi> roov rov rttagrrjiioQiov {IOIQ&V 9

xavova Jtgbs rag bucxQitistg r&v itaQakka^s&v 7tl

t, 6Mdia $ ^, obv v [iv ro5 20

rag rov rraQrrîo^Cov [toiQag 9

1. dvo] B B. 2. o vd ITJ] corr. ex ov 81, (i in ras.) r\ D,

et similiter saepe. 3. T|] supra scr. D. 4. o (sec.)] in

ras. A. o (quart.)] eras. D. 5. ccdicicpoQei] corr. ex dia-

cpoQSL D. 6. adiacpOQco] corr. ex dicccpOQOJ C 2D 2. JortV]

comp. B, -v del. D 2. 7. G^SIOV'] cg D, ^p D 2

,et similiter

saepe. Tcgog] fl D, ut alibi. 8. H~\ N B. 10. IWca]

1<J B. 13. &7t8Q nqoiv-sito ditâi] D 2,

:r>j D, supra add.

(uel OTtfp) I'det dftiat D 2. 17. Ttaââ^ts D, corr. D 2

.

18. rcbv] om. C. Tfra^TTjôt^tov D, corr. D 2. SisyQutyev C,

corr. C 2. 19. xavovia C. 20. ncd.iv\ om. D. 21. 9] corr.

ex b<? C 2.

dia dvo drjAovori, xv\v TtaQav^rjGiv avrcbv

iv ds ro5 dvrQG) ra impdkkovr

^rjxo6rd r&v j]faaKcbv itaQaMd%(ov ,iv de r&

rag xara rbv itQ&rov OQOV ryg GEh

5 iv $ r<p retaQtcp rag vjtQo%ag r&v TOV

OQOV JtCCQCchkd&MV ItCCQCC TKQ TOV JT^COTOV, V $ TG)

rag Kara rbv rQirov OQOV 3rapaAAag, iv de

rag VTteQo%a$ T&V rov TMKQTOV OQOV TCCCQK^-

itKQa rag rov tQirov, oiov &g 7tl t^g x&v A

10 ILOLQ&V 7taQa&6G)g ra o a K rov Ât'ov, 7ti,ra |^g

ra o K & rov TtQ&rov OQOV rrjg GfA.tjvrjg xal f^g ra

o t^, oig vitQ%i 6 dvrQog OQog rbv jtQcbrov,

ira Tiochiv ra, o^L rov rQirov OQOV KCCI flijg ret o

t/3 A,

olg vitQ%i xal 6 rraQrog OQog rbv rQirov. VXv15 d rov xal rag iv rotg iira%v rcbv anoyCc3V xal r&v

KBQiysi&v a7to0rt]îa6i 7taQaM.d%i,g avahoyog rolg xara

[iQog r[nj[jia<ji,v dnb r&v Kara rovg MXfipwovg ti(5-

GaQag OQOvg itQo%iQcog {i&odvi,v dia rr^g r&v

xotfr&v jtaQa&(5G)g ra Aoma Îv rQia 6kidia

20 i^Tcrai JtQog ri\v 7taQa&6i,v r&v roiovr&v diacpoQ&v,

2. IxaffTco] |a

(|4 D 2) stidcrcp D. r^fiari] T[ir][idTG>v D,

T(OV D 2. 3. S^TJKOGTCI xwv] om. D. TW r^troa] rwt

D, t- eras. 9. -tgixov] T' B, y D. oiow CD, corr. D 2.

om. B. rcbv I] corr. ex ^ D 2. 10. rd] supra scr. D.

Post STtsiTa del. TC D 2. e&jg] inut. in |f ? D 2

. 1 1 . ra (pr.)]

iav.f? D 2.del. D 2

. Mg. ra o a. xs D 2. 0e^7jV7]g] corr. ex G^r]viav.fj?

12. dtvTfôg] corr. ex ^ D 2. OQOS TOV TIQ&TOV] corr. ex

rov a D 2. 13.

ft]corr. ex jto D. TOV] corr. ex TO D 2

.

rgCrov] y D, ut saepe. |r?s rd] || B, f^rjxoffra C. 14.

rov] corr. ex TOV D 2. 15. |u.Tav] comp. D, corr. D 2

,ut

saepius. 16. anoGrripaGiv D, -v eras. Supra avcdoyws scr.

ov D 2. 17. TWV] T D,

vadd. D 2

. lisi^svovg C,

vov? D. 18. f^rjTtoffTwv] || BD 2, | D, ut saepius.

MA0HMATIKHS STNTASESS E'. 433

XCCi CCVT&V TOV 7tt-

TOV

BH

TQOTtOV TOVTOV.

GTG) yao 6 6e-

7tol xdvTQOV TO JB, TO $

TOV diCC {1<5G)V TG)V %O)diG)V

xccl Tr}g yfjg XVTOOV TO

AE4Z dt^O-to ^ ZF5, 10

Xdl 7tV%&G)6CClT BE xccl

1} FE,Guv itl TJJV AdTOV B

f}B H, ano

d TOV Ffj Fid, XCCI V7CO- 15

TtQGOTOVr\

AB 3lQl(p, ^

0TG)6a TOV XCCTCC TO AaxQi/Sovg xccl agog TO Z

KBVTQOV &G)QOV[lVOV CCTtO- 20

ysiov [loio&v Aoyov VXVOIHJCCV I",

G3<JT XCcl TJJV VTtO

BEH ycovCav, oiojv [iv101V CCi d OOd'Ccl T%, TOi-

OVT&V LVCCi 1, OiCOV d' CCI 25

/3OQ&Ccl T|, TOIOVTOV QX^

XCcl diCC TOVTO TT]V [LV

TOiOVTCOV yCv<5&ttl OX, OiCOV

1. oov] supra scr. D. 12. xa-foroi ds ij^&coaav'] v.ccl

D. 25. elvat] in ras. B. 28. yivsa&ai] corr. ex

edrlv o nsol TO BEH oQ&oycDviov xvxhog T%, rv\v d' enl

Trig EH TCOV AOLTC&V [Eucl. Ill, 31] sis TO rj^ixvxhov .

xal T&V V7toTivov6G)v aga avTag sv&ei&v ^ pv BH6Tai, TOLOVTOV (Vy VS, o'lOV 6TiV

fjEB dldflSTQOg ^

5 r\ds EH TOV avTov f. AA' OTav TO E XSVTOOV rov

tl TOV CMOySlOV fjTOV ZXX8VTQOV, A.6yog 0TLV

ZE yfQog TVJV EB 6 T&V % ngbg TK T' xal oi&v

6Tiv fjEB sv&sta LS, TOIOVTCOV xal

fj [iv BHfarcci d Ay, r\

de EH ev&sia ~0 A^, ^ $ HEZ oAi?

10 |/3 Ar?. xal itl TO aito trijg ZH [iTa TOV anb Ti^g

HB itoi,i TO ditb 1% ZB [Eucl. I7 47], h'tiTai xccl amy

TOIOVTG)V %fl JU/J7,O

f

lOV 0TIV TO [lV ZA TOV TtQ&TOV

OQOV CCTtOGTrjlLCC |f Zf, TO d$ Z^t TOV dVTOOV OQOV

vd'pf,

TO d A/l didyoQOV T^g T&V dvo TOVTCOV

15 V7tQO%ilg ~i A. xal TO xaTa TO B &QK didtpoaov

TOV TtQ&TOV OQOV TOLOVTOV 0TiV ft f, OiG)V oAoV TO

didyoQOV ~i A' co6T xa^ oi&v fatlv TO ohov didyogov

1, TOLOVTKtV (5TKl Xal TO TOTS dld(pOQOV id O. TttVTK

uoa 7caQad"t]6o^v sv T& % <?fAidtc? rc5 ^rt%C3 TW TISQIB-

20 %OVTl TO iJlllGV TOV T&V | KQi&llOV, TOVT<5Tl,V

Tolg A, dt TO xal oAag Tag xxsi,^vag v TK>

1. d'] 6*8 B. 4. di.d[iTQos] comp. in ras. D 2. 5.

mg. C. 6. 77] corr. ex j]v D 2. IGTLV] comp. B, -v eras.

7. EB] corr. ex ES C 2, tJ3"mg. C 2

. 9. EH] HE D."J3

"

plri AC. 10. TOV &7to] post ras. 6 litt. D, -v a.- e corr. 12.

icTiv'] comp. B, -v eras. D. 15. rl] corr. ex Tj A. 16. TOV]

corr. ex ro D 2. TOLOVTOOV] corr. ex Trotovvrcov D. SGTIV]

comp. B, -v eras. D. 17. I] corr. ex 4 A. ro olov] 67ov

ro D. 20. rovrf'dri^] comp. B, -v eras. D. 21.

a BD.

rov xavovog 9 [101001$ TO %u<?t> 7tQi%LV r&v

Kitb rov A inl rb 4 [IOIQ&V ~Q%.

xara ra avra de, xav r^v .Tz/ 7tQi<pdQiav vito-

ftcctusd'cc r&v avrcov, ^ $v F dsiffiijtietai, roiov-

rcov d ky, oiwv 6rivfjEP en rov nsvrQov ~s Ts^ i\

5

ds E@ biotas ft Ii?, toutti dsr]Z r&v avr&v v

%/}' xal dia ra ccvra 17ZJT vnorsivovGa v Ay. aitso

dAiv catb r&v rov Ttacbrov ooov %s Is ra

p/} svQTJGonsv %rjxo0ra ovra rov oAov diacpo-

oov ^d o- a xal avra 3tccQad"tJ6o[iv iv r& avrcp 6- 10

Aidtcj Ttgbs r& r&v | aptttytcd dice rb xal rqv ABF7tQiy>Qi,av fivai {lOiocbv ^w,.

TtdklV VJtOXl[lVG)V r&V aVT&V 7tQHpQ(,G)V V0l-

6&G) rb E xvraov inl rov itSQiysiov rov XXvrQov,XCC& V &0LV T rQlTOS OQOg 7tQl,%Tai, XCtl 6 T- 15

raorog. Jfd ovv xara rqv roicivrrjv frfaiv Aoyog

6rlv rrls ZE Ttgbg rr\v EB b r&v \ Jtobg ra y, xal

olov CCQCC fjBE yivtrai r\, 6vva%&ri<5ertti, KOI xccroa

yisv r&v BH xal F vd~iS)v^ orccv xal xarQK r&v

AB Koi Pz/ yrOi(pOicjv | {loiativ vTCOKBrircci^ roiov- 20

1. rt^LGv] mg. D 2

, t> D, [_ D 2,ut saepius. 7tQii%u D,

sed corr. t&v] bis D, corr. D 2. 2. A] akcpcc AC. Q7t] corr.

ex QN D 2. 5. $ ty] B, corr. ex Lty D^^y AC. 6. E

] corr._exE2 D 2

. 6(ioi<og~] corr. ex o D 2. ZTJ] corr. ex Jr\ D 2

. i/J]

corr. ex f D 2. 7. ZF] Z- corr. ex F in scrib. C, TZ B.

8. aqpf^ovTfff] -16- e corr. D 2. 11. n^os] om. D.

ins. in ras. 1 litt. D 2. 12. dvai\ om. D. Post

ins. ~ D 2. px] Q- ins. D. 13. K mg. A. 14. TO] TOO A.

E] in ras. D 2. 17. ltnv] comp. B, -v eras. D. 18.

corr. ex F D 2,ut saepius. 20. KCCI] om. D. vno-

D, ante t ras.

rov g vg, olcov e<5rlvi\ZE sv&elcc |, xaroa $ r&v

EH xal E r&v avrcbv 8 o- &6r xal rijg plv ZHyivousvys rcov avrCbv <?, -rijfg

ds Z bjioicos vg, dia

roc avra xal xv\v {isv ZB vjtoTivov6av

5 %d %y, tr\v dl ZP roiovrcov v$ scg, OLOV

rov rgfaov OQOV ^ ZA ev&eia %rj, % ds rov rov TQL-

TOV TCQOS rbv reraQtov diacpogov *YIAd sv&sicc tg.

sav [isv KQCC ra |d ocy cupeA&nsv anb TCOV |^

fotipfhfosTffi f][jilv y Af, artsy rcbv tg TOV oAov

10 901; efyxoGta yivo^isvcc 1/y Ay T

TO) rcbv A aQi&{i(j) iv rep oydoq) 6'skid LG). E<XV de ra

v$ K$ dcpA,G)[iv anb r&v avr&v

~ia A^, a xal ccvra r&v Ig rov o'Aov diacpogov

yivQptva, \iy xd jtccQcc&rjdoiLSv O^LOLOS rq) r&v a

15 v TW KvrG) 6ydOK) (jfAt^tw.

ra v ovv dia xrt iv r

rovrov

rov rooitov xr&iJ6rai,) ra ds dia rqv avrov

rov Bnixvxhov xara rbv xxvrQov ndoodov

20 <?ofti> ovr&$.

6t(D ydo 6 xxvrQo$ rrls G^tfvrjs xvxhos 6

1. g] S 4 B. 2. EH xat] HE e corr. D 2. E&] seq. ras. 1

litt., E- e corr. D 2. 3. o^ot'wg] corr. ex |Vl D 2

, mg. ofiotcog D 2.

6. rov TOV] scrips!, roi) ABCD. 8. ra] supra scr. D 2.

xara^ftqpO-Tfcfrat] -^tt- corr. ex dw D 2. 9. roi)] corr. ex

TO D 2. 10. iy iy] in ras. D 2

. 11. I apt^w] supra scr. D 2,

infra est ras. 3 litt. 12. v$\ corr. ex re in scrib. A. 13.

corr. ex H D 2. 14. ofiot'cos] comp. D, corr. D 2

. f a^fO-f

corr. ex 1? D 2. 15. avrw] om. D. 18. avtov] om. D.

19. tTrtxvxP.ov] post -t- del. nedov? D. 21. ABTJ]AEP C.

MA0HMATIKHS STNTASE.QS E'. 437

xvx-

7tol Kvroov rb E Kal did^roov rv\v AEF,vositi&G) rb Kvroov rov dice [ifawv r&v

Aov TO Z, Kal dia%&i6r]<:; ri\g BZ4 v

KarQcc r&v vjtb AZB KCCL JTZz/ y&vi&v roiovrcov

,otwv efalv aC d ooftal T|, ortQ ^v^ccLvei rri$ cbro- 5

?,orav nv iitl rov B y rb Kvroov rov sjtiKvxkov,

V7tCCQXOV<Srl$) rav $' 1*1 rOV ^/, [lOlQ&V ^K.

Kal S7tit> V%&l<5G)V r&V

Kal E4 xd&roganb rov E jtl r^v 10

fi EH.roCvvv

r\vitb

BZA ycwtcc roiovr&v

0rlv o%, OLCDV ai/3 6^-

T|, ty av Kalfj

15

7tl Tij? EH 7CQi(p-

BE

QSLK roiovrcov x

farlv 6 XQl rb EZH

TO

d' M rrjs ZH r&v Kout&v [Eucl. Ill, 31] i? 20

v I' xal r&v viz avras Kocc zv&si&vi]

1. Sidpfrgov] corr. ex ^ D 2,

ut saepius. 2. Supra vo-

add. f^V^co D 2. 4. AZB] corr. ex BZA D 2

. FZJ]corr. ex FZA D 2

. ycovw5i>] corr. ex ycovfa D 2. 5. 60<9m']

supra scr. D 2. 6. ^] corr. ex r\v D. 7. I] corr. ex a in scrib. C.

9. %ca] oin. D, comp. mg. D 2. E4] corr. ex E^f D 2

. xatff-

ros] corr. ex T D 2. 11. BZz/] in ras. A 1

.i] EH] add. A 1

.

12. ITTFI] corr. ex inl A. 14. at] t^fflv at D. 18.

J<mV] corr. ex stair D 2. 20. ^' ITU] ^a Ttf^t D, ^s

litt D 2, 19 d

j

Iwt mg. D 2. 21. >tat] om. D (macula obscu-

ratum?).

[iv EH 0TaL TOIOVTGOV Qy vl, oiwv sGrlvf)EZ

v7toTLvov6a px, fjds HZ T&V CCVT&V |. &6T xcct,

o'icov 6tlvf) iilv EZ iisra%v T&V XSVTQ&V 7 #,

^ (f X TOV KSVTQOV TOV XXVTQOV [& JLUX, TOl-

5 OVTWV i(frai xalfj per EH ev&sta y vg, ^ df Zff

T&V avrcbv 7i 7. âl exel TO KTCO Tys BE hsltyccv

TO KTtb Trig EH 7t0i t anb T^S BH [Eucl. I, 47],

SGTCCI, xal exaTBQK [Eucl. Ill, 3] T&V BHxal AH t&v

KVTC3VÎ/rj wy' KHSTS xal oA^ {lev r\

ZB TOIOVT&V i<5t\v

10 vd y, olcov IGTIV % [isv ZA r&v itQ&T&v OQCW ^, v\

ds ZF T&V dsvTSQ&v OQCOV A-01

Kfi) rjd' v7tQO%r) av-

T&V K A^, AoiTtr] dfj

Zz/ T&V KVT&V ^/y jtZy.7td

OVV TK I T&V [lV V$ y V7tQ%Sl v, CC7tQ TG)V X A^

TOV o'Aov dicccpdoov ^xo6Ta yCvsTai, i^ !/rj,T&V d

15 Ijiy [iy Tolg 7g tj? KTISQ xccl ccvTa TCOV K A^ t,r]xo6TK

yi'vTai, {i xa, ra ^v tf 7^ dÂovdrt xaQOCJhltiopev v

T& vaTG) êAtdtcj TOO T&V A KQi&iup Tvjg ajro^g, ra

df fij jftt TG> T&V ^3C, TOVT0Tl,V TtdklV TCS T&V | dttt

TO tfpos Tatg 9 ovro^ roi) TtzgiyeCov i<Sodvvccîv XCCTOC

20 TO KTtOGTrilLtt TYjV T&V 1 aTtO^V Tfi T&V ~QX.

1. py] in ras. C. EZ] -Z in reparat. D 2. 3.

corr. ex H0 D 2. 4. 5' x] de|x A, ds\t* A 1

.

TtfcVrov C. 5. ftftca] (7^ D, -v del. D 2. 6. BE] EB D.

8. BH 9. ccvr&v] om. A, BH H4 mg. A 4. 9.

jZrj] corr.

ex (I7r C. olrj] -A- e corr. A. 19] supra scr. D. ^rtV]

comp. JB, <'D. 10. Z^] ZHJD. |" 20. px] mg. D 2. 11.

ZT] corr. ex ^P A. Ante Hd- del. Toto-yrcov D 2. 12. ZJ]

corr. ex Zz/H C 2,J Z D 2

. 13. ovv] comp. ins. C 2. 15. fly (alt.)]

supra scr. C 2. ansg v.ai~\ supra scr. D 2

,KKI etiam in textu.

16. iv] ins. D 2. 17. î/arw] AC, $ BD 2

. 18. waiterw] A,

cornp. BC, r;'rot D 2, supra scr. yg. r

f D 2. 19. -tuts] 9 D 2

,/' supra

scr. D 2. 6Wog] -TOS supra scr. D 2

.

MA0HMATIKHS 2TNTASE&Z E'. 439

TOV KVTOV dfj TQOJtOV XCcl 7tl TG)V akhcOV 7tQL-

ra ywopsva sfyxoGTa r&v diatpogcbv iiti-

Kara rag>

xzsd'i,[i8vcc$ TQSIS vrtQO%<xs

7tl

TG)V V TG) XKVQVl KQl&[lO)V filCt TO KCCl Xtt CCTtO t&V 5

7tl TK 7tQiyLa polkas ^7t TtQOs talg rov

c, [loiQcug KTtagxi&Gftm, Jtags^'na^sv (p'

TG)V

dice

- 10

ra

tit avr&v rcbv

r&v dia rotiovrov

7tl r&v QrjxoGr&vW. xaC itinv 6 xccvav 15

Na

Y.U- mg. A 1.

comp. AC, corr. ex

e corr. D 2.

2. yn/d^fva] yiaD, et similiter saepius.

-craft- corr. ex Gaiy, D 2. 4. T^Tjftara 5. nuv6vi\

5. &Qi&ii(bv\ corr. ex g D 2. 6.

D 2. gn] corr. ex QN D 2

.

9. [IVZOL] corr. ex ftfWoo D 2.

D, 8- e corr.; mg. y(>. s<x(jiOi-

D 2. 12. yivo(isvr]s aîoloyov D. 14. vnsgo^&v] in

-Q- inc. fol. 117V B. fiijrs D.

OVTOS add. B fol. 117V :

îrjrs D. 16. Post roi-

v.a.1 tnl T&V 8C ccvr&v xat TOV

a'. 01 Hoivoi ccQi&noi ot sv TOO a. OEhiSifp inl [lev TOV B*a! r J f Z cefodLov nQi%o<vGi Tag WQIGKOHEVCCS &v TO> B ctU-

diat TOV T&V ycovi&v navovog lâffrotf sni TOV KCITO. KOQvcpi]v ini

rbv TJI.IOV T) Tj]v G&r\VT\v otxfi'ooff 7fQL(pQeLccg T&V di' KVT&v yqcc-

cpO[iva)V


snl de rov'

nal rj

f

GsUStov rag anb rov angifiovg

anoysCov rov sniY.vY.kov snl rb Y.svrgov rfjg tff/bjvrjg i}u,iGsiag

polgag :

snl ds rov -91

'

Gski8ov rag rfjg pici^g &no%f]g [loigag rfjg

Gslr\vr\s tfroi anb rov fjMov 7}rov Kara Sidpsrgov avrov Kara

rr\v syyvrsguv SidcraGiv :

B. 5rorpaHa|ftg ^Mov inl rov diu rov nuru xogvcpriv ncti

rov nivrgov rov rjMov yQCCfpopsvov ptyiGrov Kvyikov :

T. rov GTtwvY.'kov rfjg Gefajwrig uccra rb anoyeiorarov rov

iwsvrgov ovrog v.a\ rfjg ce^vrjs nccra rb anoytiov rov sitiY.vKl.ov

ovarjg TCKQKMct&Lg lit\ rov diet rov Kara. xoQvcprjv cr]îtov v.ai

rov yiivrqov rrjg Grtrjvrjg yQcccpopevov [isyicrov *v*%ov :

A. rov 7iLHvy.l,ov rfjg Gfhijvrig sni rov anoysiov rov

ovrog, rfig Ss Gf^vrjg Inl (rov eras.) TttQiytlov rov

ovGiqg, r&v ywopivcov rfjg G&r\vr]g naQaM.df(ov naga rag T

ijrot rag anb rov anoyBLOv vnQO%dg :

E. rov iTtwvnkov ri}g ce^vr]g enl rov ireQiysiov rov

rgov bvrog, rfjg ds G6î]VT]g Inl rov anoyeiov rov

g. rov 7tiKvy.l.ov inl rov Ttsqiysiov rov iy.y.ivrQOv bvrog,

rfjg Ss G^vr]g enl rov neqiyBtov rov smy.vY.'kov,r&v yivo-

[itvcov 7taQuM.d,(ov viiSQO%ag Ttgbg rag rov rgirov OQOV nag-

Z. rov tiiiy.vy.'kov rijg Gtlijvrig Kara rov anoyeiov rov

uivrgov bvrog, rfjg de GfX^V7]g ptra^v rov anoystov v.al

yeiov rov fitwvKlov ovGr\g, diayoQai r&v roiovrtov anoGrr]-

[idrcov rrjg Gf^tjvrjg ngbg rb peyicrov ccnocrrjfia, ol'mv ecrlv

T] rov [ifyLGrov anoGr^fjiKrog ngbg rb &d%iGrov v7tBQO%T] f rl'

H. rov iniY.vv.\ov ri]g GS^vrig Kara rov nsgiysiov rov SK-

ovGr\g, ri]g 8s Gsl.r\vj\s inl ra [lera^v rov anoytiov noi

rov STtiy.vY.kov ovGrjg, diacpogai r&v inl rf]g roLavrr\g

nagodov rfjg Gf^vr^g anoGrrîdrcov nqbg rb snl rfjg rov nsgi-

ysiov rov SKKSvrgov ftscscag rov iniY.vY.7.ov psyiGrov

ol'cov scrlv i- T) rov psyfarov ccTtoGrrjfiarog snl rfjg

ftsGstog rov sniKVY-'kov ngbg rb s7.d%iGrov dnoGTriîa Siacpoga

ovca :

MA0HMAT1KHS 2TNTASE&2 E'. 441

&. TOV STtiy.vY.'kov rf]g 6li]vr]s snl T&V peTa^v irccgodav OVTOS

rov anoysiov v.a.1 itSQLyeiov TOV KKVTQOV diatpoQtxl xo*v yivo-

[tsvcav UTioGTrjiicizav snl T&V st^rifisvcov [isrcc^v nagodcov rov

STtlV.VY,l,QV TtQOg TO TOV KY.ivtQQV KCLtO. TO K7t6yLOV CCVtOV

GTOV anoGTTHLU, oRov IGTLV r) v7tQO%r) TOV psyiGTOv

fiaTOff TOV IY.V.VTQOV TtQog TO &d%i6TOV CCVTOV anoGTripK ?c "kr\'

OVGCC : (des. fol. 117V).

tn^OX^K-

X

*x:

-<

5i

cy5S

^>-3St

a^

442

Tl

MA0HMATIKH2 STNTAgE.QS E'. 443

SfW

i-f i i. i if^r^ri 11

,-V o*S-5-x3SS 53 ?<" .

baaaaaaaeaaa

DOC 000

ite-lfejiiSJIIPISlsll

ooooooooo

>! s- o '>5_\<^> i/> a--

|JJ/. O O O O

-s

<'~3;^5p< Si^ '3.

<! i^:c>*' ^ fl ^= ^.

S IHii r.

yg rcbv itaaaA.A.d&cov di,axai6G)g.

f

'Orav ovv TtQoaiQ&yisQ'a, hapfiavsiV) noGovf] Gshijvr]

xa& xa6rrjv r&v naoodcov 7taoaAka66i, nacbrov eni

rov di ccvtijg xal rov xara xoovcpyv 6r]{iiov yaacpo-

5 [ifvov peyitirov xvxkov, 7U6xil>6[id'a, tt60a$ farjpsQL-

catfysi, rov [leGrjiiflQivov Kara rb V7toxi[ivov

xal rag VQ&foas ffawfyxovrfs ig rov r&v

y&vi&v KKVOVK rov ofasCov xMparos xal rov

dodeKarrîOQiov rag 7taoaxi,[ivas ry &Q10 rd5 dfvrQG) GffadiG)

7} oha$ ^ rag 7H,â^

[iQi, rrjg aoag f|oftv, ag K7tt%si rov xara

6r){iiov i\ 6krjvr] 7tl rov di avr&v yQayo

yfarov xvxkov, ag i6Vyx6vrg fig rov r&v Tt

kd&av uavova 6xty6iid'a.>xara Ttoiov 6n Grfyov

15 rov tto&rov Gekidiov, xal ra 7taoaxcîva rc5 aQt,&iiG)

v rotg cp%rig [ira rb r&v fihiax&v 7taoa^d^G)v

r66ao6i, skidVotg ,rovr<5nv r& r y' xal r& d' xal

rd)f

xal r& $\ X^Q^S xa6rov aTtoyoaôîâ' 7tira

rbv xar' Xtvrjv rqv coaav diaxexQiîBvov ri]g avco-

20 [laMag aaL&iibv nobg rb axoifog anoysiov hafiovrfg rj

avrbv ^, lav vjtfQTtiJtrr] rag ^t iLOioag, rbv fainovra

1. i-O1

'] C, &L B, om. AD. SICCKQIGSCOS] SmcpOQ&s D. 2.

iQ03{ie'Q'K] corr. ex TtgocaQOVfif^cc D 2. [email protected] iv ] GY.O-

D, yg. kct[ificcv" mg. D 2. TCOGOV] bis D, corr. D 2

. 3.

. 4. criptLov] supra scr. D 2. 8. ofasi'ov (alt.)]

-- ins. A. 11. xi]g] corr. ex rccs C 2. 12. di' avr&v] corr.

ex dia. r&v D. 14. navivas D, sed -g eras. 15. c^tofyiw]

g"* D, q D 2, mg. KQL&IKO D 2

. 16. TO] add. C 2. 17. TOVT-

6Ti D, comp. B. 18. ^TTftra] corr. ex EHITK in scrib. A.

19. tov\x5>v C. 20. KQiftpov] sov

D, et similiter saepe.21. rag Qn] TCC CQTC C. Supra" rov add. a D 2

.

ig rag r% TO rîiGv Jtdvrors rcbv ovrcog

i0Vyx6vrg eig Tovg avrovg doi&iiovg 6x-

a, notice ^rjxotird icaQaKZirai ro5 aoi&iHp x&glg'

xalv\ oÂtdtG), xal o6a yfsv av v TGJ %

Q&f}, TK ro6avTa %rjxo6Ta 2,afl6vrg rov 5

sv rc3 d' GfhdiG) dioxpogov 7tQo6&ri<50[iv aid Tr} rov

TOLTOV Gskidiov 7taQaMd%i,, o6a d' av v rco r\<5z-

ra rodavra Qrjxotira Aaflovrfs rov iv

diayooov 7too6&ri6o[iv aiei rtdhiv rfj

rovf

(3îdiov TtaQttkkd&i nal r&v ovrog ysvoîBvcov 10

dvo 7taQaA,A.d,G)v xd"rj06^â ir\v vTtSQOj^v î]g $

&apovrg, o6ag UTtiisi {leGcog r\ <3A.ijvr] {loiQag r\roi rijg

rihianrig 7} rr^g ravrrjv dia[jirQOv6iig Kara %v\v iyyvri-

oav bnorsQag avrcov didtiratitv^ i60L6o[iv xal ravrag

fig rovg v r& a 6kidC(p doL^ôvg^ xal o6a av 15

ai, itaûv QrjxoGra v r<p &' xal

ra rotiavra ^xo6rd hafiovrfg, rjg

rcov dvo TtaQahkaÊ&v VTCô^g^ ra yevopwa 7t

60[iv atel rt] ha66ovi,) rovretinv ry x rov y' xal

6' tifkidiov diaxxoiiivr]) xal ra 6vva%&vra ,o(iv, 20

a 7taQakkdo'6i, 3] Gfkrjvr] 7tl rov di? avri]g xal TOV

%ara xogvcprjv 6r]{iiov yQacpoîsvo

avr6d'v artkcbg xal

1. rag] corr. ex td\ D 2. r^] e corr. D 2

. Travrort] -v-

e corr. D 2. 2. iGe\vyv.6vTSs A 1

, 6ia|fi;fyxdvrfff A. 4. rf]

supra scr. D 2. 5. ia^dvovres D, corr. mg. D 2

. 6. ctki-

Stuv B. 7. TQLTOV] 7 BD. aelidfov] supra scr. D.7;']

dydoco C. 8. ra] supra scr. D 2. 10. ovr(o>| D. 12. TJTOI]

Om. B. 15. a:'] Trpcbroot C. sdv] &v BD. 16. Ttagd-

D. jraltv] supra scr. D 2,ndhv C. csfodLo) KCU

oD. 17. /La^tovrfg A. 18. ywopsva D, corr. D 2

.

19. lld.G6ovC\ corr. ex g mg. D 2. TOVXSGXLV\ comp. B, -v

del. D. 21. jraeodaget D, corr. D 2.

Kara rqv bpoiav &6iv f'vfxa rcov

fx rcbv iv rc5/3' tiehdiG)

rfj TtrjAlXOrrjri, rfjg djtO TOV KCtrK XOQVCpYjV

5 Lva ovv xal rqv xobg rbv dia {isG&v rcov

rots yivojisvrjv TtaQKhkafciv diaxQivoyiSv Kara rs [ifjxo$

xal Kara nhdros, rag ccvrag xdfav far)[iQiva$

&S aitfysi, rov [iftiypfigLVOV % 6hijvr]

sis TO VTO [ifyos rov r&v ywvi&v xavovos iti(5K-

10 il>6[id-a rs xaQaxi,[ivas r& apt-fruca r&v &Q&V ftot-

gaS) av plv TtQO rov n<5rnifiQivov fj % ^fA^V^, rag

iv ro5 y' tiehditp) av d [ira rov [isGrjupQivov, rag

sv r& d\ xav yiv dvrbg r&v Q poiQ&v &6w^ avrag

ajtO'yQaip6{id'a) iav d' VTISQ rag 9, rag tentovtiag ig

15 rag ^Mt' roGovrcov yap k'tiraii\

ka66G)v rcbv itsgl rr\v

KKL^Lvriv ropfjv ycovi&V) OL&Vj] fiia 6od"?i 9. rag

a7tO'y'yQa[i[ivag ovv poiQag diTtk&Gavrsg sfaofaopEv

fig rb r&v iv xvxhG) SV&M&V xavoviov avrdg rs xal

rag ksntovtiag lg rag ^JT, xal bv av %r] Aoyov rj rrjv

20 r&v dfdiTthioiiw&v poiQcbv itai(pQiav vitorsivovGa

vd-ta Ttobg r^v vitoruvovGav r^v teiitovtiav fig rb

v,

rovrov | rbv Aoyov ^ xarcc itkdrog

g nobg xr\v xara ^tijxog, f7tfi,drJ7to ai xr^'ki-

1. fVtxfv D. 2. iv] s A. 5. iitccov] corr. ex jwf'dca D_2

.

7. Kara] om. D. 9. ycovi&v~] corr. ex yco^ico A 4. 11. ??]

corr. ex T\V D 2. 14. a.TtsyQutydyisQ'cx. B. d

J

] $s D. VTZSQ] -E-

e o6rr. C. 15. git] Q7t polgctg D, -n e corr. D 2. sldcoav]

I D, corr. D 2 et in mg. 16. Post ofav add. av D 2,sed del.

17. flaoico^isv diTtiwcccvreg D. 18. x-yxAra] nv D. 19. avcorr. ex &it%'fl D 2

. 20. vnoTftvovcas fv&tias D, sed

corr. 21. rag Hfinovcas D. 22. r}pwvKhov~] o_ D, dcorr. mg. D 2

.

MA0HMATIKHS 2TNTASE<> E'. 447

Kavrai rcbv xvxAcov itEQtylQSiat, adiayogovGiv

itokv7ika6idt,ovr<s ovv rov aQi^îbv r&v

v&icov 7tl rr^v VQi6xoiivr]v cog && T v diet rov

xara xogvcprjv Giftitf&o yQacpopilvov xvxAov Tt

xal tec yLvopfva pQ%ovrg lg rov

rov iLQt,Gpov Gwayoiifva police Qopw iv\

xara

OTttV (iV TO XCCrd XOOVCpYjV 6r][llOV 7t rOV [l6r)[l-

r rov ror 6ovttvovvros rov 10

TG>V

nobs ii0r][if}Qiav avrov, orccv dl vori(brQov $ TO XCCTK

xoovyqv rov [i6ovQavovvToS) ngbs rag KQKTOVS fj

arog 6rai 7taQccM.ais, iitl $ t&v Kara ftijxo^,

at ytrj^t,x6rr]Tg rear iv TG) xavovt, TtaQaneiyid- 15

v&v ycovicbv rv\v ait' KQXT&V 3tQt,d%ov6i T&V dvo rcbv

vnb rov 7to[ivov r^tjfjLaros rov diet [i6&v xccrQO)&v

TtQi%oyiVG)v, Ttfc plv Kara itAccrog TCaQaMd&cog itgbg

CCQXTOVg yiVOlLSVYlS, <XV [lV [1%G)V % 6^0-i}g ^ XXl-

ycwia, ig ra TtQoriyov^va rcbv fydicov f)Kara 20

TtaQaMa&g, iav de &a66G)v OQ&ijg, ig

rd 7t6iLVK) rrjg $ xarcc nhdrog Jtaoa^^d^fcjg agog

yivo[ivr]g avuitaKiv, eav [ilv [ififav r}

r\ xxLîvrj yoovia, fig rd jtoîvcc r&v

4. orjjLtftoi;] D 2, comp. D. 5. Y.CU TK] supra scr. D. 10.

97] corr. ex r\v D. TOV (alt.)] TOV\TOV D, corr. D 2. 1L Supra

7) add. g D 2,sed del. 12. vorsiOTfQOv D, sed corr.

r]] corr.

ex r\v D. 13. rag] om. D. 14. itctTog] corr. ex nldrovs D 2.

^f] supra ras. 3 litt. D 2. Kara] v.ar- D. 15. Y.O.VOVIK> D.

16. 7t8QL%ovGr) D, corr. D*. 17. *enfya&ev] -ftsv corr.

ex ve[i D 2. 18. n^drog] corr. ex nldrovg D. 21. sidecar]

S D, ttdrrcov D 2. 24. OQ&TIC] corr. ex oQ&rj D 2

. yoovicc]

comp. D, ut saepe.

rj XKTK [if}xog <5TKi TtKQccMa&g, eav d skaGGcov OQ-

'a fifVrot rots

i TOV tfhov G>g p?#v ccfad-yrbv KVTOV

5 (SovTog ovx ayvoovvTsg, on rtouJGfi, TLVCC TCZQI avra

xciravvor][ivr] xal TCBQI avrbv x t&v

tt&s ,aktf 7ti pi} ovr&s c^rfkoyov

ra (pKiv6^VK dice rovto 7tccQaxoA,ovd"ij-

nvcc

10 avv rijs roiavrrjg 7ti6Td6G)$ $$&%&$ ye

oûotog d xal agog rccg

rjQX6frr][jLv ratg agog rbv dta {ifaov rcbv

xvxhov yivouwcug vitb rov dice rear 3t6ka)v

rov oQôvrog yQayoyiwov yiyi<5xov nvxhov ytQt,cp-

15 Qffaig r xal ycovicug ccvrl rfbv ngbg rbv Ao|6v rijg

6^YjVrjg &O)QOVlt,VG)V ,1ti TO {lV V rctlg fXfolTtTl-

xaig GvQwyCttig (S6îvov itaQa rovro didtpogov avsit-

afa&rjrov i\v, TO db xccl TavTa

T Tcclg di%6i,v xccl Qi

yc)dg iv Totg

20 G)Ql6[lVG)V Xtt&' Xa6Tr]V TG)V TCi TOV

d&v T^g ^^vrjg xccl T&V aTtb TOV tfwdfap&V

)akka xal Totg pzyi&sGiv xal Talg &<5<5iv ccvTCitg

iva d' vxaTav6rjTov yivr\rui TO teyoiiwov, IxxsC-

1.|u.7)xo?] supra (i- macula A. 8s] d' B. &dGa<ov~]

^ D,

V) D 2. 5. &yvoovvTs] &y- in ras. 1 litt. D 2

. 6. avr&v D.7. s^S D. 8. TtsQi] supra scr. D 2

. rovro] corr. exrovrov D 2

. 9. OJGTE D. nvcc] -v- mut. in ft C 2. 10. yf]

AD 2,TS BCD. 14. OQI^TOS D. TifQLcpSQSiais rf] -SQSIKIS rs

e corr. D 2, neQicptQicpsQEictis re C. 18. Post TKVTKS del.

auras D 2. 19. deit-toi D. 22. utys&eGi D. d mg. A.

24. d'] 94 D.

MAOHMAT1KHS STNTASE&S 449

to filv TOV diK pfacw T&V tydiov xvxkov

TO ABF, rov ds Ao|oi) Tyg Gf^tjvrjg TO

xccl 6vvd6{iog {Lev v TO A Grjpetov, Trjg

TO

z/, xccl

dnb TOV

dux

sill TOV

TCOV ca-

TOV

ds itokog

TO E 10

KOI ys-

di CCVTOV [ie-

TO E4 Z, dice ds TOV B

qv4H TtsQKpeQSLccv, 15

dia ply TOV XWTQOV trifc

TO EB, 7taaaMcc66sTG) TSi\

xal 'ysyQccy&GxSccv tit,' avTov nobs Tag B4 xccl BZ oofrccl

CCL H KCCl HK, &6TS T&V [lV KKTCt [1^X0$ d,7tO%(bv

TOV GwdEGpov xr\v ^LSV ccxoifiii yCvsti&ai TY\V AB, Tqvtie <pccivo[ievr]v TTJV AK, T&V $ xaTa xhaTog anb TOV

dice ii6(ov TV\V plv axQiftfi TV\V B4, Tqv df cpcavo[ie- 20

vyv tv\v KH, xal T&V axb T^g 4H Ttobg TOV fe

&G)QOV[lVG)V TtaQCdhd&GW XCCTCC ^XOS 1*>V TT}V

rri H, xaTa nbaTog df Tqv foyv TTJ

1. rb (Jilv rov] rov [t,ev D. 2. r(ifj(iu TO] corr. ex

TO$ C 2. 4. KSVTQOV] x/ D,

ovadd. D 2

. 12. 81 UVTOV] corr.

ex dice rov D 2. 14. did (pr.)] corr. ex rt D 2

. EJZ] corr. exW txy

EAZ D 2,mut in EJ"Z' B 3

. 15. nsQLcpEQStccv] t, D, 7 D 2,

nag. n D 2. 16. 8C avrov] corr. ex SLU rov D 2

,6Y uvrov H

Halma, fort, dice rov H. B4~\ corr. ex BA D 2. BZ] ZB D.

17. xca] om. D. 21. r&v] corr. ex tr^v D 2. 23. &H]

"H0 B. fojjv]'

M D,^ add. D 2

.

450 KAATAIOT IITOAEMAIOr

fad ovv fj pV AH xaadMa&g fvafaxfrai, dta

7taoxr&i,[iVG)v rijg EA 7tQi(pSQiag doO-ft'tft?^

xarf

oa $ r&v A xal H TtaoaMafeov rrjg vnb

PZE y&viag Sofafays 9 ftfiflg d' v rotg [i7tao6d'v

5 aitd%aiiv rag itobg ra do&wra rov tydiaxov Gq-

[iia yivopevag rov did rov xard

r xal ycoviag^ [i6vov d' %o[ii

rov did [i6(ov GYjpftov rb 5, tpavfoov, onrift

EB 7tQt,(paia 6vy%aG>nd'a avrl rijg EAy rr\ $ VTCO

f 10 FBE y&vta avrl rijg vnb FZE.b [iv ovv

r

'l7t7iaQ%og 7te%CQri6e [iv xal rqv roi-

avryv diOQ&cotiiv TtoiiJGaG&ai, ,Jtdvv d' dvfrtiGrdrwg

xal Jtaad rbv Aoyov avry <paivrai

jcocorov [ilv yag pia diaGraGft, rrjg Ad15 xal ov%l Jtdtiaig T) stA^to^fcv, ortQ %v dxoAov&ov r&

xal xegl r&v HIXQ&V dxaif$oAo'yi6d'ai,

iti,ra xal nfaiotii rotg droTt&rfyoig fAaO1

.

itd yaQ xal avrbg rag r 3tQig)aiag xal rag yoviag

rag jcobg rbv did pfe&v r&v a)diG)v

20 rvy%avv 3rQoajeoddi%(bg, xal on rrjg

fiAH hapfidvfrai,' rovro ydo iv rw nacbrG) r&v

3. &H~\ corr. ex 01 B 3. 7rapaHa|fcor] pr. -a- eras. A.

4. TZE] corr. ex IZE D 2. 5. r. do&evr. D, ut saepius.

crjfitlu ywopsvccs] compp. in ras. D, corr. D 2. 6. rov (pr.)]

in ras. D. dia rov\ bis A extr. et initio pag. 8. 6r]^toov C,

c?D, CH D 2

. 10. i,no] v D, add. D 2. TZE] corr. ex

ZE D 2. 11. fwf^ft^rjdf] seq. ras. 1 2 litt. D, corr. ex

cnts%KLQr]G B 3. 14. Ad\ AE D. Gvy-AS^grixai] -y- corr. ex

v D 2. 15. nlsioGiv] -ft- in ras. A. 17. nteloGi\ corr. ex

itteCoGiv D 2,mut. in nteioGi C 2

. rots'] om. C. aroncorsgoLs]&- add. C 2

. !&cc&8v] -v del. D, Hafts B. 20. trvyXuvi- BD.

7fQoanoSdi%o)g~] -to- corr. ex 3 litt. D. try?] A, anb rri$

BCD.

MA0HMATIKH2 STNTAEE.QS E'. 451

Qb$ rr\v T^S

7tQl(pQlCCS $6(5LV TTj T EZ 7tQl(pQia Xttl 11]

vnb EZF ycovfa &s ddo[ivais' ovr&g yaQ iv rat

dVTQG) TYJV Zz/ 7tl,A,0'yi,Gtt[lVOS KCCi

vnoTi&Tai,. nagriyaysv ambv ptvTOi TO

diori TO B xal ovyl TO Z 6rj^t6v i$ri TOV dux

TO dfdoiiwov, xal dia TOVTO T&V TS

EB dfdoTat, Kal ovyl f}EZ xal T&V ywvi&v fj

VTCO

EBF xccl oi)%l r)vnb EZF. k'v&sv KVL\ ngbs to 7toir[-

TLVK xav [iQMr}v didgftcoGiv KeuivriTcci nob- 10

yi,vo[jivr}s afa&rjTfis itavv diacpoQag T&V EATCCS EZ dltt TO 7toAi> H&M.OV KL-

v&v avTccs ^ dfdoG&ai,) Tijg d BE Tijs t& ovn ds-

donwrjs -Y\ XQOS xr\v Ed dicctpoga TO nkei^Tov dioitist,

[IOVG) TG) TijS B4 XCift' XCC6Tr]V T&V CCTfO TOV 6VV- 15

TO pvrQi Tils Math fbv vyii] TQOXOVaxohovfi-ov ysvoiT* civ fjjilv VTC

<5TK> yag c3diaxb$ 6 ART KOI TtQog byftaq CCVT& 20

6 4BJS, i\df Gfkyjvr] iJTOi, XCCTU TO 4

r}KCCTCC TO E

Kara nhccTos TOV ABT dia [i6cov T&V %&-

1. naQcdKY.Twwv D, corr. D 2. ccnodsfavvGi D. nqog] Ss

B. 2. Ez/] corr. ex EA D 2. 7tQupSQ8ia] corr. ex ^

at

mg. D 2. wi 3. ycovtoc] mg. C 2

. 3. EZT] E- corr. exr in scrib. C, -r ins. D 2

. 4. Zz/] -J e corr. D 2. 9. ov% D.

11. ywo{ivr]s] -g add. C 2,

corr. ex J^ D 2. 12. itoliv] -o-

corr. ex v in scrib. C. 13. tie] <? FE C et B (F- e corr. B 3),

corr. C 2. 14.

17]corr. ex xf\i D. TTJV] xr\ A. EJ~] corr.

ex EA D 2. TO iffaiGTov] TO nte?- in mg. transit D. 17.

V.KTCC] -TO. supra scr. D 2. 21. z/BE]z/-e corr. C. TJ] in

ras. D 2. 22. wra] bis D, corr. D 2

. AST] AT D. r&v

-AVV.\OV] om. D.

29*

dfav xvxkov dedo[ievqv ftfiptqp^p&at^ olov rrjv

xal rv\v BE, &6re rag pev Ttgbg rb B 6r][ieiov rov

<pdi,axov 7tQi(pQiag anb rov xara xogvyijv xal yco-

viag dfdoG&cu, fyrsZG&ai, df rag agog rb 41}

rb E

A

E

lav plv dr) roiavryv %y ftltiiv 6 fwdtaxdg,

agog ogftag ycoviag slvai r<p dia rov Z tf^fm'ov, o

rt6hog rov OQôvrog, xal dia rov B yoa-

vxAep, olov rcj Z5, GvimeGstrai ov-

10 rog dr]kov6ri, rfi 4E TCSQtcpSQSia, xal ^ l*<v y&via f)

ra z/ xal E fteoaovinEvrj adidtpoaog etfrai rijg

rb B vjcoxsi^vrjg' ooftal yao xal at dia rovrov

rbv tydiaubv ywopsvai' ri\g de ZB<i] plv ZJ thaGGcov fGrat, ry BJ, rj

ds ZE15 rfl BE dsdojisvaig xal avratg.

sav ds (Svintiitrri 6 ABF fydiaxbg rti dia rov

xara

2. Supra v.af add. tf D 2. 3. 7ttQicpSQiK$] om. D, 9" supra

scr. D 2,

TC mg. D 2. 4. TO (pr.)] corr. ex ra. C. 6. %ft D.

8. 8ia] supra scr. D 2. yâqpo^vo)] -w e corr. D 2

. 9.

/nfytcrca] corr. ex neyLGros D 2. xvxôo] -w e corr. D 2

. ZB]BZ D.' 6vv7tf6ircu ABC.^ 11. z/] corr. ex A D 2

. 14.

corr. ex 2,A D 2. skaGGcov] comp. D, s^drrtov mg. D 2

.

15. BE] corr. ex KE D 2. 16. cv^mnrr]] -vfi- e corr. D 2

.

17. yQKcpotitva)] corr. ex I^w/ D 8

.

MA0HMATIKH2 STNTASE3S E'. 453

xal V7to&[ivoi, itokov rov bgiôvrog TO Arag Ad xal AE, xal avrat, dioitiovGi rijs AB

<pQiag xal ai vito BAd xalA

BAE y&viui rijs {irj ovdiqg

7tQorQov. didovrat, $ ai $iv

Ad xal AE rov Aoyov ovrog

G)g 7t' V&IG)V dia TO

aTfo r rijs AB xal

xal BE dfdopwcov ra

ait avr&v 6vvr&vra 10

ra ccTCo r&v Ad xal

AE [Eucl. I; 47]* axohovftog

$ avralg xal ai VTCO BAdxal BAE y&viai.

rijs ^ vov fydiaxov &tia)s yxxfa[ivr]S) &v aitb 15

rov Z jrdAov rov b^Lôvrog 7tL^v^G}îv rag ZB xal

ZHd xal ZE* dfdouwr) u,v 6rai ii r ZBxal rj vnb ABZ ywvicc xccl itccfav dÂovdrt at

xal BE. o(pikov(5i,v d do^vai ai r Zz/ xal

ZE TCQi(pQiai xal ai VTCQ AHZ xal VTCO A&Z 20

yovmt, didovrai, dl xal avrau xa&rcov affiziGtiv 7cl

rrjv ZB r&v AK xal EA.

7tidri ya() i\VTCO ABZ y&vi'a

2. AA *ai AE~\ e corr. D 2. 3. at] i] BD. BAJ] corr.

D 2. xa^(alt.)] xalvwo D. 4. ycovfai] rm

atD, ycovicc D 2

.

5. didovrui] supra scr. D 2, mg. dtSovrut 8t D 2

. 9. xal

BE] 8 D, p D 2. 10. &n'] corr. ex vn D 2

. 11. TWV

rf)s D. 13. at] i] B. BA4\ B- postea ins. D. 14. xat

om. D. 16. 87ct,&vcQiiv~\ -f- corr. ex | D. 19. xcu(pr.)] om. D.

oysttovGi D, -GI e corr. D 2. 20. xal vno] xal at vno C,

om. D. 23. c'jmdTf] -drf in ras. 1 litt. D 2. yap] supra

scr. D 2.

TtdvrorYI

VTtb ABE, didorcci, roc BK4 xccl BAE 60-

froycbvicc xccl A(fyo rife ZB Ttgbg ras itsgl rr\v OQ&TJV,'

tiersTtd xccl Ttgbs ras 4B xal BExal CCL Z4., ZE vTtOTwov-

do&riGovrai, did rovro

xccl ai VTtb 4ZK nal

b EZA ycovicu vit8QO%ccl

r&v STti^rovfievcov

^ ftt> yctQ VTtb AHZ ftt-

10 o>v serlv rfjs VTtb ABZtfiVTtb^ZB, % ds VTtb AZttdttav rijs VTtb ABZ TyVTtb EZA [Eucl.I; 32]. <pcc-

vsgbv d\ on, xal TtfofaTYi

15 yivsrai dicctpoQa rri$ av-

rrjg KKX& Tthdrog atfo^t

OTKV rb B GriiLslov avrb % to xat<x

Ttgbs rb B yi,vo[ivr]g ycovias KI Ttl ra

rov xccroc KOQV(pr\v ogd'ccs Ttoiovtiw Ttgbg r& Sco-

20 diccxa y&viccs' r&v d 7tQi<pQi$)v ,orccv

r\ ccvr^ &-6i<3 r]' pydfiuag yccQ Ttdfav ywopwrjg Ttgbs rb B TtQi-

<pQi'ocs CCL TtQbs roc z/ xccl E ryhxccvrcu faovrcci,, r\U-

rCbv [lev

xccl E

1. ndvcoTt] -ro- e corr. D 2. BKJ] BJK D. 69^0-

a

ywvia] ogftoyavi D. 2. ZB] EZ D. 3. rag] supra scr. D 8.

JB1 mut. in BJ D 2. 4. af] rj

B. ZJ] ZJ wi D. 6.

v.di (alt.)] yicd KI D. 7. EZA] corr. ex EZA A, ex ZA D 2.

10. HTTtV] comp. BD. 11. JZB]'J- e corr. D 2. Ss]

3' D. 12. ABZ rjj vnb EZA] in ras. A 1. 15. ym-rca] yive-

renouat. C 2. 17. 77] corr. ex i]v D. 18. yccQ~] comp. D,

corr. D 2. TO] D, rca D 2

. Y.KL] supra scr. D 2. 20. 17] A,

avrfjs rj BC, Kvrrjg C 2,

TE D. 21. ij] seq. ras. 1 litt. D.

TO] mut. in TW D 2.

MA0HMATIKHS STNTAgESiS E'. 455

av (btfiv xal aC ri}S xara itkdrog Ttagodov rr^g <5e-

xal orav dgfrbs f] rtQOS rov (pdi,axbv 6 dice

rov xara xogvcpijv' oty yap nafav rq Kara

itKQodcp diofaovGi rils ZB al Zz/ xal ZEev ds rats aMcug &60i,v tyxfavoiisvys rij$ 4Errjv ZB ai re r&v TtSQicpSQSLcbv KOI aC rcbv ycovi&v

V7tQO%al lid TO sAarrov 6vvayftri6ovxKi. &6xe xcu\

orav ILSV ILOIQCCS fj 6A,ijvt] Kara, nAdros KTttffli rov

diet [i6G)V) fj jtfafarr] diccfpoQK r&v rtccQccMd&cov 6rat

dflxcc k'yyitira, QrjxoGrcbv aC ycty rov psyfarov dicctpo- 10

QOV T&V 7tQt,CpQLG)V yiOlQai T06CCVrK TtOlOVGlV ^-xotira itaQKM.d%&$ iitl r&v ^yfat&v viCQO%G3v xal

orav $ r^v ev ral$ $\kioi-

itdgodov ait%fl' avrrj d

yivtrai [nag poiQag fyyitira xal fjpfaovs' ra l'6a %ij- 15

xotira a /.' didyogov e'Grai, rijs TtagaMd&Gos rov roi-

ovrov Gitavi&s 6v[i7tfarovro$.

% jifiWot p&odos ^ XQOS rqv roiavrrjv

rcbv T y&vi&v xal rcbv jtQi,(pQiG)v ysvoiro av

%iQog rolg f}ovko[ivois &$ & ovr&s piXQotg Ad^otg 20

rov TQ6jtov rovrov. xa&okov yccQ rov rcbv

1. <a6iv\ -v eras. D. ca] cci &no D. 2. rj] seq. ras. 1

litt. D. 3. yap] ^ D. 4. ZB] seq. ras. parua D. xat]

om. D. 6. ri\ corr. ex XL in scrib. A. TtfQifpeQSi&v] 9 D,

^5 -^2

>et similiter saepius. 9. TtteiGrr}] -i- corr. ex a in

scrib. A. 10. SSKK] corr. ex Ss <5* C 2,T D. fyyurca] ir1

*

in ras. D 2. f|r]xo0rwv] ff renouat. D 2

. psyiGrov] e corr. D 8.

14. sKlefys D, -GL add. D 2. 15. jipfaovg] in ras. 1 litt. D 2

.

d mg. A. 16. a/.']

in ras. D 2. 19. r&v (alt.)] om. D.

20. ebg iv\ cbfv B. 21. rov (alt.)] corr. ex robv C 2. rwv]

c

corr. ex rccg D 2. ycovi&v\ corr. ex YOJ D 2

.

v di7th(b6avrg Kal sfasveyxovrsg fig to r&v sv

voviov ra 7taQaxi[iva avrti r xal

TOJ tefaovn sis t&S t&v tfvo OQ^COV poiQag QX X&Qlg

7tokvnka(Sid6avrg rtl rag rov nAdrovg potQag rb QK5 exarsgcov Kjcoyâô^sâ xal ra IK r^g itQ&rrjs ycovias

ysvopsva a<psfov[iv psv ajtb rfjs vitoxsiiisvrjg dnb

rov Kara, KOQV(pr\v TtSQiysQEiag ,orav enl ra avra

fi

rip xar& xoQVtprjv f] 6s^v^^ 3tQ06&"iJ6o[iv da, orav

sill ra wavria, Kal ra yv6^Lva itoi,ij6avrs eg? savra

10 6vv&vrs r rolg BK rijg kencovGris y&viag ywopwoigKal avrotg r&v <5vva%&vr&v rv\v

ra x rijg keiTtovGyg yavi'ag d

KarovraKiKaieiKo6aKi, itoiriâvrsg Kal

15 ig rag fvyqiievag 7tgi(pQiag r&v rotg

itaQaKtiptvcw itQi(pQiCbv V r& Kavovi r&v

rag Ji(U<ffa$, av plv pziCfav y 17 dt,G)Q&a)[ji,vr)

<ptQia rr^g TfQcor^g^ 3tQ06d"tJ6o[iv ralg rijg

y&vCag, av dl ^d66c3V^ d(p^.ovîv avr&v, KOI

20 Kal rqv ycwiav di&Qd-oiLwyv.

dl VXv ftfrMttltfJNo ?tl rrjg

fj pl

1. comp. in ras. D 2. 2. Y.UVOV

LOV C. 3. TOJ]

TO D, r& 1 D 2. 4. tov~\ in ras. D 2

. px'] px A. 5. yeovfog]bis C, corr. C 2

. 6. yivopEVK D, corr. D 2. 7. rov] -ov in

ras. D 2. TtSQitpegfiag] comp. renouat. D 2

. $] seq. ras. 1

litt. D. 9. eavta]- ins. D 2

. 11. zrQccya>via&i6iv D, sed

-v eras. 14. !xaTO*>raxntai(.xo<JGx mg. D 2, Q v.ul x D. 17.

ri^LGfiag] in ras. 1 2 litt. D 2

._ lav] Kaijdv AB, xat del. A 1

;

S fdv C, corr. C 2;av D. ^] con*, ex r\v D 2

.

CD, corr. D 2. 19. iKdrrav in ras. 1 litt. D 2

. 20.

CD, corr. D 2. 21. Ss ?txfv] corr. ex d' svwev D 2

.

MA0HMATIKHS ZTNTAgE&S E'. 457

i]$ V7tb ABZ ycovia roiovrcov A, oi&v

r\

9, XaTQa d TG)V 4B XO.I BE T0$ TthdrOVS [lOLQ&V .

roCvvv rats $v directs r&v A IIOIQ&V, rovr-

reels I? TtaQaxurat, sv&eta rîrjîdrov f, rats $

is t&S ^vo OQ&ccSi rovrs'tirw rats Q^t

sv&sta rîrjîdrcov yd Jtyyitira, yivsrai, Aoyos

rijs BA TCQOS AE b r&v | Jtpog ra yd. 6 d* avrbs

[Eucl. VI, 1] xal rijs BK XQOS 4K, otWvovtia ~QK. jtokvTthadideavrss ovv sxdrsQOv rcbv

fi&v 7tl ras [loigag rijs vnoruvovGrjs xal rb QX' 10

avr&v A,afi6vrs %o[iv xarQav [iv r&v KB xal BAr&v ccvrcbv

/3 A, warfyav $ rcbv 4K xal EA 6[ioiG)S

d x. ra drj ($A TtQ&rov, av îev xara rb E 6r][itov

i] GfAyjvr} i)itoxBrirai, d(p&6vrs rcov rijs ZB 7tQi<pe-

[loigcbv jidia rb itl ra avra rco xard xoQV(pr\v 15

rrjv xara ithdros axo%fjv rrjs ^fA^V^g, rovr6ri,v

dia rb dîg)6rQa T) vonc&rEQa i} floQi,6rQa tivat, rov

Z&diaxov, %0[iv rqv ZA poiQ&v pfl I, ihv de xara

rb 4TI r\ &^t]vrj^ TtQOG&wrfs avrats di>a rb fvavriov

1. to'] d' D. ycovia] supra scr. D. _ 2. JE] A- e

corr. D 2. 3. TOVCSGTL D, comp. B. 4. | (pr.)] in ras. A

r

corr. ex D. (alt.)] J- D. S\ comp. ins. D 2. 5. 8vo\

ftBD. rovrtszi D, comp. B. 7. 5^1] corr. ex BJ

g (pr.)] fi D, ut saepe. ra] om. D. 8. z/X] corr.

ex AK D 2. vnorivovGK A, sed corr. in scrib. 9. SKUTSQCOV D

t

corr. D 2. TWV] ins. D 2

. KQL^&V] s D, ss I>2

- 10. 9%']

^x AB. 11. xat] om. D. 12.J3 I] pi BC, ut saepe.

J3I TCOV] mg. A 1

. xca] corr. ex x D 2. 13. Post x

litt. (s?) ins. D 2,sed del. E GTULSLOV] corr. ex SG D 2

. 14.

VTtOHflTCCL D. 16. TOVTSGTl D, COmp. B. 17. @OQi6t()CC i)

voziwTSQcc (corr. ex voreioâ D 2

)D. ftvat] supra scr. D*

18. eo<haxO'u] diet IIEGOV D, dta fif'ocov D 2. 19.

17] corr. exD 2

.

'

v tr)v ZK ftotpwv ft L Gvv&evttg ovv to outb

XcttQag t&v ZA xal ZK %G)Qlg pera tov anb excc-

tfyag t&v 4K KO.I EA, tovt6tw to aito t&v d K

perd re tov aito t&v pf} A xal [ita tov CCTCO t&v p A,

xccl r&v GvvK'ffievr&v %fogls hcc(l6vrss rqv Tthevgav

XCil %r\V [lV ZE 7tQt,CpQi,aV ILQLQCbV {lf$ fAS

[id. Aoinbv df tec 8

x KatovrccxMcci,Mo6dxi, noiKvts^ Keel

ra[i fg xa ytccQcc ta p p

10 tr^v plv EA tOLovtcov t/3 rj k'yyrfra, ol&v <5rlv q ZE

oicov Grv

{lV t&V l(l YI V&iy 3tQl<pQl,a [101,QG)V Ta XCil

ry d r&v I {_' y' rtQi<pQi,a poiQcbv I y15 &v ra riiifari kafiovtsg t& plv s xcd d

f

rijg VTCO

EZA y&vLas atpttoiLv tcbv trig vitb ABZ y&viccg

V A diCC tb Xttl trjV ZE 7tQl<pQiO,V A.CC660VCC

1. Ante ovv del. avrais 8t>u tb ivavriov D. 2. ZA~\ -Ain ras. D 2

. xat] om. D. ZK~\ -K in ras. D 2. 3. xca]

oin. D. Towcton D, comp. BC. 4. TB] supra scr. D 2. ^(pr-)j

ins.D 2. perd (alt.)] ^ D. TOV

(altOjJns.J)2

. 6. ZEJEZD.jig] v? D, [ifi py ty mg. D 2

. 7.fttf]

vd D, p pccv mg. D 2.

8. MKTovTccKMui,* D, coir. D 2. 9. ft^] N<5 B et, -s e corr., D;

fi? supra scr. D 2. pd] ^v8 D. 10. roiovrm D.

ifi]i- e

corr. D 2.

jj] corr. ex x D 2. 11. 8i] om. BC. F /.' y']

in ras. D 2. 12. Z^] corr. ex ZA D 2

^ 13. ^] e corr. D 2.

sv&ftai nsQicpfysiai, CD, corr. D 2. ta] -a e corr. D 2

. ']

A, C, ^ BD.A, C, ^ BD. 14. /_']in ras. D 2

. TtfQLysQsictiC.

y'] -v F y' in ras. 2 litt. D 2. T(alt.)] postea ins. C.

in ras. D. 15. &v ra]m ras. D, oo- corr. ex o D 2;

ante

ras. B (rav corr. ex cov B 8). ^^tVT]] in ras. minore D 2

. e']

ABD, C. 16. TWV] corr. ex rov CD 2. 17. f] in ras. D 2

.

ZE] corr. ex Z D 2. &rf<HFova] s* D, 4i

a D 2.

MA0HMAT1KHS STNTAEE&2 E'. 459

slvcu rife ZB xccl sôîev r^v vnb AZ ycovtav poi,-

Q&V xd \ ra ds s g' rfjg vnb AZK yoviccg

tots ccvroig A dta ro teal ti}v Zz/ :

elvai rils ZB 6%oiiv xotl r^v vitb AHZy&viav [loiQ&v A g'* outey jtQOXi,To yi&odev6<x,i. 5

1. A0Z] -0- e corr. D 2. 2. F g'] g C.

xA, "ÎXD. 4. jLtfôva] âD. ^/fZJ -K- in ras. D 2

.

In fine: KlocvSiov n-totepuCov â-d-rjârtxwv F AC,f*a-9-rjfiartx?j5 dvvralecog F B, Klctvdlov

i/ FAD.

s-

Td$ VE6uv lv rco g' rcov

a. JtQi Gvvocov Keel

5 /3'. TCgayiJiCitetcc xccvovicov [i

y''. M&etiis r&v xccvovi&v.

re JCEQiodixac; xal rag axgifletg

f

. 7tQl r&V fXfalTtTMKtV QQ&V fjMoV XCCi

10 g'. neqil rijg diaGrdGecos r&v sxfoiitTM&v [irjvcov.

XCCVOVL&V exfaiJtTM&v.

rcbv fKAeiJtTM&v xavovi&v.

15 ltt. 7tQ\ T&V V

rag JtQo6vv6i$

2. rdd' D. r<m>] rfjs B, om. D. IIroten(xiov~] om. D.

lLKQ"r}yLCiTiKa>v] \LuQ"r]^Kriv.i]<s GwrdJ-scos B, om. D. 4. a'] etceteros numeros om. I). 5. TtQccypuria C. 6. y' nctvo-

vi&v\ om. D. 7. rag (alt.)] om. D. 9. JxATjTrTixeov D. fyiovKcxl G&r)vj]<i\ compp. BC. 11. ^'] in ras. A. v.uvov(ov D.

12. r\'--

nccvoview'] v.ui comp. D. 13. SICCKQIGIS 14. ^x-

foftyfaw] om. D. 14.^lax^tctg]

in ras. D. 15. m'] ca B.

negl T&V] g nsQt T&V in ras. D. fxAfityfcrtv D. 16. t^'j

fit,B. T&V~] om. D. nqovtvctis A. diccyQucp&v] $ D.17. ty'] yl B.

KAATA. IITOA. MA0HMATIKHS STNTAgESS <S'. 461

Ilegl Gvvod&v xccl

dq rvy%ccvov6r]g rrjg itegl rag

tiv&yictg f}Mov xccl Gshtjvrjs jCQccynccrticcg,

rai itdfovfj

rcbv axQifl&g fo&Qovpwav Gvvod&v xccl

itavGskriv&v sjtfaxetyiS) attccgxeiv [ifv fiyovped'cc TCQOS 5

iv\v T&V roiovrov TtQcbrrjv xccrd^rjîv rag aitodsdeiy-

[is'vas xu& SXCCTSQOV r&v cp&Tcov 7tQi,odt,XKS re xccl

avaiicttovs xt,vtJ6i,s dwcctov dta rovrcov yivQpivQv

rotg iifjxaroxvovGi rag xccra pfyog ccvr&v 7to%ag

xd<5TOT GvyxQivfiv fXiA.O'yt&Gd'cci, rovg re r6itovg xccl 10

rovg %Qovovg t&v 0oîva)v 6vvyi,G3v r&v re ngbgroc [i6cc xwtfiiccTcc A,cc{ificcvoit,sva)v xccl rcbv [JLETCC rijg

dv&llCcMccg aXQlfiGbV 0[lG)g df, IW 7tQO%l,Q6T()OV fftltV

xal ccvrai ii&odev&vtai,, 7tQOXT&L[iVG)v f| erotpov

r&v T xccra rag TCfQiodixag Gvvodovg xccl jcccv6^vovg 15

XQOVCOV xccl TOTCCOV xccl xojv xccTK tovg [i6ovg %QOVovg

7to%&v Kv&iicdiag r xccl Ttharovg

&vij

T Ttgbg zccg axQifatg 6vvyiccg

xccl ccTtb TOVTCOV fj TtQog rag xî7trt>xccg^

0dii&cc JtQog rrjv roiccvrrjv 7ii6Ketyiv xccvovicc 7CQL%ovra 20

rbv rgoxov rovrov.

1. a'] om. AD. 2. foj] corr. ex &v D 9. wGutTwa.? A.

3. xcu] TS v,ui D. 4. cvvodcov] c- in ras. D. xat] re

V.GCI D. 5. Iwtcxai/x-ff] -n- corr. ex t D 2. 6. v.ccrd).r}{iipis D,

sedJLI

eras. 7. SKdregov] corr. ex stsgov D 2. 8. dia] D, re Sid

ABC. 9. xaTOKVoutf) D. snoods] ~tr corr. ex >l D 2. 10. #(>o-

vovg ucii rovs ronovs D. 14. [tsd'odevov'ccci CD, corr. in scrib.

C et D 2. 16. XQOVOVS] %gov- in ras. D 8

. 18. ytVstca] suprascr. comp. et mg. D 2

.

ar eicc xavovi&v [i6a)v

Tlg&rov plv yap, IW ndhv nal rag rcbv

&<5ttQ Kal rag aMag, ano rov a k'rovg Nafto-

aoov GvcfrrjG&iisd'a) ryv ctTtodEdeiypevriv iv r&

rovra) G)& vBo^via, nar Atyvitriovg ri]g

ajto%ijs poiQcbv ovticcv o Af Tt

TO j]êQîov [isdov xivr

fij Ay ? cog itQQ toGovT&v ysyovsvui

TJJS v ty v0{ir)via rov co-fr îfffrj^^âs JtQoye-

10 yovvlav [i6r]v Gvvodov. xalr\ f|ij? aga ysyovsv

iiT& %yxo6ra fidgets picis [id i^ rijs iv ryiv $ rats ny [id t, f][iQcu$ 6 ft

ioigas ity

15 avG)[iaMccs pv [IOIQCCS rlrj i,

ridft me. 7ti%v d xal v TTJ rvjg

ftgia rov cbO1

ft<?cog 6 ply ijfoog 'Iffivcw

jjf, curb $ rov aitoyfiov rov tdCov dice rb

lioioas 6% tf, fj$ 6&rjvr] auoÂtag pv ano rov

20 K7toiov rov

1. p'] om. D. 3. ^trovg] post I- ras. 2 litt. B, corr. exinl TOV$ C 2

,ex h D 2

. NafiovaoccQOv D. 4. Gvotrjcoped'a C.

Trjv] corr. ex rjT D 2. 5. IVft] corr. ex IVrj D 2

.

-tea in ras. D 2. veo(ir]VLa] a in ras. D. 6. o] seq. ras. 1

litt. D. nctQCifidnovTSs 6, corr. D 2. 9. veoinqvia] a D

r

yp. vovfiriVLK supra scr. D 2. cb-O

1

] cofr rf]s D. 10. &QO]comp. C, di D, yg. CCQCC supra scr. D 2

. ysyovev] -v eras. D.11. HyyiGTcc] $y- e corr. C. 12. TOVTSGTIV] comp. BC, -v

eras. D. sr)*o6rd] || B, comp. in ras. D 2. 15. ri ^] B 3D 2

,

Ttrj ABC, TITJ D. 16.

|3 xa] jhia A. f'jrf^f D, -ft- in

ras. D 2. vopj}VLag\ -o- ins. C 3

;a D, corr. D 2

. ^Gt](ji^r D,

corr. D 2. 17. rov ob-fr]

om. D. ju-oâg] om. D. 19.

o- corr. ex A. 20. nidrovs] corr. ex nldtos D 2.

MA0HMATIKHS STNTASE&S ?'. 463

dnb rov fioofiov Ttsgarog rov ho%ov xvxAov poiQagrvd IS. Xal iv TG) TCQOXSlpdvG) CCQK %QOVG) Xi] flrd

rr\v v0[ir]vi'av fif'tf^g Gvvodov 6 psv ijfaog xal ^ 6s-

Atfvr] [ifa&s aTtsfyov d[i(p6rQOi rov faiaxov ditoyeiov,

rovrfanv r&v sv rots didvpois poiQfbv A, fto^agd\ GsAtfvrj dv&iiccMag [iv aito TOV axo-

6ir] v% is, nAdrovs d' onto rov j$ooiov

ttQaros {lotoag rrj it, MX.

ovv jto&Tov xavoviov

f, 6fadiG)v d f, xai jtaoad"t]6o^v iv rots 10

itl [iv rov jfQ&rov tiekidiov rb a'

frog Napovcc66ccQOv ,iit\ $ rov dvroov rag rov

(&&& vj[iQccg xd [id tf, itidri ra 7tovrcc QrixoGrK ryg

iv rfi xd' 6rl ii6rjn(}oiccg, lid ds rov roirov rag rqg

7to%r\g anb rov anoysiov rov fjMov poiQag tiny 15.

3tl d rov rfrdgrov rag anb rov anoyeiov ryg

avG)yiakiag poiQag (Sit] i/f tf, sTil $ rov

rag aicb rov j3ooiov 7toarog rov n^drovg

rrj tj xd. tTtsidri de xal iv r& fftiiGfi rov [i-

6ov [irjviaiov %QOVOV rj^ioai [ilv 7CgiB%ovrai idji

vs 20

8s ri\g plv fifaaxyg 7to%ijg id Ky ifa

rr\g de 6hr}viaxr}g dv&iiaAiag @9/3 vd A, rov ds nkdrovg

Q<j x ^ 9 dcpshovrsg rovrovg rovg doi&povg ditb TCQV

2. I?] i- in ras. D 2. 3. vov^r\VLav D. 5. rovrtirctv]

comp. BC, -v eras. D. 6. d] comp. supra scr. D 2. 7. itka.-

rovg] corr. ex nhdrog D 2. 10. iv 11. cxi%oiq] om. D. 12.

hog'] corr. ex t,' D 2. NafiovccGaQov D. dsvr^QOv] -ts- e

corr. in scrib. A. 14. &mV D, -v eras.; comp. B. 17. as-

s] corr. ex G^vr\g D 2. Ts] corr. ex st D 2

. 19.

corr. ex insi D 2. TJfu'ffft] -ft- e corr. A 1

. (irjviKtov. 20. 7?/i.cu] -at renouat. C 2

. nQii%ovtcti\ -at

renouat. C 2. 21. poiQai\ -at renouat. C 2

. 22. Si (pr.)]

ins. D 2. 23. fyifyiovg] gs"* D.

fis

]

D.

Gvvodov rovg hoiTtovg ngordônsv xal

avrovg Iv r<p dsvrsoa) xal bpLOicog %ovri, xavovicp,

7tav6A,rjViaxG) ds f'tfoftfVca, xara rov avrbv rots ngors-

ooig rooTtov xarateiTtovrat, ds fjiisQai, [lev & vri x/J,

5 polQat, ds anb plv rov dnoysiov rov fjfoaxov tfod s

Ar], av&iiaMas d' aitb rov anoyeiov rr\$ GsAtfvys x?

/3 /if, TtA.d'covs d' cutb rov fiogsCov Jtegaros Qifi v^ is.

XCci V K

10 uTtctQriôvraL, ual fTtiAaiiftccvst, nsd*' oôvg

b plv ijfaos [loigag tvy vfi Ad Zy, ^ $*

yLv {loiQccg vt, KM [id a, TtAarovg ds

3 fid1

vd, ra plv ttQGbra tiMdict rcov dvo uavo-

jtccQccv,ij(jo[iv rolg %s sr6iv^ ra ds dsvrsQa V7to-

15 iLid)6onv rolg o(I [i e, rcbv ds koiit&v ra psv rgira

ytaQav%il<}0[jiv rolg rvy vfi Ad ly, ra ds reragra rolg

v xa /Ltd a, ra ds itipitra. rolg QI, i$ pft vd.

rovroig d' d<peij$ rdôêv xav6viov tviavtiiov iitl

Grfyovg xd xal akko vrf avro ^vLalov 7tl Grfyovg

20 t/3, tiefodfav ds sxdrsoov rcbv i'G&v rolg nQ&roug, xal

Irii [ilv rov [irjviaiov Ttagaftevrsg iv rolg Ttoaroig

6rC%ot,g BTtl [isv rov itoarov tiefodfov rov TCQ&rov [ii}va,

7tl d rov dsvrsoov rag rov (irjvbs ^soag x& Aa v y

2. TW] del. A 1,om. D. 3. TCQoartQOig A, ngmtoLs CD. 5.

ds] d' D. rjh'ov D. 7. nldtovs] corr. ex nlidtog A 1,

-I- e

corr. in scrib. C. 8. ds xca] d' D. fasaiv] comp. D, corr. D 2.

leCnovGi D. 9. ffjijxotrrofs] &l B, "| D. dvaiv B, B D.10. 7uafi/3cb't] -i ins. A. xvxZovg] supra scr. D 2

. 14. rots

16. n<XQKvrioo[isv~] bis A, corr. A 1. 14. et6w~] comp. D,

fT86i D 2. v7to[iia>60[Lv B et pr. loco A, corr. A 4

. 15. rots]

-i- ins. D 2. o ^] o|3 A utroque loco. 16. rsTccQta] -rcc supra

scr. C 2. 17. Post vd del. a D. 18. fqpt|^g] -gpe- e corr. in

scrib. D. 20. d\ d' D. 21. sv] ? B. 22. no&rov} corr. extva D 2

. 23. v n\ C 2D 2, ^ ABCD.

MA0HMATIKHS 2TNTABE&S S'. 465

X, 7tl $ TOV TQLTOV Tag V TG) T000VTG)

yo[ivag TOV r^Mov [lotaag x& $ wy a, iiti ds TOV

TTKQTOv Tag Tijg dvcaîaîag Tijg 6^tjvr^g x yL& o77,

itl d rov its^Litrov rag rov TthaTovg iioioag X jiid Q"

7taoav%ri<30iiv $ %ol rccvrci rots ccvrots aoid-pots xccl 5

7tl T&V rtocbrcov <5ri%ov XXiiivois. 7tl d rov

VlKV6lOV 7tCCQCCd'VTS V TOL$ JtQCOTOig 6ri%0l$ 7Ci {LVTOV rtQMTOV 6fadiOV TO TtQ&TOV TOg, 7tl d TOV $V-TQOV rag 7tiA,cc[if3avo[Lvas iv rots ly (irjtilv ÊQCCS

I/YI ~vy vfi JLt/^,eitl d rov roirov rag iv rd) rotiovrw 10

%QOVG) rr^g riîccKrlg ixovtiiag poiaag Irj nfi v& 1^, 7tl

$ rov Tfrdorov rag rijg 6hr]vici%fjg avoâUag iioiaag

rfa Ag a va, 7cl $ rov Jtfynrov rag rov nhdrovg

poioag A^ ~py y we' 7taQav^0oîv d xal ravra 7tor

ftev ralg xxiiivaig roL6Kaidxa^voig &rovtfuug, 15

7tor d ratg d&dsxaptfvoiSi ^ GwcfyovGiv f][ioccg [iv

rvd xfi a ji, poioag d rijg plv ykiaxijg &to%rjg T[i&

T$ Ag 7g, rrjg d 6&rjviaxijg avG)[iaMag r& ^ a [ifa

rov d Ttharovg j\ |8 /u/fr ft/3, itgbs TO rqv xg&vriv (p'

oAotg AlyvjtriccKoig T6iv tfvfvyfav fi[ilv &ct&s6&W 20

rag pivxQi rtaoa&6i,g aQX6i, ^XQ L r&v devvfycw. xat i<5tiv v T&V xavoviwv xar-

1. x] corr. ex iis D 2. 3. o

j\\ corr. ex OTJ D. 4.

om. D. I> 18] Ijud corr. in ijt id A. W] del. D 2. 5. ds

supra scr. D 2. TCCVTO] corr. ex ravrag D 2

. a^tôtg] g D,

gffd^

D 2. 8. Tr^cbtrov] ^ D. 7T(>corov] a BD. srog] comp. D,

corr. D 2,ut saepius. 10. v^] va D. 14. fioi^ccs] ftoi^" D,

comp. C, ut saepe. de] supra scr. D 2. 16. at'] supra scr. D,

renouat. D 2. 17. K

|Z] a/I AC et corr. ex &p D 2. 18. 5] mut.

ra scr. D 2.

'

in ^r D 2,S supra scr. D 2

. 20. stzGiv'] -v del. D 2,Urea B.

,corr. D 2

. 21. a^xscft] -e- alt. corr. ex i in scrib. A.

corr. ex r D 2. dsvTsgcov t,r\v,oGra>v~\ -TSQOOV s

in ras. D. 23. TOiavrr]] des. fol. 136V D, fol. 137 r uacat.

1JI

--g

X *

^ ^~s~

to

" ^ 3^ O ~

* <fe ? "^ s <fc > <)03 a **T C ** MS 5 i^^

I

to ^

ts.*

<'

i

- ^.^gc

tfc?

3*8-3,

X & O Or XIP 55 IP a IP

*QP51 Q d^P' 2 ^~e i _e *. x . . . "i. ^

.

4?Q:o

. "^,oQ S^^-.0^.

S

-^1

MA0HMATIKHS 2TNTASE&S ?'. 467

** OU3

Qn *a.*

IF

2 * *t.U *-* -a

=4. P" if.

a.-srs- a. x

>**h

>. ^ ^ ?>. ^ ?. Qa.oa.ca. ca.ca.co.XXX XXX

a u> s

I*-*^ IP s IP 5J IPSk Q O X ;* Ql-^-

33 3 3

u> a

<*rl S^

-S d "S P

.11-

DQ a

^|oc3"

&J

til .

M f^

"S .-S

30


2" 4

\p 5^! aC*

JO

It"4$ t -

srs

10

I

.8*,_

a *t

SI-I-P

a a- v>d5>5^ a. * x

t

to *o

Q, Or

**fcj-a

^s* * ox

l

a.. . S"*r.Sw

V

I ." ^r-n^'"'^> ^ *

-a a ^ *> "". ^S"

'vo

3 s ^>

a wg o:ik

.rC> ** O O vS Oc3 ^ O O w X

MA0HMATIKHS <=>'. 469

ds in "035=-

oa. u>

t SI:

.

rs.

**Stt*

S" 2C2-

B- gE- S- iB S5- R- P- c- P

8* 8- 8* **IP a \fl

S ?k333 *u> a

II

jSto-w'iOoe-.^B'S? J3 ^ *i ST1

. W ** ^d

^ a B^^ OX"? S

ias -


El?

.*

Va 8 8 IP

Q^ Q/

a. a. s

2 a oi

a ?=- a

^

300.

IQ

IP *J ST

O

^O *CO ^ v^

Ij-Si4f!'

u S ^iO

a

^ to Tn -ri

" 2 ? QrHCO-*^ 2^ 8.

MA0HMATIKHS STNTA3E&S

"2 g"^^3

2

"

8

^*0X ?!

3 3

-g-

8

-O 'O

-I ^^ ~o o

co to

^ a

11- -aV V

11

II

I

00.KQ,

8 5J

t

a. -*

B 00.

471

?r ?> oo.

Vp Vp J\

j

oo.

ka -

- ^

d'.r

&$ dst rag TS TtSQiodLxag xal rag dxoifatg

"Orav ovv TtQoaiQcoiiE&a xara nva rcbv

[ivoov viavrcbv rag pfaeog ^cogov^vag Gvtvyiag

5 Aa/5tv, Aoyufdfievoi, jrdtftrov 6rl rb vitoxeC^vov rog

dnb rov a' f'rovg NafiovaGGaQov ,xccl 6xeil>K[isvoi,)

noloi rbv agi,&iibv T&V STGIV Gxiyjoi 7teQi%ov<5iv ex re

XG)V iv OTtOTSQG) TG)V 7tQG)TG)V dvO XCCVOVLG)V elxoGOC-

TtewtasTrjQid&v xccl sx rcbv xaxa TO rgfaov xctvoviov

10 eviavGicw, xa itaQaxstpsva rots 6ri%oi$ d^cporeQOLg iv

rots %fis Gehdfois 7tc6vvd'ô^sv olxeC&s snl psv x&v

Gvvodixcbv Gv'Cpyi&v ra x rov Ttoarov xavovog xal

ra ex rov rgfaov, 7tl $ rcbv itav6J.r]viaXG)V ra X

rov dsvrfyov xccl ra x rov rgirov byLOicog' xal X

15 ftfv r&v xara rb dvroov <5kidiov

V rbv djcb ri\g agîis XLVOV rov rovg

JCQOVov, oioV) av GwafficbGiv fîdgcd, xd

[id ^rjxo0ra rijg v rr] xd' rov

xal Ttakiv, av Ad ftd, {ira ra i'6a %rjxoGra rijs iv

20 ry d' rov (Da&cpl yiSGrnLpQiag, x d rcbv xara rb rgi-

rov rag cbro rov drtoyuov rov fjMov yioiQag, x ds

rcbv xara rb d' rag ditb rov aitoyBCov rijg dvcoîaâg

rijg 0^tjvr^g^ x d rcov xara rb n^nrov rag dab rov

1. d'] in ras. A, om. CD. cog] it&s D. 2. cvgvyias]--

in ras. A. 4. ju-scroog] corr. ex psaus D 2. 5. nocov BC.

6. a'] corr. ex S D 2. NapovvaaaQOv D. 8. navovav D.

ftKOGiitEVTaeTrjQL'Soov D. 9. %a viov A, corr. A 4. 12. cvv-

vyi&v C, sed corr. Tt^cbrov] a D 2,8 D. 15. xara] V.K D,

xar' D 2,ut saepius. 17. i&v\ corr. ex av D 2

. 18.

'|| B, et similiter saepius. 19. pera] Jra A.

MA0HMATIKHS STNTAEE&S '. 473

itQarog rov ithdrovg. xal Tag (p%f}S ds dxo-

jlav re Ttdtiag Mv re nvag kayifidveiv itQoai-

did rCbv iv rco [irjviaiG) xal rfrd^ra) xavovim

Kara rb otxetov 7ti6vvd'6G)v e% eroipov Gvvemho-

yiovpe&a {ira(pQOiiVG)v stp xd<5rov rcbv %QOVCOV dia 5

rb v%Qri<5rov r&v rrjs fniQag B&puxft&v ft

pivrvi 17 dw^yîvYi r&v

cog r&v vv%&r][iQa)v o^cdcov ovrcov ^ ravrrjs ,

afel rrjg xaLQM&s xaraA.a{i{lavo[ivr]s, aMa rrls

avG)[idA,G)v ywouwwv r&v vvft&rjiifycov' di,OQ&G)- 10

b roiovrov ^rdôvrss^ cog vjtodd-

,TO xaQa rovro didyoyov xat, lav plv ^^mv

fi 'Y] Jtgbs rqv dv&naAov dia6ra<5iv litovGua r&v %QO-

vcw, dcpai,QOvvrs ccvrb dnb x^ 6ftaAGog GvvriyyLBvris,

lav de fhdtiGcov, XQOtiri&wrfs afar}. 15

dij rbv rgoitov rovrov rov itQQ rag

&G)QOV[ivov Gwodwov rj Ttavdekiq-

vianov %QOVOV xal rCbv xar' avrbv dv&iiafocbv <p'

xarQov r&v cpcor&v v^ra%LQL^rog k'Grai xal 6 rife

axQifiovg 6v%vyia$ %QOvog re xal ronos xal nr\ 20

xard Hydros rijg 6^vrjg xdgodog X rijg 6vyxQi6cogr&v dvcopafa&v. xa&' xarpav yap av-

l, ri\V Iv TO) XXl[lVG)

did ri}g VQi6xoiivr]g itQo6d'a(pai(}6

v ii^Cov r xal tffAî^g xal jtAdrovg, lav {ilv 25

xal ovrcng L06îoi,goi vj did[irQoi zvQitixcavrai) rbv av-

8. cog] corr. ex 6g C 2. 9. ahi] corr. ex &et D 2

.

mut. in &Mr}s C 2, aUaHrjg D. TT)S cb?] supra scr. D 2

. 10.

SioQfi'wGoiiev D. 11. vnodtdeKTcci. D, sed corr. D et D 2.

15. iKmcrtov D. 16. xovrov rbv TQOUOV D. 21. r?)g cs-

htjvriS V-KTCC nldros D. 22. r&v] om. C. opu'ki&v D, corr. D 2.

24. viav.coi^vr]s A.

rbv s%o[iv %QOVOV xal rijg aKQifiovg Gvtvyiag, sdv ds

Aa/36vrg rag rijg diatirdiscos avr&v poiQag xal

avralg to dcodmarov avr&v, dv&' ot> 6

ijfaog fyytfra STtixivsttai, tfjc^d^-frtf, v itotiaig tigaig

5 fariiLSQivalg r\ Gehijvr] tag rotiavras poiQas rore avo-

vri&riGs'tai, xal tag ysvojievccs cogctSi &v psv

fi f] KKQifiris rijg Gehtfvyg itdgodos rrjs rov

Qo6d"tj0oîsv rco %$6vG) t& rtSQiodixG), sav ds

, dg)shov[iev an' avrov. GMICCVT&S de xal ccv-

10 rag tag tr^g dicc&rdasog avr&v poiQag (ISTK rov dco-

dsxdrov Ttdfov avrcbv, lav {isv skaGGczvTJ rj

Kara rbv

TtsQiodwov XQOVOV dxQifttjs rtdgodos ri\g Gehrfvys rijg

fjfaaxris, jfQOtf&faceg avrfj, iav ds TiheC&v, ayekovreg

ait avrr^g xard rs rb [ivjxos xal nkdrog rov rs rf\g

15 dxQifiovs 6v%vyCag %QOVOV sô^sv xal ryv iitl rov

Ao|oi) xvxkov rijs GsAtfvrjg dxQifiij ndgodov syyitircc.

A.a[if}dvsrai, pevroi sxd<5rors rb xara rag

rijg ds^tjvrjg oaQiaiov dvco[iaA.ov xivyiia rbv

rovrov' sfa(pQovrsg yao rbv xard rbv

20 %Q6vov rcbv rrjg dvcopaMag poiQcbv doi&iibv slg rb rr^g

av&iLakiag rijg 6s^vrig xavoviov A^^dftfO'a sx rrjg r&v

3iaQaxsi,[iVG)v avrtt jtQoG&acpaiQSGscov vTCsgo^fig ri\v

diayogav r& svl rijg dv&iiaMag r^-

1. xat] om. D. 2.jurj]

vno D, vito del. D 4.

6ta>s] post -s- ras. 1 litt. D, -OTKG- in ras. D 4. 3.

i$ D. ctvT&v] corr. ex CCVTOV C. 7. zldrxcov D. fffZtVrjg A.

9. U\IQV C. 10. diccGrdGfcog] -Gtd- in ras. D 4. doi-

Ssudrov] t|3D. 11. sldtrcov D. 12. %QOVQV'] %~&, ut

saepius. 13. nteiov C. 14. TO] om. D. 15. sôfifv

XQOVOV D. fr\v\ om. B. 18. ccvw[icdkov C. 20. x&v]rov in ras. A, corr. A 4

. KQI&ILOV] &QL D, -ILQV add. D 2.

23. TjHTjjtiaTt xat] -i v.- corr. ex JK A.

MA0HMATIKHS STNTASE&S S'. 475

part, xal TtokvjtkaGiaGavrsg avrqv litl rb coQialov

dvcojiaMccs p6ov xtvâ ra o A/3 fto ra yv6[iva,

lav plv 6 rrjs dvopaMas doid-pos lv rots litdvo

rov Kara prjxos MQIULOV peGov xivr)[iecTos r&v o A/3 5

v$ o, lav d' iv rolg VJCOXCCTG}) 7tQo6d"tJ6o[iv rots KV-

,xul ra fyv6êvK SÔÎEV^ a rots ^ 6hyjvrj

ovv

6vvyicov OVT&S v\\n,lv nf&odm&rjGttai, dua rb 10

xal rag rto%as aitaâg xgbg tbv di''

p,6riiiLfigLVOV ti\v r&v cdQiaicov %QOVG)V 6v6ra6i,v

fpBVKi' Qadiov 6s aito T&V v 'Afo&vdQSiy %Q6vov xccl

rovg v oitoi&dtjitorf nUâti yvr]6o[ivovs TJJS ccvrijs

Gv^vyias VQi6xiv do&wros rov xar' avrrjv Jthij&ovs 15

r&v far]n,Qi,VG)v cagav rijg dab rov p,6riyifiQivov ebro-

îj^. ano yciQ rqs r&v otxij6G)v diacpogas

rov dia rr\g 3tt,r]

lioiQccis dicc(p8Oi rov di 'AAl~civdoias<) ccv [iv 6

dta rqs 7t^rjrov^vrjs K&QKS [i6r]n(lQivb$ an' dvccro- 20

AcbvYI

rov di,' 'AA.%ccvd()ias<) roGovroig %QOVOI<S v6r-

QOV Xl do&i rsrviQriG&ai rb (pcci,v6^vov^ lav d djtb

orfoov rots avrotg, r&v dxaitvr %o6v(ov

piav d^Kovon noiovvrcov cooav

2. ft o] \L o corr. ex ô A, ^ D. 5. eb^tatov] -i- corr.

ex a in scrib. C. 6. o] om. I). S'] mut. in 8e D. TCQOO-

D. 9. ysvofifvos D. 11. ndaag D. 13. %QQVOV C,sed corr. 14. ysvo[ivovs D. 15. n^&ovs] -&- in ras. A.

~

B.19. rov~] corr. ex rov D 4. 22. Terr^tiGftKi B. SO] 8' D.

24. coâv] corr. ex &QCOV D 2.

'. JISQi T&V KhL7lTiX&V OQCOV IjAt

TOVTCOV d' ovrog <pG)dsv[i8VG)v <xx6A.ovd"ov civ f

ra <5vvrivovra agog rovg wtentriKov

5 OQOVS TK)V TS TOV JjMoV KCil TG)V TVJS (?/Lt?V?? STCITCQOG

) ivcc, xav pi} 7id6a$ rag TtSQiodixas

ds

10 xcc6rrj r&v

iv [iV ovv r& ago rovrov Gwraypan [Vp. 4217 3]

,ori rijg 6^t]vrjg fj did^r^ogrov Kara TO fi

f>

yi6rov avrr^g

15 yQayoyiBvov 7tQi TO KWTQOV rov tydiaxov iiyi

xvxkov [lias {loigas t,r]xo6Tcdv ha x, dta dvo %,%.-

^(DV yyvrniVG)v 7tQi TO a7t6yiov avri]g rov 7ti-

XVX&OV TO TOLOVTOV iltl'kQyi<5a\LSVQl. Xal VVV d'j

7tl

rovg iLyi<5rovg T&V iKfaiTtriKCbv Gv^wyi&v OQOVS TCQO-

20 aiQOV[jid'a hafatV) OVTOL $' ltilv 01

vr]s itQi TO 7tQiyL6raTov ovtirjs rov

dia dvo Tt&hiv r&v itQi TO

kltyK>V) 7tl,dfl fiia T&V

a6(paA.()TQOv avi'rj

ra roiavra dfixvvfiv, arjfa'

1. f'] om. D. 3. erpoSev^vcov C. 4. TtQoa&fjvcci CD,

corr. D. 5. rfig] ins. D 2. IninQOGQ-rjCEcov A. 8. &7ts-

GELV D. 9. yCvETcu C. 10. bY.a.GT'ri] corr. ex sKccGrccig D 2,

xatfT7]s A. 13. OTt] otl

D, ut saepius. 15. gcoduxxov]

S$f D. 20. d'~\ 8s D. 22. TO] corr. ex x&v D. TISQL-

ysiov] corr. ex itsqiytia D.

MA0HMATIKH2 2TNTASE&2 S'. 477

xal svrav&a 7tQi,(pQiav bîoicog j] Tr\ Ê^rjvrjg did-

TOIVVV'

ETEL <Z>tAo^ro00., o Itirw (pod' dnb

KKT AiyvTtTiovg âîsvcad' xtj sis ity'

ditb Gjoccg 17' aQ%oiisvr]g &$ i Arj'yovGrjs iv'Ate&v- 5

fj Gskijvr] rb Ttteidtov an'

ovv 6 ftsVog %QOVO$ yzyovev

~fi L' &Qas xaiQixas rov peGovvxxCov, ai fa

Qivca /3 y' dux TO rbv ijkiov E7t%iv axoifi&s TKVQOVteal GwdysTcci 6 aito rrjg e'jro^g XQOVOS 10

Alyvntiaxcbv

Xttl fjlLEO&V ^ Kttl COQ&V l^liEQlVCbV aTth&S [IEV id y\

nobs de ra 6{iccA.a vv^d"^^socc id /w/dvov, xa^' ov %QO-

VOV TO KBVTQOV T^g Ge^tjvrjg ftfVog {16V 7ti%SV 2JXOQ-

jtiov H,OIQK f pO") axoificos ds poiQas ^ 7?, xai ditb 15

H,EV TOV KitoyEiov TOV EitiMJKôv [loigas Q^y |iZ,aitb

ds TOV PQQELOV TtsgccTog TOV Aooi> Kvnkov [IOIQCCS 9^ >c,

yavEQOv, ort, OTCLVriK noigag dcp6Trixr] T&V Gwds'tipcov

TO XEVTQOV T^g 6^nvn$ id> fov Ao|oi) xvxkov Ttegl TO

kd%i,6Tov ovtiyg djcoGTrjiicC) xalri

iitl TOV yQacpopEVOv 20

di CCVTOV ttobg og&ag TGJ Ao|w Kvxkco iiEyitiTov KVX-

TO KEVTQOV Ttjjg 6M,&g ,XttO1

'

J]V TCKQodoV CCL [l-

T&V E7tl,6XOTYJ6G)V KTtOTEÔVVTtti,

TO [_' XCCi 1$'

drj T& K Ti Trig tQfays xccTa Kdkmjtov 25

)o i^nv y dnb NccflovaGO'dQOv, KKT

3. (?TH/] comp. B, son D. cpod'~\ <po8' eros D. 4. Na-aGaQOv D. 5. a^ôftsvi]?] corr. ex KQ%ov6T}$ D. 6.

C, corr. C 2. 7. ytyovs D.

IS^fiovov B. 14. tnsfye D.

21. ccvtfjs D. 23. L'] r|T A, i^BCD. 25.

ABCD. 26. NKovvKGaov D.

riovg Tvfll /3' si$ rr^v y' &OKQ s' ao%o[ivr)S ivr

ijoâro xA,i7ti,v rj GsAijvr] xal 7t0xortjd"rj TO

KTtb vorov daxrvlovs y. sitsl ovv Tt^Kiv xal

rj plv aQ%r} rrls Mfafyscos ysyovsv nob dvo ct

5 QM&V rov iisGovvxTLOv, 0.1 fiâv iGruiSQiVul sv'

re xcti sv 'Aks^civdQsia |3 yf

dia rb rbv ijfaov sjts%iv

axQip&s *TdQo%6ov poiQcis rj,6 ds

w rb TtfotGrov 7C6xortj^"rj^ TIQO K L' yr

forjlieQivfjs rov peGovvKrCov, xai GvvKysrai 6 aitb rfjs

10 rto%ijs p%Qi> tov {i6ov rijs bclsfysog %QOVO$ ertbv

%$ Kal vunsQcbv OKCC xal faocbv

ttgbg ra d[iaha vv%d"ij[iaa I xal gr

,

ov OVOV r

15 rov anoyeCov rov frtixvxAov [loioas oor] jitg, aTtb d

rov ($oaiov 7toaros itl rov Ao|oi) xvxAov (loioccs &ji

AST, tpccvfobv KCil vrv&v, ort, orav i AS: poioac; dcp-

rcov 6vvd0iG)v rb

fo r avr

20 rov xvroov rijs Gxi&s iv\v xoivrjv ro^v 7t%ovrosrov r di,a ii6(DV uccl rov dia rov mvroov xv\ <3A.yj-

v*l<3 nobs oo&ag r& Ao|c3 yQafpo^vov [ifyfarov XVKÔV^

ror rb rtragrov psaos ig rf}v Gmav [ut6lrai, rijg

1. y'] ZQitTiv C. 2. sv.lL(indviv D. 3. xat nakiv BC.

4. ysyovs BD. dvo] |3BD. 6. lv] om. D. y'] A,

i' y' BC, /.' D. to] %s C. 7. rj] /.' D. 8. Post y' suprascr. fu

vC 2

. 13. ensile D. 15. (loiqas 16. xvxôv] mg. D 2.

16. Inf] om. D. ponces G7t A?] corr. ex pcnte D 2, ft ^r Z?

mg. D 2. 17. OTI] o D, o' D 2

. F] f xat D. 18. r&v\ anbr&v D. 19. CCVTOV C, corr. C 2

. 23. TOTS] bis C, sed corr.;om. D. TfTa^Tov] d'

1 BD. 6%idv\ seq. ras. 2 litt. C.

MA0HMATIKHS STNTAEE&S 5'. 479

l' <xv plv rjxal y' poiyac;

7tl rov Aooi> xvxhov rb xevrQov rrjs

xal x' $r}xo6ra pices {IOLQCCS snl rov dia r&v

avrov yoa(po[ivov [ifyfarov xvxhov

rov dice [isGcoV) otccv df dsxa ÎOLQCCS xal yT&V 6vvde6(iG)v uits'm xata rov Ao|6v KVXÔV^ vd /_'

yr

,rjxo6ra [it,as [lotoag tni rov diet rcov itok&v avrov

yQCKpopsvov psyfarov xvxAov dUtirarai, rov diet iisG&v.

jtsl ovvfj [lev rcbv dvo BKtefye&v V7tô%ri rb rgixov

, rilg GEArjviaxijs dialerQOV, fjds rcov exxst,- 10

rov xevroov avrrls sitl rov avrov neyfarov

dvo dia6ra6G)v ano rov avrov 6q[jiELOv rov

dt,a [i6a)V) rovr6nv rov xwrgo

â /LtJ, dijAov, on, xali\ dt,d[irQOs

ffitoretvst, rov xara rb Ad%i6rov avrrjs 15

yoacpoîvov Ttegl rb Ktvrgov rov ^cpduaxov

xvxhov 3tQHpQiav ^rjxo6r&v {loigas [lias

yyi6ra. STCEI d xal iv rr[ dsvreQa r&v mfai-

xa&' tjv rb d' zxtekoC'itEL rqs 6^vLaxrjg SLK-

[iroov, a<p6rijxi, rb xsvrgov rijg GEAtfvrjs rov [iv 20

xvroov rrls Gxias E^xo^ra vd /_' y ',rov ds

xa&' o rBîvBi rfjv ryg 6xia$ itsoicpSQEiav ^

vvovGa avr&v ra XEvrga, rb d' r^g diaperoov ri}s

1. aHa A. anÊi D, corr. D 2. 2. TO 4.

bis D. 2. H&VTQOV D. 3. xca] supra scr. D 3alt. loco. xj

mut. in y B, om. D. 4. [leyfarov XVHÔV] om. D alt. loco.

5. $8~\ supra scr. C 2. ns^nta] 'ss B, s

aD. 8. SUGTCCVTCCL A.

9. TQLXOV] y' BD. 10. TOV syiyiBi^svov C. 11. TOV (pr.)]del. C 2

. 13. Tovrtcn D, comp. B. 14. ju-tag poiQ<x<s~\ om. D.

ict\ corr. ex 18 D 2. (ttr]s D. 16. TO] supra scr. D 2

. co-

SIU-AOV~\ ^~ D. 17. TtEQifyft,1

D. poiQKs piag\ om. D. 19.

D.


o fanv QyxoGr&v rj /_' y', (pavobv avro-

on xal % IK rov XSVTQOV rffc Gxiag xara TO e2.cc-

%i6rov rrls ^s^tjvrjg a7t66rri[ia xaraksiTtsrai, QrjxoGrcbv

JLtg*xaC 6Ttv ddt,ay>6QG) {isifav rj

diTtkatiiov xccl tots

5 TQLtil JtS[l7tTOlS {1%O)V tr\ X TOV XSVTQOV T^S Gshtfv'rjS

sfyxoG't&v ovtfys t, rB. akka xcclfy

^x rov XSVTQOVrov fyfov vjcorsivsi TtsaKpsasiuv dpofag tov w* Kv~

rov yQccfpoîsvov nsol rb xtvrgov rov ^cpSiaxov

6rov xvxkov sfyxoGrcbv 7f ji' fadxis yao

10 [V, 14] xarccîsroovvrsg rovs Idiovg xvxhovg o re

xalfj Gsktjvr] xara rb sv ralg Gvtvyiais {isyitirov CCTCO-

orav CX.QO,rb (paLv6^svov xsvraov rijs Gsktjvrjs

rov xsvroov rov fjMov etp' sxccrsoa rov dia

ioioas o ky x, r6rs rtgcbrov dvvarbv

15 etirai r^v (pcuvopevyv fttGiv rijg GsArjvrjs xara xv\v

STtacprjv yevzG&ai, rov fjJitov,

oiovj sav VOYJG&IISV rov [isv dia {isticav r&v

xvxhov rtSQicpeQsiav rqv AB, rov de Ao|oi) rrjg

VYI rf}v

20 ii%Qt> yz rav xara rov$ sxfaiTtnxovg %$6vovs

xal dia r&v rov Ao|oi) x6A.G)v yodiltcoiiev

xvxkov TtSQKpsQEiav Tqv AEP, votfG&iisv ds xal

rb A Grjjistov rb rov i\Uov fiiiixvKliov, itsol de rb Erb

2. ort] om.C. 6. r*~\ r ABC, FB D. Mg. tf AC. 7.

r -D. 8. Supra ygacpoiisvov add. ft O D 2

. q)8i,aKOv

xvxôv] D. 12. Ante nsvtQov del. TO C 2. 14.

potgas] om. D. rotf] supra est ras. A, & SGTIV in r&v

KVTQ(OV KflCpOT^QCOV T&V CpWTCQV TOT B. TT^COTOv] COrr. 6X Ci D 2.

15. i-Gtcci] om. D. 16. ylvtoftcu D. 17. eodtW] ^co D.

20. tnleaeift D. 22. itegt] nsgl ^v D. 24. rfjg] * rfc B.

MA0HMATIKHS 2TNTAEE&S g'. 481

TOV flfaaXOV XCCTCC TO Z 6^iOV^ f] AE 7tQl(pQlCC, $V

d(p0TrjXv TO E (pcciv6[ivov XVTOOV Tijs Gfhrjvyg TOV

A qAlCCXOV) dvVCCTCCi ItOTS yV6^CCi TG)V XXL^lVC3V O

ky x. aM? v Tolg ccitb MfQorjg Tovtoig, oitov % [ie-

yiGtiri JIILSQCC WQ&V itinv Utlfr&Ql- 5

v&v ly, p>%Qt> Tobv fxfioA&v Bo-

ojtovfj yisyCGTri

0TIV farjHQ{,VG)V Ig,

aoxTovg TO 3tfal6TOvrj

XCCTCC TO TG)V Gvtvyi&v 10

TOV

TO

15

xcc

TCQOS [i

TO TtfatGTOV O VTJ. 3tO.QKM.d<56l $ KKI XCCTK

TtfaltiTov, OTCCV ^sv TO. orj agog Tag aoxTovs

3tQi TOV ASOVTCC XCil TOV 4ldv{lOVS O A SyyiGTCC, OTCiV

ra o vrj rtabg [ie6rj[i(lQiav ,nsal TOV

'I%&vas o Ts syyitiTcc. sav aocc TO

KSVTQOV vnod'to^d'cc XCCTCC TO z/, xccl STU&V-

\v z/JSJ Tys oAqs 7tccQaMd%SG)S) ^ ^ V ^F r/^S 20

XCCTK ftijxog k'yyiGTU h'tiTai 7tccQccMd%O)$) 17dl FE Trjg

XCCTK rtAdTOg. K)<5T, OTCCV [lV Kit' CCQXTOVfj i] GfAyvrj

TOV fjMov xal 7tccQccMd66r] TO TtfatGTov nobs fi6-

TK>V o T ^ AEF

1. AE] A- e corr. D. 2. aqp&Jriptf D. 4. x] xa C.

om. B. 10. nctQullaGsi D. 6vvyi(bv~\ corr. ex

A 4. 12. nccQaUd^

sD. 13. <'] e corr. D. 14.

TO TtteiGTOv] om. D. nccQ<xUd<)8L D. Ttort] supra scr. D 2.

Post xem del. TO D 2. 15. TtKgoi7.la.GGri] Halma,

ABC, TtccQaUdGrj D. 17. rd] om. D. 19. v&a>iie&cc D.22. oroiv] GTS C. 1^ Gflrjvri rj

D. 23. nuQcil.l.a.GG'ri] Halma,TtaQaMdGGei ABCD.

a Act syyiGta. xal snel A,6yog 6tlv trjg djtb roi)

iti to P ytQLcpOiag TCQog trjv TA xata rb

t&v ixkemtix&v oaav did^trjîa^ bv %i, ta

la // 3t$bg to a' vxatav6r]tov yag rîlv tovto yivz-

5 rai dia tcbv ytooccitodsdsi'ypev&v enl ty

GsAymaxov xvxAov xal avtjj psv ^ cuto tov

pov sjtl to F h'titai {loia&v tf Jcg, [ita $ tijs

t&v avt&v i% jia. otccv d' aito [i6<S/

q[i(lQfa$ ov6cc tov

ri^Cov to nfalGtov xgbs agxtovs 3tccoaAA,a66r] , rj [iv

10 4T 6tai, tcbv o A, i]$ AEP o'A?? tcbv o

jita, xal

dice ta ccvtafj [iv aitb tov ovvd6[iov Inl to F yioi-

o&v g v/3, ^ $ pttu t^S F4 o'At? tcbv avtcov ij xf$.

otav aacc to Kvtaov trjs tiMjvrjg axQifi&s KTtiyr[ bito-

tQOV tCOV 6wd6[JiG)V 3ll tOV Ao|oi) XVKÔV TtOOg ftV

15 aoxtovg ILOLQCKS I't, fi, nobs ii6r]iipQiav de {loioccg v]

xf$, t6t Tta&TOv v tolg XXLîvois t6rtot,s trjs xa&

lxovîvrjs dvvatbv eGtcti tqv cpcavo[jiEvr]v ccvtfjs

xctta tqv 7Cd(prjv yV6&cu tov oÂt'ov.

i to [iv ti\ fjkLaxrig av(D[icchias ntelo'tov

20 dicupOQOV a7idsi%ftri ILOLQ&V /3 x/y [111, 4], to df t^g

6A,r]VLCCxrlg to itQi tag GvQwyiag {LOIQQOV a [p. 337],

dvvatbv k'titau not xv\v Gekrivriv a(p6tdvai, tov Âtov

xata tag ttOLodwag 6vvyiag axQificbg [lotaag J xd.

1. [LOTUS'] seq. littera macula obscurata A; 6/noi'cog D,

mg. fta la D 2

. icrt D, comp. BC. 2. iiti~\ corr. ex

C. TifQtcpeQEias] ~S postea ins. C. 4. /_'] ^ D. 5. ccno-

D. 6. otvxZov] Q C. Kmr\~] avrr] B. 9.

&QKrovs~\ post v. del. G C. TtaQaMaGr) D. 11. ru KVTO]

TOV D. 13. orav] -KV del. D 2. 15. ds [i6r]iipQiccv D. 16.

D. 18. KCCTO.] corr. ex KK D 2. 21. TTf^t] 7r D.

23. axtcos om. D.

MA0HMATIKH2 ZTNTASE&2 S'. 483

iv o6G> di,SQ%ercci TccvTccg y Gfhijvr], 6 per ijfoog

TO iy' CCVT&V syyiGra, TOVTS&TIV o A#,

iv o6G) df ndkivfj GsArivr] TCC o Ad sitixivslTat,,

disksvGSTCU, xal 6 tffaog to iyr

CCVT&V ra o y(bv OVK&I yivsrai, TO iy' d^Moyov. sav &QK rd inl 5

to avTO o Ag, a yivtxai T&V f'| dp%ijg g ttd ft()og t/3'9

Tatg Tijs rjAiccxris dvcoâîccg ^lOiQcag /3 scy,

[toiQccs y } atg TO nXsltiTov dioiGovtiiv T&V iv

Qiodixais Gv^vytccis [istiov naQod&v îtjxovg TS

xal it^KTovg syyiGTO, ca dxQipeZg. xal OTCCV aget rj 10

rtdgodog TOV XSVTQOV Tijg Gehtjvrjs dfpsdTijxr] T&V

7tl TOV loÔV XVX&OV TCpOff [lV KQXTOV$x jia, agog psGriiiflQiccv 8s poiQccg Tec xfi, TOTS

TtQ&TOV iv TOlg XXL^VOLg TOTCOig dvVCCTOV 6T(U TYJV

(pKivoyLSvriv avTrig frstiiv XKTCC TJJV sitayiiv ysviGftai 15

TOV fjMov. xal did TCC avTa^ oTav 6 dytb TOV

3ioaTog TOV Ao|oi> xvxhov Tijg 6Aijvr}g 6

[p. 471] Tcctg TtSQLodixaig tivfryicug T&V

pbg iJTOi, TaZg dab %& i& [i%Qi<g yd xfi r) TKig dab

4ttcc tiwsftxfattyi) TOTS povov iv Totg 20

XXl[lVOig TOTtOig SvVKTQV S6TO.L 6vyifti]V(U TO 7COO-

xsiyisvov.

1. ravra B. 2. ty'l if* C, ut saepius; I r corr. ex ri D.N

3. GfHijvri] <[ D, ut saepius. litMivltai\ corr. ex sni-

MEfrcii A 1. 4. iy'] i y' D. 6. ;|] corr. ex ih. D 2

. t^'Jcorr. ex iy D 2

. 7. ^^lax^g] i\- e corr. in scrib. C. 8. Si-

D. 9. Teas] T?? D. 16. 6] om. C. 17. 6] om. D.

18. rats] *?<? D, ut saepe. T<MV JLIOI^COV] fi D. apfd-lfAog A,

19. pi-iQi, D, corr. D 2.

r/'] seq. ras. 1 litt. D.. D 2

.20. ~svr\\ -J] e corr. D 2

. ^X9 L D- cvvf^ninrfi, C. 21.

TO 7tQOY.ipitVOV 6Vfl^f]VCCL D.

31*

xccl T&V rijg Gehtfvrjs sxteiitTwcbv OQ&Vx TOV XEVToov

rb kd%i<5Tov KVTri<s djt66Tr][i

O fc JZ, ^ 6s X TOV XEVTQOV Trjg

ov6K xal ri rots XQitii ktyuctotg

v rv\ IK tov XBVTQOV rijc; GeAtjvrjs tivvcc-

yetai, r&v avrcbv o jie vg, dijAov, on xcci, otav rb

XSVTQOV rils Gshtfvrjs dxoifi&s ccit%fl TOV XEVTQOV Tijs

GXL&S BTtl [ISV TOV dt' CCVTG)V Xttl TG3V 7t6k(QV TOV

10 Ao|oi) yQCKpopevov {isyiGTOv xvxhov l(p sxccTeoa TOV

fiotoccv a y Ag, iitl ds TOV Aooi) xvxAov

d(p' OTCOTBQOV T&V GvvdsGp&v XUTK TOV

TOV vbg nobs TCC Id /.' Adyov poi^as t/3 ifi

TOT JtQ&TOV dvVCCTOV 0TKi TJJ

15 Gxi&g. did Td avTa $ Totg ytgl Ti}v dv&iiKUav dito-

xat, OTCCV TO xccTd TJ\V {lEGrjv Ttdgodov

M-VTQOV Trjg 6^tjvrjg dytEGTijxr] T&V 6vv-

l TOV Ao|oi) xvxkov [lotoag Tf t/3, GXSTE Ttdfav

xccTa Tovg dub TOV fioQsCov TtEQUTog doi&-

20 povg i'g T Tovg dnb od ^ p%Qt' ^ i>Pxcti *t$ Tovg

ditb 6vd ^Trj ^B^QL GTCE i/3, rdrf itQ&Tov dvvciTov <5Tai

Tr]v QEKv\VY\v ttJCTEGd-cu Trjg (Sxicig. Jtaoad'rl(30fiv ovv

Tolg 7tQOXi,^ivoig T&V Gvtvyi&v xavovioig xal Tovg

1. ([smg. C. 5. nsfinrois] f' B. 11. loov] ante |

ras. 1 litt. A. 12. &cp'] corr. ex tap' D 2. onorfQov D,

corr. D 2. TOV] om. CD. 14. ngmtov] K D. ftyrca] om. D.

rr)v] corr. ex rfjs D a. G^vr]v] comp. D. otyafftfm D.

15. TG>V avcoiLcch&v D. 16. ft\v} om. D. 17. aqpfffrrjx^-

p. 485, 12. rip/] fuit etiam in mg. sup. D, sed eras. 19.

xara] corr. ex xa D 2. 20. xori 21.

tJ3] mg. D 2. ft's

rovs] efc D. 22. KipaGftcii D.

MA0HMATTKHS 2TNTASE&S S'. 485

r&v re fjhax&v xal r&v 6s^viaxcov oocov rov

rijs GsAijvrjs apt'ityiovg, iva xal rr\v r&v dvvajiEvcov

[i7C6Eiv didxoiGiv e% eroCpov

g'. IJegl rijs dia6rd0a)s r&v sxkEiitrix&v {lyvcbv.

Kal 8ia noGcov d' fag iniTtav ^vcbv dvvccrbv 5

Herat, rag Gv^vytas Exteinrixas yivEGd-ai,, %Qtf6i[iov av

sty rovrois itgodd-elvcci, TCQOS rb Accp6vras pfav Bito^v

xfat,7tri,xri$ 6vvyiccs ^ jfccGag xdAiv rag s'gpsl-ijs, aAAa

rag dt' o<?v av vds%6[ivov TJ [irjvcbv sx^s^iv ysvi-

rcbv OQ&V EJtfaxEiluv itaQaAappavsiv. 10

rb [iv ovv $L $% [irjv&v dvvarbv slvai, rov re

ov xal rqv 6&rjvr]v fafafaeiv avro&sv av si'rj

xara itAdrog Ttdpodog rijs

ev rots <5 [irjGiv tfwdyfl ^to^ccg QTtd a us, aC ds

r&v sxfaLitrixcbv OQ&V TtSQicpEQeiai, xal tnl rov 15

xal eitl rr\g Gshijvrjs aC {LEV svrbs fiinixvxMov

avr&v HOLQKS jtEQi,E%ov6i,V) aC & VTCEQ rb

TtAsiovas' r&v rs yag fifaax&v oo&v TCQOS

ras agxrovs drtohaiifiavovrov acp' OTtorEgov r&v

rov Ao|oi) xvxXov rils ^E^tjv^s *&S 20

[p. 483, 10] potaas x jita, ngbs d%

potoas Ta xfa xalrj pv ait aoxr&v dvsx-

poiQcbv ohy A^, fjd' ditb

1. re] om. CD. xca] re xat D. x&v (alt.)] om. D. 3.

A. 4. s'] BC, mg. A 4

,om. AD. 5. dvvccrov]

supra scr. D 2,Svvatcov C. 6. yevzoO'cti, BC. 7. TtQOG&fjvai D,

sed corr. 9. sxieii/jftj yiVEGftui D. 10. nccQaJicc^dv \

C.

14. 5] gg BC. pj\Gi D. ^rd] ^t C. 17. t] -I posteains. C. 18. i]iu.Y.vY.).iQv] TJ- corr. ex N A. 22.

'

ft D. xcu] om. D.

486 - KAATAIOT HTOAEMAIOT

OiQ&v Qvt, Zs, r&v rs Gshyviaxcbv aito-

ig sxdrsga ra [isoy rov did [is6G)V snl

rov avrov uvxhov [loigas aito r&v 6vvds6[LG)v is t/3,

xal sxatsQcc r&v dv^sCitrov Ttsoiysosiav Gwdysrai,

5 {loiQcov ^ftO" Ag.

on, ds xal dia tovr&v r&v VTto&sGs&v dvvarbv

dia rijg

rjv 6

10 ldoi[iV av ovrcog'

7ti8ri pay v rfl [itey 7tVTcc[itfvG) xv\v

KKTQOV t&V

litl rov STUKVKkov ^lOioccg QX&,rovtcov

15 df ccC [ilv o{i A/3 rov rikiov ^LOIQCH, Kara rv\v scp %d-

rov ttQiysuov [isyfarrjv Jtdoodov

rqv [teGrjv [loioas d A^, ai $ rov

r?ls 6^tjvris QX& * poiQai Kara, rr\v iy sndrsQa rov

aTtoyLov &a%i6rr]v xdoodov dcpaioovGi,

20 poiQas y P) v r& XQOVGJ aoa rijg fA<?^g

orav 6 [ilv ijUos rfv psyfarriv itoirpai rtdgodov, i\ds

ryv &a%farr]v, sn TtQoriyov^Bvri 6rau rov

rats f' d^igjorsocov r&v dv&tiafa&v

Qais 1/y 1/rj.&v nakiv rb i$' Aafiovrsg

25 did ra JtooaTtodsdsi'yiisva s'^o^sv [lolaav a xal s%rj-

xotird g fyyiGra, r^v 6 TJAtog TtiKivrfov\6rai p%Qi rov

1. tg] corr. ex vg D 3. 6. dvvccrov] dwccrav A. 7. GB-

D. 8. TOVTEGTIV] comp. B, -v eras. D. 15. 8\D. 16. bulappdvowiut D, -v eras. 17. at] corr. ex

Sid D 2. 18. [taigas C, corr. C 2

. 21. TrotTyrort] D, TtoifmaABC. 24. lunpdvovTes D. 25. nQodtdsiy^vcc D. 26.

ante ras. 1 litt. A.

MA0HMATIKHS 2TNTAEES <;'. 487

V7CO T^g tffA^V^g. 1tidr] OVV X 116V

T^g iSiag av&paMag jrtAr?<pt (loiaag d xal

A??, x ds Trig pfyQi tr]g axQifiovg (Svtvyiag

[lOLQccv a xal z^xoGTa ,Etittu xal

fj

naga TJJV (isGyv 7tsi,hr]cpvttt Kara 5

xccl t,r]xo6Ta [id. ToGccvrag ago.

GTCC ncclfj

xara rtkaros Jtl tov Ao|oi) uvxAov

fl<3 0^t]vris 7ti,Ar](pvta 6xai [IOLQCCS rots

\Li6v\v jifvrcc^vov ffvvayo^voig Ttlarwolg

Qvy KK fyyitira' &<5te nal q axQifl&s &G)QOV- 10

xccra nhdros xaQodog iv TTJ psyiGrri Ttfvra^vc)

QV& KKl %r]XO6tK)V . AA' 01

<p' xdrQa tov dia [i<5cov x2.t,nri%ol Kara TO

rijg G'fA^V^g OQOI 7tQi%ov6iv iitl \JL\V

TOV dia T&V nolcov TOV Ao|oi) ygayoyidvov \ityi6TQv 15

[lotaav [iiccv lyyiGTU dia TO T^V ply XCCTK TO

slvai [lotaav a ~y Ag, Tr\v ds KKTK TO piyi-

GTOV &vvd'y6d'ai o v$ xd, iitl d TOV Aojoi) xvxhov

ano T&V 6vvd6(iG)v T^^JLCCTCC la A, rjd [iTcc,v av-

xal dvx^L7tTos 7tSQi<pBQt,a dice TOVTO GvvdysTai, 20

o, af

iTive$ ^KTTOVS i<sl T&V xaTa TJ\V

itiKaâvQîvKtv TOV Ao|oi) xvx-

Aov oi,QG)v V& xccl xo&c&v TriaGi, dvdl xal

1. f'x] coir, ex ^ C. 2. fTrfdrjqpft] -I- corr. ex ^/ A,

post qp del. -O1 C 2

. 4. Y,CU f^rjxoffTa ?] e; D. 6. (IOLQKS]om. C. xca f^jtoara] om. D. 7. rj] om. D. KCCTO] -TK

add. D 2. TtvxAov] uvnlov

r\D. 12. xal rjxo(>T<a?>] om. D.

14. nQl%QV6lv] TteQliÔVGi TOV loÔV D. 711 - 15. TWV]bis D, sed corr. 15. TOV AO|OV] om. D. 16. jtuav] a BD.

17. fld%iGTOv] hinc inc. A 1fol. 175 (quatern. %y). a] jiitav A 1

.

21. ftfft] mut. in tt'atV C, sed -v rursus del.; comp. B. 22.

-o- in ras. A 1. 23. QV& v.ccl I |rjxo(7T<m'] 9? ^f D.

B.

. <pavQbv ovv lx rovr&v, <m dvvarbv

<5rai r^v 6eAijvr]v ivrift peyfavfl Ttfvraîrivc} xard rrjv

no&ryv navG&rjvov xfafaov6av xura r^v dcp'

QOV r&V 6Vv86p,G)V KJtO^COQîV XCcl V

5 jtavGsAtjvG) rtdfov exfafasw xccroi rfjv iitl tbv svctvriov

tQOtfodov anb t&v ccvr&v pSQ&v rov dia

sv aiicpOTQat,g ral<$ sxtefysGiv rijg eTUGxoTijGs&g

xal ovdejtors aitb rear svavri&v.

on jiv ovvYI iLfyfaTi] ytvra^r]vos dvvatai, dvo

10 TtQivfiui GfArjviaxas fxtefyfis, ovr&s rîlv

or i, $ dt,' itra [iqvcbv advvarov 6rca rovto

fti]vai) xav r^\v lka%C6rriv fjtrd^vov V7to&co[id'cc, rovr-

qv 6 {lev ijA

d 6&ijvr] ityv iifyfoTrjv , i'doi[iv av

15 CiVTOV TQOTtOV CpodVOVtS

7tidrj ya$ jtdkw iv

y ^t, ^ d' v TO) 3tixvxA.G) ri}g 6-

[toiQag ^r jity, TOVT&V d' at plv ~6y

20 rov i]Uov xara T^V (p xdra rov

1ii6r <

Y\v nccQodov acpaiQOvGi, rijg

d/Lt/3,

CCL df rov 7tixvxhov rijg

xaru rr\v (p' fxarfya rov

jtQoed'yovGiv rri \ii^ poiQag 0- v^5iv raj %QOVCO ago,

25 rijg listing 7trtt[njvov ,orav 6 plv ijfaog rrjv

3. &cp'~] A 1C*D*, V BCD. 5. TOV] T&V C. svavricov C,

sed corr/ 6. TtdgoSov D. 7. ixlffyeti D. 11. a.8vvoirov\coir, ex dvvurov B 2 C 2

. 12. TOVXKGTI D, comp. B. 17.

nard] corr. ex v.a D 2. 18. d'~] de D. 22. QTC jZy

ft gn fty D. 23. fieyiar C. 24. nqocdyovGi D.-fr]

corr.

ex o D 2. 25. pearis] A 1

, i\aîerrig BCD; cfr. p. 493, 14.

MA0HMATIKHS 2TNTASE&S S'. 489

6rai rov yhiov r\ Gshtjvr] rats f| cip-

riibv av&uaAi&v Gwccyopsvais poCgais idjit.

dia ra avra TO ifi AccflovTSS xal rtQoe&svTSs ratg

&[iaMccs zhkekoiTtviaig [lOiQdig d pp 5

[IOLQCCS vs syyiGra %0[iV) oGais ij

re Kara pfjxos ndgodos ev ir\ ikaîGiri 7tra[irjvq) v6ts-

sv ffi ftfV^, xai % XKTCC rtAdros axSavr&s

et r&v XKTCC rrjv iifayv ^XK^VOV 6vvayo[iva)v

ft/3*v rfj lka%C6Tri CCQCC eTtraiirivcp inti- 10

xccra jrAatog v\ GfAujvY] eitl rov Aooi)

xvxhov riirniarcx. ^rj [i oAys r^g psraZv rcbv

x&v xccra TO pfaov anoGrri^K T&V trig

TOV Aojot) xvxhov peyfarris ytSQKpsgeias rov re XCCTK

rrjv nooGcc'y&'yriv rov sregov r&v GwdeGiicov xal rov 15

uccra r^v a.TtQy&gr\i5iv rov eva

ov6r]s isy o. ovx CCQCC dvvarbv eGrai rqvovd

1

iv fi\ A.ct%farr]

Kara rr^v TtQarrjv TtavGeArjvov oitcotidrjitoTE xal Kara

r^v rztevraCav TtavG&rivov hi, Exfafafiv. 20

dfixrsov drj nakw, on xccl rov ijAiov dvvarbv

6rai, itaga rois avrotg dig MfafaEiv iv rr\

xal xarcc jtdvra ra

fi ya$ iv ry \Ltyi6xri Ttsvra^vG) rrjv xara 25

Jtdoodov rr\$ 6Aijvr}s a7Cdâiiv [p. 487, 10]

QV& rife dvExfafarov 7tQi,(p()iag iitl rov

xara TO [iGov ano^rrnia T^S GfArfvyg r&v av-

1. noiSiTca C. 7. iv Tj]] coir, ex Jyyiffra D 2. 13. r&v~]

om. D. 18. ovd'~\ ovSs D.' 20. hUni-iv D, corr. D 2;item

lin. 22. 26. tfâVrg A 1.

r&v yivoîsvrjs 015 k% SIM fb xal rovg il

ooovg avrov rov dia psticov aitiîv 7tl [ilv rov dia

r&v itoh&v avrov xvxAov rîtjîara oA/3 #, siti ds

rov Ao|oi} tils tiskrivris [lotoag g /3 syyiGxu, dÂov,

5 on ^dlv ply TtccQCiMattovGrjs r^g GeArfvyg ctdvvatov

TO JtQOxsipevov dia ro [i%ovcc elvai rrjv ccvex-

tys sv rfi psyfa

7tl plv rov Ao|oi)

7cl ds fov itgbs oofrag iti dice ^d^cov o

10 OTCOV ft av dvv^TKi TtaoaMccGGsiv ovrca^, co6re rag iv

OTtorsoa rCbv axocov Gvvodcovrj

xccl rug 6vvaî(porQ03v

7taQcdhd,i,g ra oft vxsofldMsiv ,

sxet dvvarbv

xal rag axoag Gvvodovg aî(poroag xhf,7tnxag

15 7tidrj ovv idstifrpsv [p. 486, 20] iv red %QOVG)

yLeyiGrvis 7tvra[MJvoV) oravrj [iv tfehfan} rqv

6rr]v itoi,r\ra,i jtdgodov, 6 d ijfoog rqv [ifyfarrjv anb

r&v dvo iiQG>v rijg JlaQ&svov ^%oi rcov dvo

rovf

TdQo%6oV) Jtoorj'yovêvrjv BXI rov r\îov

20 htfvrjv ralg x r^g a[i<porOG)v r&v

~iy Irj) ravrag $ xal b'u rb i$' avr&v

on rov

25 TCfvraîTJvov %QOVO farat iftLSQcbv opy xal faoatv1/rj

xal dia rovro rf}g Ttocoryg xal itQl ra dvo

14.

TttVTCi-

5. ftj>] om. C. 10. TtUQcduGGtLv A 1. rag] om. D

\6ftai D. 16. iifyiGrrjs] -ijs in ras. A 1, fi&rrjs D -

/u.rjvo'u]IT- in ras. A 1

. 19. 7tQor}yov[jiVT]v] -j\v comp. add. C 2.

20. r&v] om. D. ccvapccUKS D. fiotQccg C. 21. i(3']

t'^' A 1

(" in ras.), C. 22. fiG\cog mut. in [ts\Gcos A 1. WQUS C;

comp. D, ut saepius.

MA0HMATIKHS ZTNTABESS '. 491

yi,vo[ivr]g Gvvodov % TEtevraia xccl JCEQL

ra dvo pegr] rovr

Tdoo%6ov ywopEvr] noorEoov 6rai,

rats tg oAag r^iEQag fainovGaig agcac; g.

aga, jtov Kal TtoTE dvvcttai, % Gektjv'r

r\XOl V t& StZQCi rCOV JtQOKSlllSVCOV dG)dXCCrr][JiOQlG)V 5

iv r&f

Tdgo%6G) tys iv rrj

TG)V

CCQXTOVS jiV ovv ovdapij rrjg xa.& JHJL&S ol-

)%a&' ov ftgrfxccfiEv tgoxov, ffbyfaxeccu TOG- 10

ovrov 7taQah%d66ov6a rj <3^vrj' o&v ccdvvcctov yi-

rb iv rr) psyiGrri Ttfvrcc^vG) dig mteiTtsw TOV

xara rfjv anb (t4qpfiya$ rov dice pfacov

itdgodov, rovrfatw orav XKTK plv r^

Gvvodov aito%G)Qri rov xaraflipd&vTos (Jvvde^ftov, 15

xata $ rr\v rskevraLciv Ttgo^dyr] r& KVCC^^CC^OVTI'

yipftofav ds 6%dbv onto r&v fira xov fay-

oiKOvvtcov &$ itQOQ rag KQXTOvg dvvctrat, rb

roGovrov iv a[icporQOi,g rolg xxt,(ivoi,g dodwccrrjiio-

Qtoig Kara rr\v itQO 2 GZQ&V ftteiv 7taQaM.K66i,V) 20

orav ra plv r^g Ilag&svov dvo [legy Kara ri\v JCQO)-

rrjv Gvvodov itl rijg xaradvGf&g vnoxfyrai,) ra df

rovr

TdQO%6ov Kara r^v devrtgav tivvodov 7tl rov

Kara pay rag rotavrag &E6i,g vafaxo-

ETtl rov pEGov aTtotirtfiiarog nobg 25

1. Trap D, ut saepius. 2. vdgo D, ut saepius. 4.rj]

in ras. A 1. Tta.ga.lla.GG

A\

C. 6. vdQr]%6o) A 1. 7. ntefav C.

10. TOGOVTOV tvQiGKerai D. 11. 77 Gs7.r\vr]'] om. D. 12.

Jx/lftjrftv] supra -fat- add. i D 2. 15. aTro^cop^] D, ccito%co()i

A^C. Kapifidfrvros D, corr. D 2. 22. VKOKSLTCCI D, corr. D 3

.

25. Post 7t$6$ locus relictus ob naturam pergam. D.

rrjg r\^ia-

xi]g TtaQaMd&cog vitb [ilv rbv farjpfQivbv v {lev xr\

rr}g UCCQ&SVOV fteGsi [loiQcts o xf$ fyyiGra, v ds rfi

rov *T$Qo%6ov o id, onov dsi\ psyfaTr] r^neQa

5 Idrlv ifi /.',XCCTCC [isv TYJV Tijg naQ&svov &<3i,v

o x xardi de v rovf

TdQo%6ov loiag o

rag

O

rovg POQLOTQOVS ad rojcovg

10 xaQaMd%G)$ yivo^vrjs yccvfyov, on xal paMov addvvarbr ztixcu, rots v avrotg ofaov6i, dig v

(5rri itVTa[itfvG) (pawfjvai rbv ijfaov xfofaov

pswoi rqv an aQKtcov rov dia [i6a)v rqs 6-

TtaQodov, rovrttSnv orav 7tl pv rijg

15 xtefy(Qg aitoG)r rov avaf$

r] rip

rtdfav, on, xal v rr\ ifajfatft

dvvarbv 6rai, dig rbv ijAtov Tiaoa rotg avrolg

7tiv. 7tidr] yaQ v ry &a%i6rri BTtra^vG) rr\v xara

20 n^drog rrjg Gfhijvrjg xdaodov dnd%a[iv [p. 489, 10]

rcov EKketTtriKcbv OQGOV 7tQi(pQia rov Aooi>

rqg ano rov xara rj]v itgoGaywyfiv rov MQOV 6vvd6-

uov ii%oi rov xara rrjv aitoi&QriGiv rov wavruov

4. 8i] -s in ras. D 2. 5. iott D, comp. B.

om. D. 6. x^] corr. ex v.$D 3

. [IOIQCCS] om. D. 7.

om. D. 8. ^TJ] corr. ex Se D 2. 10. (i&Uov ccd dvvarov -v

ccd S- euan. et eras. A 1

(NA//J). 12. snteinovTcc]-- in

ras. A 1. 15. ano^co^ri] D, ano%a>Qi A^C. 17. i^viA D.

18. rbv rjliiov dig D. TCCCQCC TOI$] post ras. 5 litt. corr. ex' D 2

. 19. Post &a%i<nri del. rjj C 2. 21. S'] Ss D. 23.

6- in ras. A 1.

MA0HMATIKHS STNTAgESS g'. 493

tivvd6[iov Gvvdyerut, xal STtl rov fjMov rj roiccvrri

did0ra6i,g itl rov psdov rife Gîjvy

pq/3 xd, dijAov, on [iqdsv per itdfov

rijg ^s^vrjg ddvvarov 6rai, rb

did TO [t%ova slvat, r^v rfjg A,a%0T'r]s 7Crcc^tjvov rov 5

Ao|oi) Kvxkov 7iQi<pQSia,v rijg vnb r&v

OQGOV rov Y\Mov [isyfaTrjs djto^cc^ftccvo^

7tl [isv rov Ao|oi) xvxhov Tg 3cy, iiti $ rov diet rcbv

rov q)diaxov a Jci, oTtov d' av dvvyrai, jtaQak-

og, &6re rag iv OTtoxsga r&v KKQCSV Gvvo- 10

d&v rjxal rag evvaufporfyov aua itaoaM.d&ig vitQ-

iv a xie [lotoav, Xl dvvccrbv 0rca nal rag

ovv di%a[iv [p. 4887 24] v TCO %QOVG) rr}g [i

7Craît]vov ,orav

i\ pey 6^vr^ xv\v {iyfarr]v itoii]ra,i 15

vtdoodov, 6 d ijfoog %v\v &a%farr]v aitb r&v

rovr

Tdgo%6ov p%Qi> r&v ILSG&V rrjg naQfAykvd'vtav ijdrj rr\v 6J.tfvr}v rov ijfaov dxaifl&g \LQI-

gaig idji, rag $ roGavrag [toioag xal sri ro i$' av-

r&vYI GfAijvr] Kivelrou, [i0G)g iv fjlifya [iia xal coQatg 20

7 (pavoov, on, rov %QOVOV r^g iieGrjg 7traît]vov 3t-

Qis%ovrog fmsoag ~6$ xal coaag i^ fyyiGra 6 rijg &a-

%farr]g 7tra^vov %aovog h'tirca yiiQ(bv 6 xal

fc/3,xal di,d rovro 6 ri\ reXevraiag xal itol rd

3. fiev'] supra scr. D 2. 9. nccQcdccGEiv D, alt. I supra

add. D 2. 10. rag] m D. 11. xca] om. D. nagulJ-a.&is D.

13. ylyvE6&\cci D, yLyveGât

\

D 2. 15. iisyiGryv] corr. ex

'arjv D 2. TcoLeucci A a C. 17. nKQEtekv&victv C, sed corr.

18. /LUHpcag] A 1

CD, comp. B. 20. rr\v ctlirjvrjv D, sedcorr. ^GCOS] om. C, a ly fifffco? B. fita] a C. 21. xf)s]

seq. ras. 3 litt. D. 22. tat] comp. postea ins. C. 24. 6]

postea ins. D.

Tijg nagfrsvov Gvvodov %Q6vog {tTd i$ cogag

TOV rils rtQ&trjs xal itegl TO, 6%ccTK TOVe

Tdoo%6ov.

r]Tr]Tov #(>, itov xal Ttors dvvaTair\ Gfhtfvr] nkeiov

Tf}g a x poiQag itaQaM.d<56iv r\roi iv t<p Toc) x&v

5 itQoxi,[iVG)v dcodsKKTrftioQicov rjiv d^cpoTSôig xccra

TJJV dia i$ cdQcbv #tfiv, TOVTS'GTW orav TO per

,to df TQOV ccvctTekkri, dice TO

Tag htefy&g d^(poToa

apKTOvg [iv ovv nakiv ovdccfjii} rtjg XK&

10 OMOV[lVr]S XCCT* Ol)d[lLaV ftiGlV TOGOVTOV VQfaXTCCl,

3taQaAA,d66ov6a i\ 6^vrj jLtT/d' ccvTotg Totg VTCO TQV

fay[iQLVOV iilov %r]xo6T&v ~wy Tijg xaTa TO

KKTK ithaTog jtaQaMd&cog'v Tfi eka,%<5Tri fjrta^Vcj dig

15 7tlV TOV ij&lOV KttTCt T^V OLItQ /X(???fl/3(Mft:g TOV did

(i6G)v Tijg 6^vyg ftdgodov, TOVTBGTIV OTCCV xaTa fti>

TYJV TtQOTBQKV GVVodoV TCQO^d'y^ To5 dvKîftdÔVTi 0VV-

$ T^V TffavTaittV d?tO%G)Qfl TOV XCCTaf3l,-

'

itgbg ii6r][jipQiav $ Trjv ToGavTrjv TC

20 kc&>w VQi6xoiiv d7COTôvîvrjv (3%dov dttb TOV

*P6dov jc()aAAÂov, OTKV TK (iv 6%KTcc TOV

TK $ [i6a Tfjg IlaQ&tvov dvvy.

ydo v 'P6d(p xccl Totg V7tb TOV avTov

need'' xaTav TOVTCOV T&V &6G)v f 6e-

3. nov~\ supra scr. C 2. 4. nctQulaGGSiv D. 7. CCVKTB^JJ D,

corr. D 2. 8. yLyvscftai D. 9. ovv] om. C. 11. JtccQaiccG-

GOVGCC D. 12. [isigov jLtf'ywirov] supra scr. D 2. 13. Hara]

A XD, wtu TO BC. Ante oftw del. ccdvvccrov D. 14.

ytyvfTort D. inteinBiv] -v.- supra scr. C, post I- del. y D.

17. Gvvodov] corr. ex cvvohov D 2. 18. ccno%co(>i B. 22.

[IGU xfi<s\ corr. ex (iGo\/f]s D. naQ&sv C,v

supra Q add. C 2,

sed euan. Trapa/Uaaft A 1

; naQK^dcGei D, corr. D 2. 23. roig]

-S supra scr. D 2.

MA0HMATIKHS STNTAgE^S S'. 495

Kara rb [i6ov ditoGrrjpa rijg

v(pciLoov^,Evrjg nobg ^lE^r^L^Qiav dvd ojits

fag tag EV d[i(porEQcug ralg Gvvodoig 7tccoaA.Ad,Ei,g EV-

rEv&EV ijdrj pstfrvg ywea&cu, rqg [nag ILOLQCCQ xccl r&v

XE EîyxoGrcbv. Ttfaiovog d^ yivQ\LivY\s rijg itgbg fts^ft- 5

d&og EV rotg En rovrov rov ytaâ^tjôv

(pUVEQOV ,OTt dvVCCTOV iGXUl tOlg XCCT

ccvrovg oiKovtiu dig EV rfi A,a%i6TT] ETtrafiijvG)

KQXT&V rov did [IEGCOV ryg GEhtfvrjg naQodov, TOVT- 10

E'GTIV orav ETCI [iv rijg itg^r^ ExfafyEcog nQoGayri

rd5 xccrafiifld&vTi 6vvd6^G)^ Eitl ds rfjg dEVTEpccg dxo-

d' av E7tidt%cci xcci, Qti did

Evbg ov dvvcctbv EGtai, dig rbv ijfaov EXÊLTCEIV EV rr\ 15

xad"1

fjpccg otxov[iEVfl ovr1

EV rd5 avr& xMficcti, ovr*

EV dicKpoQOig, xdv itdvra rig apcc vTto&rjrai, rd prj dv-

vdiiEvcc psv 6vvdQK[iEtv, 6vMcc[iflav6[iEva d' ccMcog r<5

dvvccrbv itQiâi rb TCQOXEL^LEVOV , Asya) df, xav rr\v

xard rb E2.d%i,<5rov d7t60rr][ia VTCO^GJÊ^K^ 20

taQctkkdGGri, rbv d [ir}vcc Ekd%i6roV) iva

O'(?GJ dvvccrbv Ekct%C<5rG) ÎE^COV ^ xccrd TtAdrog [lyviatcc

Ttdgodog yivyrai, rqg vitb r&v ExhEMriK&v OQCDV rov

,xdv ddiacpOQCog ratg r &QKIS xal

2. o] ins. D 2. 3. rag sv\ TULS Iv C, TKIGVV D (t mut.

in <>?). 4. yivsG&cci] corr. ex yevec&ca D 2. 5. ytyvo/LtfVrjg D.

6. Tt] -T- in ras. A 1. 8. ftax^rroo D. 11. nQK>tr\g\ bis D,

sed corr. 14. inidttgai] -n- mut. in t C 2,

%ti ^ft|at D. dia]

post ras. 2 litt. D. 16. O%T' Iv (pr.)] o- corr. ex r in scrib. C,otirs D, otirs sv D 2

. otir' iv (alt.)] ovte D, ofas sv D 8. 17.

v.a.v} s* C. rtg] corr. ex rrj D 2. 18. Gvvlccâvoêva A^C.

20. HUTU TO] corr. ex V.KT D. 21. Ttagcddccr] D. 23. vnb

T&V] vnb r- in ras. A 1. tllimiY.&v D, corr.' D 2

.

rotg dadexaTr][iOQioi,s xara%or}6G)iid'a, xad1'

&v rag

7Cl rOlVVV V TG)ftf'tftO [l^vl f} flV XttTtt

xars'oov r&v (p&r&v yfdoodog 7tiA,a[jifldvi {isGcos [ioi-

5 Qag x& g? j]ds xara rbv ^Ttixvxôv rijg 6^tjvrjg

xefi-0

1

,TOVTGJV d' at plv x& g rov qMov

ey sxursQct rov axoyeiov sA.a%L6rriv

rrjs iitGys [IOIQCCV {iiccv r], aC ds rov

xvxhov rrj$ ^s^tjvrjs x P& ÔLQCCI, xara rr\v stp* sxd-

10 rsQa rov rteQiysfov yisyiGrviv ndoodov

9<XV CCXOhovd'COS TOtg

rag % a[i(pora(Z)V r&v

r&v yivoyisv&v y Ag ro if}'ra o

^ oig 6 t/Atog AAAot^t? Jtot,tj0oî

15 K xg xal roGovroig ôîv hd<56ova rqv rov

pyvos vt&Qodov rrjg v TCO êVoj [irjvl xard rs

xccl xccra nhdrog' &<5r', isutft'Jp&Q r\

rov pfaov [irjvbg

xccra Tthdrog ndoodog iioia&v 6rw A ji, rqv rov

Grov xdoodov yivBG&ai [loia&v x& id, ainvfg

20 Bid rov Ttobg oo&ag r& Z&diccxc!) [iyi6rov xvxAov

riMJiiKra ft Ay fyyitira. aAAa ^ naGcc r&v fxfainrix&v

OOGJV rov fjhiov xdoodog 6vvayrcci xccra rb &d%i6rov

rijg 6A.tjvr]g ovGyg r[t,r][idrG)v a g, fag

6. ju^1

]corr. ex fts D 2

. 8. KcpaigovGiv] -w e corr. A.1

C,BD (-1 in ras. D). 10. rov] supra scr. D 2

. 11.

isvoLs] it- e corr. in scrib. C. 13. yiyvopsvoov D.

14. TtoiiJGofiev] corr. ex TCOLI/JGCOIISV D, noir\6ay^v A X BC.

-roc supra scr. D. 15. a] [iicc D. s^cofiev D,

sed corr. 16. Ante nqvos del. T D. %ara D, ut saepius.17. &GT' 18. ndgoSos] mg. D 2

(5ffre), wapodoff etiam in

textu. 18. ffftir] comp. B, -v eras. D. 21. r^(ia D. 22.

D, sed corr. 23. a] ftta D.

MA0HMATIKH2 ZTNTASE&S <5'. 497

fY]v tov A.a%i6tov [irjvbg it&Qodov

a x. $f

ov ovv av sty itavtcog, sfaeg v t& vl

dig 6 tjfoog inteCitQi, rjtoi, Kara [LEV trjv toav t&v

Gvvodav prjdsv 7taoaM.d66i,v tqv tisAtfvriv, xata ds

K H, T}KCttf XCCTQKV flV

rcc avra naQakk(x,(56iv , rrjv

rcbv itaccMdcw ova elvat, T&V a

rj 6vvauq)OTQas rag ituQahkK&KS itfaiova r&v avrQv

oravi\ pkv if\% TQccg Gvvodov

, r\de tils *$& #pog p&S*ipfy{av. 10

'

ovdccprj tijg yijg iv tats Gv^vyCais ovdl xata to

ka%i<5tov aitotitrjiicc ittelovf) 6^vrj xata nhcctog

tijg yfaaxijg

ovx aga 6tca dvvatbv iv

l dig Kkei7ti,v tbv r/Aiov, otccv ijtoi xccta îlv trjv 15

t&v 6vv6d(ov {tydE

tec avta

i) Tttetovog yivo^vrjg tijg [nag [lotgag dovxccl t&v a K\. [lov&g av ovv to 7tQOXiîvov dvvcuto

,i 7tl ta fvavtta yivo^svrjg xatQag t&v 20

1. elajfTov D. 2. oj pice D. ccv ovv D. 3. 8k] 8g

supra scr. D. 6] om. D. Mg. 6 y Sis D 2. 4. n<xQ-

andGtiv D.^

5. Ante a eras, ^f D. Ixarâv] corr. ex

SV.CCTSQCC D 2, srigav A 1

. 6. TtKkiv\ om. A 1

,corr. ex ndgodov D 2

.

nctQccMdaJi \

D. 7. S' vnQO%r^v] corr. ex dvongo%i]v D.

8. nteiova] D et post ras. 5 litt. A 1

, nleipvaaBCD 2

. 10.

&QKTOV D. 11. TKts] TgC D. KKTCc] X/ : D. 12. KKtK,]corr. ex ds Kcitd D, %ara TO C. 14. Svvarov] corr. ex ccdvvu-

rov C 2. 16. Gvvodcov] Gv&yi&v D. i] cslrivi]] TJG D, 17 c D*.

A 1 C. 17. TtUQct'kl.dGri D. 19. a] pia. D. TO]ins. D 2

. Svvairo] corr. ex dvvctirov D; dvvcctui C, sed uide-

tur corr. C 2. 20. aviccLvsiv TO ffvtveiv C.


r&v a

tivvdyowo. rovro d' 7tl diuyogov psv otxov[ivr]g v-

d%6[ivov h'Grai 8ia rb dvva6&ai itaoa psv rots POQEIO-

rfyoig rov fayiiegivov rcbv v ry natf V^LKS OLXOvpEvrj

5 JtQOQ [isdrjiiflQiav TtccQcckhccGGsiv r$\v ^s^tjvrjv^ naga de

rolg voTicoTSQOis rov farjpLeoivov r&v avn,%&6vc()v ua-

ccaxrovg 3tccQKA,Ad66t,v fisra ryv rov

v cato o jcf ^%Q^ poioac; a, enl ds

ofaov[isvr}s ovx av itors 6v[ipair] dt,& rb

10 rtteltirov rqv (Ss^vriv xccQcdhaGGsiv fatiavrcos XCCQK

[ifv rolg bit' avrbv rov t6r][iQi,vbv ov ntelov efy-

xo6r&v xs agog ccQxrovg rs xccl [isGrjiipQiav ,TCCCOK ds

rolg poQiordroi,$ i) von&rdroig ccvr&v[irj xfalov enl

ra dvri,KL^va rr\ 2tQOXi[ivr]s [nag [lot'oas, &s xal

15 ovr&s k'ri, hd66ovccs 6vvdy6d'ai, 6vva[i(porQccs rag

rcbv a H riirjiidr&v itoM.ca de

rtov [ircc%v rov r l6rj^iOivov nctl rov

xaraag rcov avrMi[iva)v rtccQccMd&Mv del

3tQOx67troi, av sri n&Mov nag avrolg rb

20 advvarov. itaga, plv rolg avrolg CCQCC ovdafiij ri\

dig v rca vl [irjvl dvvccrbv b'Grai rov j\Kiov

diacpoooig ovdci^Lij rijg avrijg ofaov[i8vr]g' ccit(>

dl%(U.

1. a] (jiitt D. T/irjfia D. 2. owdyoi D, corr. D 2. 6.

corr. ex VOXSLOTSQOIS D, et similiter saepius. l6r\-

I- ins. D 2, -QI- e corr. D. avTi%&6v? D. 8. xf]

dx B. 9. oHovjLtfVrjg D, sed corr. 12. iisasfi^Qiccs D, se

corr. 19. yiyvo^vjig D. 21. yhov] et seqq. multis

compp. C uersus finem fol. 188r .

MA0HMATIKHS STNTASE&S $'. 499

'. UQccyîareiK xavovi&v exAeiitrixtov.

Iloias psv ovv dicc6rd6is ribv Gv^wyicbv sis rfvrCOV exhefye&V OtyfttopfV 7Caoa^CC[lftdvl,V^

did rovrov ri[iiv yeyove dijAov, OTtcog de r&v re xar'

ctvr&s {i6G)v %QOVG)V diKXQi&Bvrov KCil r&v v avrolg 5

7taQ6d(*)v rfjs GsAtjvrjs eitikoyiG&siGCbv sal [iv rcov

cfvvodix&v 6vvyi,G)v r&v (pccLvoîsvov ,3tl ds t&v

t&v ocx^tft&v^ dia rCbv xccra

rag r ndvras fao(ifoas MfoiTtrwag r&v Gvtvyi&v xal 10

rovrov rd t [isysdy xal rovs %QOVOV$ t&v iti,6xoTij-

XCCVOVLK

TG)V ri^LCCX&

ds x&v 6&rjvi,axG)v Hard re rb peytfrov xccl rb

6rov rijg GeAijvrjs ajtoGrrjiict, fato&tpGVQi r^v xaQW&fyftw 15

r&v eniGxorriGe&v dice d&dexdrov [isgovs rrjs 7116x0-

exaregov rcbv (p&r&v.

rb ftfv ovv rtQ&rov XCCVOVLOV rcbv yfauxcbv ex-

)6 iteQifyei, rovs xaro, rb [leyufrov cbrdtfriâ

MfaiTtrixovs ooovs, rdôîev sitl Grfyovs 20

[iev xe., GfMdia de d. rovrov de ra [iev dvo rcc nocbra

rtoi,e%i, rqv xara nAdros rijs 6^t]vrjs eiti rov Aoôv

xvxhov (pcuvo[ivr}v itdoodov (p' xd6rys i&v 7tt,6xo-

1. ^'] mg. BC, om. A X D. TtgayâTSLcc KCCVOVICQV

>twj'] cum superioribus coniuncta D sigiiis rft distincta, etiam

mg. D 2. 3. sylsfysoov D, sed corr. 4. yfyovsv BC. 7.

TtKQoSiK&v D, mg. 7to%(bv D 2. 6vvyi&v\ 6v- supra scr. C.

8. Ante did del. * D. r&v (alt.)] corr. ex -c^g D 2. 9.

tito%rig D, corr. D 2. 10. vyi&v C. 12. TIQOS xr\v] no6t*\ C.

14. rs\ om. D. TO (alt.)] om. D. 15. xr\ GS^VT] D. 16.

xfis 17. fxarôv] om. D. 18. TO] r- ins. D 2. M&MtyMMr]

mg. D 2. 19. TO] om. C. 21. 8] corr. ex a D. o^vo] B B.

32*

TOV

6Tiv Act x, ^ d Tilg Gfhtjvrjg xal avtfi XKTCC TO /Lte-

ytGTOv dTtoGTrjpa IStfyfhj [p. 421, 3] T&V avT&v Aa x,

xal dtd TKVTK, OTCCV TO fpaiv6^vov KBVTQOV Ttfg 6-5 A.YJv'rjs d(p6rrixrj TOV pv fyiKKOv XWTQOV 7tl rov dia

TCDV KSVTQG3V <X{iq)OTQG)

TOV $ 6wd6llOV 7l TOV

XttTa TOV 7tQOXT&l,[JiVOV [p. 482, 1] AdÔV TOV TC3V

Itt A, JtQOg TO,TOTS 3tQG)TOV KCtTO, TrjV IjtKyrjV 0TttL

10 TOV ÂtOV, XCCTK ILV T&V 7tQG)TG)V <5TC%G3V TG)V 6%l-

TOV [lV 7tQG)TOV TCig ltd flOlQCCg^ TOV $

(?0^, XKTK $ TG)V 6%ttTG)V TOV [lV

Tag 95", TOV d dVTgov Tag (?|d. xccl

15 TOV Xoôv xvxAov piag noioag %r]xo6TK A,

Tolg ToGovToig av%0[ii,cc)6o[iv TCC 7tQOXt[iVK dvo <?-

dltO TG)V CCXQCOV CCQ%dlLVOl pfyQl T&V ItSQl TOVg

6Ti%ovg' rtl yap T&V î6cov Taôpfv Tdg T 9

nut Tag <?o. TO df TQITOV 6kidiov TCSQIS&L TCC

20 {lyd"r] T&V 7116X0^6 G)V 7fl [lV TG)V aXQ&V

7CaQCiTL^^VCSV TG)V Tljg fJtaqpTJ/gO O, lltl $ TK)V

KVTCOV TOV vbg daxTvAov dvTi TOV i$' Tq

Xal OVT&g 7tl TG)V koiTtCdV TG) Vi dcMTvJiG) Tfjg ItCCQ-

TOV ft<?ot> ^rt'ôv, ig ov 6

2. 6tiv~\ comp. B, -v del. D 2. 4. TKVTK] corr. ex TCC

CCVTCC D 2,

roLvra, B. 7. (IOI'QKS g] om. D. 8. TOV (alt.)

9. a] mg. D 2. 9. a] ? Jf s D. 10. T&V 0/UdtW] corr.

ex GtMdav D 2. 13. 9s] corr. ex tg D 2 euan. 15. I] e

vroig D.corr. D. 16. xoiovroig D. avô^Kocoftfv] D 2, avo[iia>6o-

(isv A^CD. TtQOKf-wK D. 18. Ante Tag del. TE D. 22.

TOV (alt.)] TO C. t{T] ffi A^D, ip B. 24. yiyvo^vr]? D.

MA0HMATIKHS 2TNTASEZ! S'. 501

T&V dcadfxa daxTvh&v doi^bg xaTavTijtiEi. to ds

GsMdiov TtEQiE&i, rag ywoitEvas TOV XEVTOOV

ytaoodovg xa& ExaGTyv EititixoTridiv, cbg fii?

)v [lEVTOi, [irjdeTCco [HJTE TOV

Gscov rov fjMov [IIJTE T&V iti,7taaaAA.d%(Dv T^S

TO ds dsVTSQOV KttVOVlOV 1CQV T\klWKG)V

o itQis%E(, roi>$ XCCTK TO eAd%t,6Tov dj

AtfvrjS xfal7tTI,XOV$ QQOVS) fdÔ^V TK [IEV

CCVTCQS X& 7CQCOTG>^ 7ll 6Ti%OV$ $ K^ XCil

dltt TO Tqv [lV K TOV XEVTQOV T^g 0^VYJS 7(1 TOV 10

A.cc%i6Tov ajtoGTiJiiaTog TOLOVTOV ddZ%&ai [p. 479 ; 14]

it, Xttl %r}X06TG)V ft,O

f

lG)V 0TiV J]X TOV XEVTQOV TOV

i\Mov TE xcti E^rjxoGT&v ji, otav d TCQ&TCOS KKTCC Tr\v

3tcc<priv ytvrjTai, TOV fjMov 17 GEkyjvr], TOTE TO (pcuvo-

pvov XEVTQOV avT^s atpEGTrjXEvcci, TOV psv yfaaxov 15

XEVTQOV xdfav poious [nag E^xotiTa ky xccl SEWEDX x,

dl GwdEGpov 7tl TOV Ao|oi) xvxAov {lOLQKS g xd'

01 (JLEV fitl T&V dxoov Griytav TOV tpcuvo-

{LEVOV IfActTOVS doi&liol TE T&V tty A^ XCil 6 T&V

60% xd xal Ttafav o TE Tcbv 9^ xd xal 6 T&V 6%'y A, 20

6 d' ETtl TOV {lEGOV TG)V dttXTvA,G)V ditt T^V

vitEQO'xriv dcodfXK daxTvAcov xal ETI TOV EVOQ

pooiov d, xcctf ov xal /ioinjg yCvETm itdgodog.

1. ^cbdtxa] i{3B. 2. riruQTov] j B. yiyvopevas D-

4. 6vv\endoyio(j,8vcov mut. in ovvf JTrtioytôftfVtov A 1. 6. dtv-

Tfôv] B B. 8. fy/UtTTTntovg D, corr. D 2. 9. d] supra

scr. D a. ^] corr. ex f D s

. 12. TJ] postea ins. D. 13. f)Mov]corr. ex rj/Uaxov D 2

. ngmrcos] corr. ex TtQ&Tov D 2. 14. fCyvr\-

TCCL D. 16. ju-tag] om. D. 17. TOT;] e corr. D, deinde del.

K-HQCOV Gtfyoi TOV cpaivoptvov n^drovg. 18. yiyvovrui D. yap]supra scr. D 2

. (m%oi D. 20. oo?] corr. ex als D 2. o]

ins. D 2. 9s] supra scr. D 2

, fs D. 22. frt] corr. ex frt xi C 2,

ex Ini D. 23. yiyvztai D.

TG)V ds 6A,r]vi,KXG)v xavovLG)v XttToov

6Ti%ovg psv jZf, GsMdux, ds,xal r& pv jrpcora) rovg

TOV xA,KTOvg doi&novg 7tccQCC^6oîv cog rtl tov {*>-

yitirov (XTtotfTriiiccTog ovff^g Tijg 0^vrjg. eitel y&Q i\

5 per SK rov KSVTQOV Tris ^s^vTjs sdefydrj xara TO

[isyiGrov a7c66rr}iia efyxoGt&v Is ji, ^ d' sx rov xsv-

roov rr\$ Gxias r&v avrcbv p ftd, &6T, orav

amrirai rys Gxiccg % 6htjvr)) ror TO XWTQOV

a(p6rr]xsvcci, rov [iv KSVTQOV rrjg Gxiag jtl rov

v$ nd) rcbv d 6vvd6[iG)v 7tl rov Ao|oi) xvxhov

oag 7 xccl ^TJXOGTK jil^,XKTCC [ilv T&V JtocoTcov

TCC%0[lV TOV T TG)V 0& ifi fylfrftiv Xttl TOV TG)V

XKTtt $ T&V G%aTCW T6v T T&V Q XCll' t

15 xal TG)V 6v$ i$' xal dice TK CCVTK rotg TtQcoToig rv\v

CCVÔîG)6iV CiVTCbV 7tOL'Yl66î%'K TOtg 7tL^DCÔV6i TG)

i$' TfjS roT GfArjviaxijs di,ct[iTQOv TQIKXOVTKTG) $ dVTQGJ XCiVOVlG) TOV$ TOV

7fCCQCid'yJ60^V G)g 7tl TOV k(X,%i6TOV

20 Tijg 6^vrjg^ xa& o aito6Tr](ia f\ [iv X TOV

avTflg sdsfyftri ffcyxoGTcbv it, jit, fjtf x TOV XEVTQOV

rrjg 6xiag T&V UVT&V ^ vg, w^r, OTCCV JtQ&r&g aitrriTai

Trig Gxiag i\ <?A^V^, TOT TO xtvtgov KVTijg a<p6Tr]Xvai

2. pe] -s e corr. D 2. n^w-toi] cc B. 4. Ante otfffTjs del.

D. ovarjs tflS Gelrjvrig] -arjg TTJS ( in ras. A 1.

ex parte mg. A 1. 7. r&v 8. csîjvr}^ mg. D 8

(17

etiam in textu D). 11. vg] corr. ex v8 C. rov] suprascr. D 2

. 15. y.ui (pr.)] nai rov D. GV&] corr. ex GVS D 2

euan. ra] -a del. D. 16. sn^dKlovciv D. 22. ft] piv C,

fdel. C 2

, mg. fZê C 2. 7T(>a>roog] nga* D, o mut. in co D 2

. 23.

ro] om. D.

MA0HMATIKHS STNTASE&S '. 503

rov {lev xvroov ri\g Guides zcdhiv oôtcog {totoav yiiav

xal QrjxoGra y AS, rov de 6vvd6[iov iit\ rov Ao|ou

[toioag t)3 xal $r]xo6ra ifl.dia rovro dy xara

r&v Tto&rav Grfy&v rd%avrg rov re r&v oj ^rov rcbv 67tf$ i$, xara df rcov 6%drG)v 5

rov r r&v Q/$ ^/3 KCCL rov rcbv 6v jit^, itdfov ri\v

av%o[ita)6i,v avr&v xoirps&p&n rolg ju/3Hoix?t rw

i$' rrjg rore faArjVLccxijs Sutpl'CQOV Ad %r]xo6roi$. ra

d r&v duKrvkcdv rgira, GekCdia, rov avrbv rgonov

7CQiEî rolg fjAiaxotg xal byioi&g ra (pîjg nal 3tgi- 10

%ovrcc rag TCaoodovg rijg Gf^vrjg natf Kd6rr]v rcbv

titi6Korri<5G)v rag r txarfyag rqg re [MtrG)6G)g nal

rfig ava7thr]QG)<5G)g xccl n rag rov fipfaovg ri^g povrig.

titôyiGayi&a d xa&' MccGrqv r&v Tti(3Kor^Ktv

rag XXi,îvag TtagoSovg r^g 6&ijvr]g yâîx&g^ 6wy- 15

1Qr\6a^voi [ivroi, ralg dEi^fGiv <bg <p' vbg

xal csg it v&iCbv dia rb rag H%Qi> rov r

lieytftovg 7tQi<pQCag adiaytootfv Ttobg ai'G&rjGiv rcbv

tin? avrag v&i,G)v xal n fog jiydwl itafav aîoôycp

ri\g iitl rov Ao|ov xvxAov 7tao6dov rfjg 20

TtaQa r^v xgbg rov dia pfa&v r&v

&scc)Qov[ivrjv. pri yap V7toA.K/fr] rig fjjiag

dion xal xa&ohov ngbg ri\v xara pijxog Ttaoodov rqg

Gfhijv'rjg yCveraC rig diacpooa itaoa rb 6vy%Qa6ft'ai ralg

rov Ao|oi) xvxhov 7tQicpQiaig avrl rwv rov dia [i6av, 25

xal h'n rovg r&v Gv^vyiav %oovovg ovx

1. IILUV] a B. 5. anp] -|3e corr. D. 7. IntfaMova D.

10. 7lBQl%eL BC. TtQl%OVTK\ 7t%OVTU D. 11. XT D.15. Gvv%Q7]GdiJisvoi, D, sed corr. 16. imnsdov'] -i- e corr. C.

21. TIJV] -r\- e corr. D. rov] -6v e corr. D 2. 24. GWIQKG&KI D,

sed corr. 25. r&v'] r&v did D.

rovg ccvrovg ditaQaM.dxr(Dg dvai rolg pfaoig r&v

aav yap djto^d^coîfv d?tb rov A tivvdfanov dvo

r&v 3taoKi[Lva)v KVKk&v i'6ag 7tQHpQiag rijv rz AB5 Kal r$\v AT Kal liti&vâvr^ r^v BF OQd"f}v aito

rov B itobg tv\v AT ygd-

avro&ev 0rai rijg filv <?-

Atjvrjg litl rov B VTtori&-

10 iiwrjg, on, rr\ AT rov dta r i

iiicbv avrl rrjg Ad diet rb nobg rovg dia

r&v jtoh&v rov fydiccxov xvxfov rag itabg avrbv Ttao-

odovg &G)QZ6d'ai rr\ Td dwitiei, rb itaaa rr\v

15 rov GfAyviaxov uvxhov didcpoaov. rov ds ^Li) rov xwroov rrjg 6ma<s 7tl rov B vor}&vrog 6 ftfv

rijg GvQwyiag %oovog k'Grai Kara rb ddidcpooov r&v

Kvxk&v., orav xai fj GfArfvrj Kara rb F ywrjrai, 6 ds

[i6og rr^g KkEifyG)g^ orav Kara rb z/5dia rb itdkiv

20 rovg [ifaovg %oovovg rcbv jc^xort]6K)v nabg rovg did

rcov Ttok&v rov 6A.rjvi,axov xvxAov &G)Qi6&ai' Kal

6 rfi<$ 6vvyiag %aovog rov pfaov rijg mfafyfcog

7tQl,(pQia.

alnov rov pr} Kal ravrag qâg 6vvitiko'yi-

1. anccQK^d^Tcos D, corr. D 2; &naUdyn;fos C. 9. VTTOTI-

D, corr. D 2. 11. 6vv%Qr}Gaiivcov D, corr. D 2

. 12.

d~\ A- e corr. D. 14. fyx/Lqcti; B. 15. ^t'ov] D.17. didyoQov D, corr. D 2

. 19. Post orav del. TO ^fV D 2.

23. Ty] r D. itEQicpEQeia D, t add. D 2. 24. v.ccl ravrccs]

-ccl r- corr. ex ar C. TCCVTCCS] TUVG D, a eras.

MA0HMATIKHS STNTAgESS 6'. 505

rag itSQHpEQSiag iv rats Kara pegog

reiaig rb pixQag slvai xal av7tai6d"tjrovs avr&v rag

diayogdg, xal on rb [ilv dyvoijGai n rcov roiovrcov

aroitov, rb <?' SVEXEV rijg iv ralg itag sxatira {is&odoig

xaraexsfaiag exovra xarayoovijGai nvog rcov rrjfaxov- 5

rcov.) fjMxa xal icapa rag vito&stieig xal naga rag

rrjQtjtisig avrag svdfyerat, TCaQa&scoQstd&at,, rov êvxara rb aTtAovGrsgov %Qrj6iiiov nkefarriv afo&rjGw ep-

noisl, rov de neql ra (pawopsva diapaQravopsvov i)

ovds^'av vjnavranatit, figa%siav. rr\v yovv bpoCav rfi 10

xa&ohov [isv ov {isifrva svyfaxopsv

[nag poiQag' dsixvvrai yaQ rovro diet rov

avrov &G)Qij[iaTog ,di,' ov xal rag diacpogag STCsôyt-

<5d[isd'a rcov rov farjpsoivov TtSQKpsgsiGbv TCQog rag

rov dta [lEd&v rcbv fydi&v cog snl r&v dia rcbv no- 15

rov fariiLEQivov yQayoyu-v&v xvxA.cov' snl ds r&v

ov pEitpva dvo ^xo0rcav^ eitEidr^yceQ^ otcov

pdv 6nv sxarsga rcov AB xal AT TtEOKpsysicov t/3'

6%edbv yaQ p%Qi ryfaxovrcov (p&dvovGiv at xara rag

exfatyeig rr\g 6e^yrjg itdgodou' roiovrov ztirlvrjB<d 20

evbg k'yyiGra' dia rovro ds xalr\Ad rcov avr&v la vrj

aj xal xarateCnsrai ^ F4 KQITI'YI dvo

ovds sxxaidexarov JtoieE niag &oagd$ rb rotiovrov axQifavsed-at, xsvodoôv

1. xara] V.K D,a

add. D 2,

ut saepius. 3. ort] ox- in

ras. A 1. j^^v] corr. ex Its D 2

. Totovrcov] supra scr. D 2.

4. sv] corr. ex ? D 8. 5. &V.QV D,

aadd. D 2

. 6. rag (pr.)

18. iGTiv x-] in ras. D. 8. svnoifiv D, sed corr. 11.

evQiGxcoiiev D, sed corr., supra sv- add. TJ.12. ydg] y* C.

13. srtsloyrjcdiis&cc A X

D, corr. D. 15. r&v (sec.)] rov B.

16. 8t~\ d- in ras. A 1. 20. TOIOVTCQV D.

'

23.

-g add. D 2. 24. Post TOGOVTOV ras. 2 litt. C.

rj (pihahrjd'ovg av/'??.

dia pv dfj TavTa xal Tag x-

Xi[ivag TCOV 7tt,6xoTrj0G)v TCaoodovg Ti]g Gfhtfvrjg fag

Ttobg al'G&rjGiv TCOV xvx&av jC7Coa /

y^ia-

:, ysyovsv d' fjptv 6 ToiovTog STCikoyiGiLog cog

6TCO yap TO [lV TOV ^AfcOV T}TO

Trig 6xt,ag XBVTQOV TO A, i]d' dvTl

Trig itEQKpSQSiag TOV tifhyviaxov xv-

xhov v&ia r] BTd, xal VTtoxsiG&G)

10 TO yikv B XWTQOV Tr]g (JfA^V^g, oTav

artTrjTai, TOV

.ag, TO df z/, OTav Ba7to%G)()Ov<ja' xal rtt,%v%d'i,6G)v TOJV

AB xalAd ijxd'o ditb TOV A snl Tr\v B4 xd&STOs q AT.

15 OTi [lV OVV) OTCCV XCCTCC TO F 'ySVrjTCCi TO XSVTQOV

Ti\g **tyMft ^ r ptGos XQ VO$ y^vsrai Tr\g sxtefye&g

xalTI pzyfaTri jUGKfaj\<Sl, (pavsgbv sx TB TOV TYIV

ply AB Tri Az/ L^V elvcci, dia TOVTO ds xal Tqv BFTtdoodov T?I Fz/, xal sx TOV Tqv AT 7ta6&v

20 dvai T&V rtl Trjg B4 TK dvo XWTQK

d', OTL xal XdTQa plv T&V AB xal Ad 6vv-

Qi%si Tag x T&V XBVTQ

xal TOV fMov r Tr Gxia r $ ATxaToag

25 /LtfVcO [lQl, Ti\g TOV xA,L7lOVTOg

3. &dia(poQovvra)v~] ante -r- ras. 1 litt. D. 4. ytyovs A 1.

5. ni%a>v D, et similiter saepius. ovt D. 6. j^t'ov]

j}tf D. 7. d'] e corr. D 2. 9.

jj] corr. ex v D 2. 10. B]

seq. ras. 2 litt. D. 13. int^v^tiG&v D, corr. D 2. 16. Tr}$

a^vris] om. C. 19. itaQov A 1. 20. KTti&vyvvovG&v] -o-

in ras. C. 23.77] ins. D 2

.

MA0HMATIKH2 STNTABE&S '. 507

rovrov ovv ovr&s fyovr&v ywd(f&<Q TC

VXv y 7fi6x6r^6is daxrvhcov y, xal vnoxffa&G)

rov rb A rb rov i\^iov xvroov. eitl psv ovv KQCC

rov yisyfarov dno6rij[iaros ovtirjs ri\ GeAtjvrjs i\ {LBV

AB yivsrui ^yxoo'r&v hot. x [p. 5007 4] xccl rb an 5

ccvri\g %7ta ft?, ^ ds AT t&v ccvrCbv

yccg iGtiv rrjg AB tots y i$' rv\$

TOVTSGTW rots S v to & &d avrqs yvp Is' &6rE xal

rb [iv coco rijs BF farm [Eucl. I7 47] rcbv avr&v

avrr} $f\BF iitjxei, x ~\[y eyyiGru, a xal 10

iisv sv Tea TtgcorG) XCCVOVIGJ r&v yfoccx&v rots

rot,6u daxrvhois xara rov d' 6&1tidfov' iitl de rov

kcc%iGrov aitoGrtfiiaros t^S Gshtfvrjs % psv AB rtafav

yivtxui Qrjxoer&v ky x [p. 501, 13] xal rb an' avrijs

J, f)ds AF r&v avr&v xs I xal rb an avrijs 15

,hombv d rb dnb rife BF sfyxoGr&v v| vfi'

xal prjxsi, aoa % BF stirai rcbv avr&v xa xrj^ a xal

avra jtaoa&TtJGotisv ev ro5ft

f

xavovfo r&v r\haxCbv

rots y daxrvAois xara rov d' Gekidiov.

rtoxEfad'G) rb A xsvroov rrjs Gxias xali\

20

rov avrov dr

rijs 6^r]Viaxi]s dia[irQov.

7tl {iv aoa rov yisyiiSrov dTtoOr^^aros t^S Gfhtfvrjs

$1 pv AB yivsrai ^yxotfrcbv ~vg xd [p. 5027 8] xal rb

1. ytyWffoho D. 2.i]\ om. C, del. D 2

. 7116*6*7)61.5] corr.

ex '7rSc<mj<ns D a,et similiter saepius. 3. ovv] om. D. 6.

avTfjg] -g in ras. A 1. ^nci] C 2D 8

, -^nu BC et 7 in ras. A 1,

Jwrn? D. 7. la-civ] comp. BD. i(T] i'J' A^CjD. 8. rovr-

ianv] comp. B, -v eras. D. f v] D, gv A^C. 11. nuqcc-

ftriGOfiai, D, corr. D 2. sv] addidi, om. A 1 BCD. 14. yiyvs-

tcci D. 19. roig] corr. ex rjjg D 2. #'] supra est ras. A 1

.

20. ri] seq. ras. 1 litt. D. 21. $'] supra est ras. A 1. 23.

D. Il-Tjxoffrcov] -|- in ras. A 1.

an avrrjg ygit vrjj YIds AF r&v avrCbv py Ad

yap 6nv ryg AB red d' rijg tffA^vfcemjg

rovT6nv roig itl rov [isyforov arto6rri[iccTog

v* rb d' Kit avrijg ^rvrj jily* &6re xccl

5 rb {Lev ajtb rijg BF KKTakeKp&ridettti coup tf, avrrj ds

riBF 6rui IMJXSI rcbv avr&v iwj jitS,

ci xal XKQK-iv t(p XQcoTG) r&v Gshrjviax&v xavovt&v rots

daxrvAois Kara rov d' tishdfov TttQiiypvia rv\v

rrjs fiMtr&Gscog ndgodov ri\v avr^v ovtiav agog ttfo&rj-

10 6'iv T?? rijg Kvaithr]Q(b6G)g. sjcl ds TOV &a%farov aito-

fj psv AB yiverai efyxoGrcbv %y Ag [p. 503; 1]

xai rb ax* avrilg d[id vrj, fjdl AT r&v avr&v vd

ra yag rijg VTtQO%iig rjv rerK^rov 6nv Ttttkiv

rb kKi<3rov art6GrriK 6&rvicixig diarov rb

15 d' ait' avrijg y /3%9'9' wy' &6T xal rb [iv aitb rijg BF, avrrj $ ^ BF ^xt, r&v avr&v

a xal avra TCKQK^Ô^V aGavrcog rolg

Kara rov d' Gffadiov rov iv r& /3' r&v

navovi&v.

20 Tt&'klV VXV T&V Xal ÔVij^ %QOVOV %OV6K)V tffA??-

viax&v ni6xor^G)v faro rb plv xtvroov r^g tixiag

rb A 6rj[itoV) fjd' avrl rijg jtai(pQiag rov Ao|oi)

1.tygii\ corr. ex OTTT D 2

. 2. scnv] -v eras. D, comp. B.

5'] supra est ras. A 1. (^VLKY.^ D. 3. TOVTSGTIV] comp. B,

-v eras. D. 4. Post ccvtrjs eras. Siitl . . . D. favq] D,

\rvTf] A 1

(t renouat.) BC. 7. ngmrfo] ~& B. 8. TOV] -o-

corr. ex co C. 8'] supra est ras. A 1.

'

10. T#] xr\v e corr. B.

12. ftg] v? C. ;13. Anterj eras, o D. SGTIV] comp. B,

-v eras. D. 14. anoGriJtiKrog mut. in ccTCOGTrîa rfig D. rd (alt.)]

ins. D 2. 15. ^S&9#] -%9 -e corr. D, BS&9# A J BC. 16.

D, a e corr. 17. x] D, âABC. 18. ^'] Â a

C, devesQa* BD.20. xat ] comp. supra scr. D 2

. 22. ntQicpSQfiaccptQfius D, sed corr.

MA0HMATIKHS 2TNTASE&S S'. 509

rrjg 6krlvr}s xvxhov v&lafj BF4EZ., xai rb [ilv B

VTtoxactd'a),

xatf ov rb xwrgov h'tircti rf\ G^ujvyg,

orav TtaotidyovGa XQcbrcog l~G)&v aTtryrai rife Gxiag,

TO df jf, xa&' ov 6rai rb XSVTQOV r^g GsAtfvrjg, orav

r ov

E

b'tirui rb xvroov rrjg 68-

,orav <x7to%G)()OvGa Ttaa-

0co^v artrrjrai, rov xvxhov

rijg <jxi&s, rb d Z,rb XVTQOV 0rcci rij

orav Ixfiaivovtia rb 6%arov

^aftw rijg 6xia$ xal

rtdfav anb rov Ari\v jBZ xdfaros rj

Ad.vovrcov df} xal v&d$

10

7tl

[t- 15

r&v

In xal rovro <pavaov, on, xal

rcbv AT xal

jK rov XBVTQOV

Ttdoodov l<5r]v rfj

rb r^Litiv rijg

r EZ

AEK

7tQi%i,XSVrQOV T^

xal rr\v pv F4 20

xal 3tQi,%i,v xaroav

Aot3tiji/ d rr\v BF rijg

ivai.

ddxrvkoi ri\ ^rovrfanv xa&' rjv rb /I xevrgov 25

1. Gtlijvris] -s e corr. seq. ras. 2 litt. D. rj] corr. ex

v D a. BTJEZl Jyd ej BC. 3. ore D. TtQOGayovccci BC.

Post ^co-frfv relicta lac. 6 litt., deinde del. novGu gcoo&sv D.

rfjs 5- &n-rr]rca] om. D. 13. Uga&sv &7trrjraL D. cm&s]6- e corr. A 1

. 15. BZ] corr. ex KZ A 4. A4] cc J' D.

19. vTtSQEfci] corr. ex vnsgo^ri D 2. 21. yt'yveaflm D. 23.

tlvca] ins. A, supra scr. D 2. 25. rovrsGTiv] comp. BC, -v

eras. D. z/] corr. ex A D 2 euan.

avrrjg IvdorEao yivsrui rov Kara rovg

OQOvg rtEoarog \Lia GeAyviccxy SiayidrQG) xal STL

Et, avrrjg, rovrfarw oravfjAd sAaGGov

ft xaroagr&v AB xal AZ, rfi ycooxiîvrj pia GfAqviaxfj

5 diaîroc) xal b'n rsrcc^rcD avrrjg [legst, Exatsgccs ds

AT Kctl AE rsrcc^rcj (legei, pices dia[it!rQOv GeAr}-

litl [isv CCQCC rov iieyfarov anoGrtjârccg

{isv AB yivsTat, r&v rtQOXi,[iva)

xccl to an' aviv\ /YQft vy? $1 & AT10 tCbv KvrGbv xe d'

fj yap rrjg 6A.ijvr]g did[iETQog itl

rov peyfarov aTCo^rârog %r]xo6rK>v zGnv ha JT not

rb ait avrijg pcrj ic, ^ $ Ad oîoicsg i^ id xal rb

an? avrijg 6g$ v%" &6re xal rb plv ano rijg

xarafaMp&rjfarai, [Eucl. I, 47] ôwry v^^ xal

15 prpiEi, k'tirat, r&v avr&v vy /tt/3,rb $ catb rijg

rka xa^ xal avrri {irjxfi, b'tirai, r&v

avrtbv1/rj 6/3, Aoiitrj $ xal r\

BT r&v avr&v Af A.

yta^ccd'ô^fv ovv r& r&v TE daxrvAav aQi&nG) rov

ito&rov xavoviov r&v GEArjviaxcbv xA,fyfG)v Kara [iv

20 rov rfrocorov 6kidiov ra rrjg {i7trG)6G)g %rjxoc>ra

Aa A i'Ga '6vra rolg rrjg ava7t&r]QG)6EG)g, Kara 81 rov'

ra rov fiiifaovg %aovov rrjg povrjg ~ir\ t/3.ETCL d rov

1. fvdorôu BC. 2. OQOVS~\ corr. ex %qovovg C 2. Post

nut ras. 2 litt. D. Tfra^rou] ^ B, item lin. 5 et 6. 3. rj]

ins. D 2. 4. AB~] -B eras. B. GB^vrjcc-A^ C, sed corr. 7.

Ante OI;(>TJS del. frjxo()T<5j; IGXIV "ka. ).' D. 8. ytyvftat D._ /,

|r])to(7rcov] om. D. 9. *.$} -8 e corr. C. ^^ji D. 11.

IGTIV] comp. BD. x] I D. 12. x, 17] %r] D. 14.

A!BC, Bony D, jfey D 2. 15. 8s] 8' D. 19. ngw-

TOV] a B. 20. TB-cdgrov] ^ B. 21. rots] ins. D 2. 22. ra] D,

rag A^C. ôvov? BC.

MAGHMATIKHS ZTNTA3E&S '. 51 1

rrjg Gshijvrjs f] [iV ABTtaklV r&V 7tOOXt,^VC3V fy> A XCtl tO Kit' KV-

rijs ,$11$ vrj) r}$ AT r&v avr&v M] 7g' f} yap rr\g

dltt[lraO$ 7tl rOV &a%farOV KTtOGtrJUCCTOS

[p. 479; 14] QrjxoGT&v ks K' nal rb ait* ccvrrls 5

o, rj$ Ad OHOL&S & W5 xal rb an avrys ro

&GT xal rb plv aitb rijg B4 xarateup&riGsrat,

tO", xal avrrj f}B4 ^X8i s'Grat, r&v ccvr&v | Ad,

rb d9

ditb rijg Td xccraA.i,(pd"ij<3rai, vxa KK, nol

k'Grai, rcbv avr&v K Aft AoiTtf} $ xal % BF r&v 10

go. xal v r& /3' KKVOVIG) rcov

rc5 r&v IB dcwrvAcov CCQL&ILG) xccra

rov rtrugrov GsfadCov ra rijs [i7trG)6G)s %r]xo6rci

ft /3IftK Ttccfav ovra rolg rijs ccvcc7c2.rjQG)6C3g^ xara $

rov s' GsXidiov ra rov ruaidov^ rf}$ [lovijs K Aft 15

LVCC $ Kal rti r&v iLra%v rov r peyitirov xal

rov &a%L6rov aitoGrrjuaros ri\g 6Atfvrj$ itl rov im-

xvxkov rtccQod&v rag 7tipakkov6a

rov o'Aov diacpogov 8ia rv\ rcov

7tao%tQ(DS kanfiavGHLBv , V7ird%a[iv roig TtQOXEiyiBvoig 20

xavovioig AAo xavoviov fiQa%v 7tQi%ov rovg rs rife

rri xara rov sniKvxkov aoi,&[iovs xccl ra iiti-

1. AB~\ con. ex ABT I). 2. yiyvsrai D. 3.

, ^j~8 C, Ajltf C 2, A^ D. AT] ay D. 6.

e corr. D, f Q@ BC. o] e corr. D 2. Ante t^- eras.

o D. xs] x C. 8.

BJ] corr. ex 4B C. 9. vxa] supra add. J A 1, rx S C.

12. xara] corr. ex g' rd D 2. 13. TfrdgTov] j B. f|?]-

om. D, |gtt

supra scr. D 2. 14. ^ f] JIp A 1 BCD.

18. TCUQodtov] -dd- ins. D 2. vitQO% D, -uTCf^o^D

2. 21.

D, sed corr. TOV$] corr. ex rfyg C 2.

pdMovra ^rjxotira sxatirr} r&v (paLVOpwcov v

X rc5v itQ&r&v xal dVTQG)v xavovicov r&v

TtfTtQayiidrmrat, <f rjîtv r\TOVTOV r&v 8&pt(Htf&v no-

6orrjs 7tl rov rtagaMaxrixov rrjs 6eAijvr)$ xavovos x-

5 re&eiiiwr] XKXK to % GtKCSiQv &s rov sxixvxhov xar<x

TO anoysiov rov sxKsvrgov dta rag 6v%vyas VTCOXSL-

7tsl ds oi jtfoZGroi, r&v rrjQovvrcov rag

xa$ 87UGy[ia6Lccs ov rats diaîdrôig rcbv uvxAov TCCCQCC-

10 [lergovGiv ra [ifysd-r] rcov 7ti6xor^&C3v^ aW cbg InCitccv

rotg o&ois ctvr&v sxiTtsdois tfjs otys&s xara rb aitkovv

ri]s 7tQo6f$ohrjs rb fpKivoÊvov ccvrb nav r& py (pcuvo-'

vyxQt,vov6rjSi nQotisftrpiKiisv rovtois

xavoviov 7tl tirfyovs y>V i$

15 rovT&v d' Iv [iv raj itQcarcp rovs i>fi dccxrvhovs rd%cc-

{iv &s xd&rov daxrvAov JtQi%ovroSi xtt&ccjtQ xccl v

avrots rots xA>i7tri,xots KUVOVLQUS, rb i$' r^g diaperQOV

XCCTQOV r&v tp&r&v^ v $ rots ^rjs ra itt,/3dA.A,ovra

avrots itttkiv dcodfxara r&v ok&v fjifiad&v., v plv ro5

20 dvrQG) ra rov fjfaaxoV) iv df rw rotroj ra rov 6krj-

viaxov. it&o'yi6dn&a df xal ras roiavras

7tl pov&v r&v yivopivov nsyeQ'&v xara rb

rrjs tfAt?Vr? ov^s' b yaQ avrbs

y rijs rrjAixavrrjs rcbv diaîrQG)v a

25 GEMS Gvvfararai, xal as tov hoyov r&v

1. xa0roi D, corr. D 2. vnsQO%cov] -%(av e corr. D 2

. 9.

STtLGYlflCCGLGOV D, S6d COIT. nCCQCC[lTQOVGlv] -V QYSiS. D, TtCCQK-

iexOvGi B. 10. aUd D. 13. GWAIVOVCJS D corr. D 2.D, corr. D 2.

14. y] tQicc BD. 15. rw] supra scr. D 2. TtQwraji] d B.

17. tp'] B, ip A 1 CD. 'l9. Post uvroLsiel. -x- D 2. >-^

o1.a>v C. 20. dfVT^QO)] B B. TQitca] r B. 22. ytyvo-izvoov D.

MA0HMATIKHS STNTASE&S

rag diaperaovg ovrog ,ov %i ra

"ovrog

513

a rOV

, olg 6

ro ev ovroz vao o AOVOQ ueratv seriv vvi6ra rov

re roiJtAaGiov 3

Ttobg rolg dexa

xara rb aitAov6rQOv 6vv%ori6aro. 5

6ro drj itQ&rov evexev r&v riîax&v fxfofyfcov 6

\iev rov YI^LOV xvxhog 6 ABT4 Tteol xevroov rb E^

6 de xara rb peGov aitoGryiia rqg (Se^vrig 6 AZTH

TtSQi xevrgov rb @ rfyv&v rbv rov Âtov xvxAov xara

rcc A xal F 6rjiitcc' xai Ixifcvz&fforjs rye BESH 10

rb d' sxheAoMsvcci rys diaperQOV rijs fjha-

&6r rqv plv Z4 roiovrcov tivcti, y, oicov dtirlv

fjBJ did[irQos tft rqv d ZH rr\s teAtjvrjs diK^rôv

rcov avr&v if$ x fyyuSra xara rbv rcov T~fl agog r<x

Ig ]n Adyoi/, di& rovro ds xal r^v E Gwdyftid'cii, 15

3. 4. CD et cuin

ras. post -0TO- B, gôju^xoffToo/Lidvoig A 1

(-co- e corr.), sfido-

ju-r]jco(>rots [IOVOLS A 4?B 3. 5. %ara] -cc e corr. A 1

. ^"f-Gccro C. 8. AZTH] corr. ex .IZTtf D 2

,

9. rdv] in ras. D 2. Y.VV.IQV\ supra scr. D.

BE(9H] EE&N D, corr. D 2 euan. 11.03 add. D*. -coSwteliointvcu C. 12. y]

14. x] supra scr. A 1.


10. TK] to C.

s D,e corr. D s

.

33


rcbv avrcbv & 1. xal rCbv 7tQi[ieracQv aoa xara rov

rov vbg nobs ra y j\A Adyov r\ psv rov

xvxAov yCvsrai, r^rj^drcov At, ft/3, fjde rov G

r&v ccvr&v A?? ftg. oftot'cog ds xai r&v oAtov

5 7CidtJ7to fiin tov uevtQOv litl rrjv TtSQiiisTQ

ithaeiKG&ElGa dvo sp/Sada rov xvxhov Ttoist, rb [lev

rov fifoaxov xvxAov Gvvcc'xftriGSTKi, ^lOi^Cbv ^Zy g, rb

ds rov rrjs 6^r\VY\^ r&v ccvr&v ai& A/3.

rovrcw dq ovrog sftovrov rtQOKsfa&G) svoslv, itod&v

10 6rlv rb 7tQi,%6iivov vitb r&v AdTZ sufiadov^ oi&v

6rlv rb oAov rov rjAiccxov xvxhov {i($adbv i/3.

jt&v%&G)6ccv dri CCL AE HOI A xal TE xal Fxal h'n

'Y]AKF udftfros.

fad ovv, olcov 6rlvjjE vd-la & t, roiovr&v

15 xarsaa plv r&v AE xal EF vitoxurat, g, Mccrfycc $

rfbv A xal F r&v avrcbv g 7, xal oo&tf 6nvrj

itabs ftp K ycovict) ia.v rfjv v7tQO%ijV) r\ v7tSQB%i, rb

aitb A rov ajtb rijs AE, rovrsGrw raft

xccl e^-xotfra /5, 7tccQaj3ccA,G)[iv TCCCQCC rr\v E, '|o/iv r^v

20 r&v EK xcd K vxsao%riv r&v avrCbv Qrixotir&v Ty y*

&6r xal xtyv p\v EK GvvKysG&cti d MJ, ryv $ Krcov ccvr&v d ft/3,

dice rovro $ xal xccroav r&v AKxal KF) STtsl facet, sltiiV) rcbv avrcbv d f'yyiGra. rov-

3. yiyvETUi D. 4. spfiodwv C. 5. TtQi^ttQOv D, -QL- e

corr. D 2. 6. noisi 7. MY.IOV] bis A 1

,corr. A. 7. ILOIQ&V]

corr. ex fiot^toov D 2. 10. ictiv\ comp. B, -v eras. D. 11. SOTI'V]

comp. BC, -v eras. D. 12. 8r\\ -ij e corr. A 1. AE] corr.

ex 4E D 2. 13. AKP] -KT e corr. A 1

. 14. oocav D. 18.

A] Tfjs A CD. AE] ci Ti D._ Tovricnv'] A 1

, comp. BC,lac. 4 5 litt. D. ra p 19.

J3] supra scr. D 2 euan. 20.

uvr&v] supra scr. D 2. iy y] supra scr. D 2

;deinde add.

avr&v j /it^Sice TOVTO 8s wi MKTSQCCV T&v AK Iff D, del.

D 2praeter If r. 23. tfatv] comp. B, -v del. D.

MA0HMATIKHS STNTAEESS S'. 515

roig d* axokovQ'&s xal TO per rov AEP rgiycovov

bv %oyLv it> vfi, rb ds rov A&P r&v ccvr&v

TtdhiV 7tl, OLCOV <5TIVf) [lV B4 did^BXQOg

ds ZH 6ftoiO ifl x, roiovrcov xccl fjAT 6vv-

xal oicov psv sGrw r\B4 diduTQO$ QX, 5

TOIOVT&V fj AP 6rai Jr, olcov $fjZH dt,dîrQog OK,

TOIOVT&V O% Vj KKl TCOV ilt VTlJg CtQCC TtfQICpSQfl&V fj

toiovrcov iQxiv my AJ 9oicov 6 ABPzl

T|, r\d AZP TOIOVTCW it vfa otW 6 AZPH

6 avtbs Adyog 0rlv rcbv Kvuhov 10

xccl r&v sâdcbv avr&v 7tob$

ra rCbv vnb rag 7tQi<pQiccs troftf'eoi/, xccl rb êv rov

ropfas [t>P<xdbv ôîv roiovr&v x tg, oicov

rb rov ABP4 xvxAov oiy g, rb $ rov A&PZrcbv ccvr&v x% VK sitel xccl rb rov AZPH 15

rav avr&v yv QI& A/5. ddt,xro dl xccl rb

plv rov AEP rQiy&vov l^ccdbv roov ccvr&v iC, vfa

rb $ rov AP oôtog Irj ^' xccl koiitov aocc rb plvrov A4PK T[IIJHCCTOS [ifiadbv ôîv 77 xd, rb $ rov

AZPK rCbv ccvrcovr\ y. xccl ohov aocc rb VTtb r&v 20

AZPA 7tai,%6iivov fyflccdbv roiovrwv 0rlv 7s xô'iKtv rb rov ABP4 xvxhov vitoxfircci ocy g.

xai, oi&v 6rlv rb rov fjfaccxov xvxAov fppccdbv

roiovrcov rb jtoi,^6^vov vnb rov fxfafaovrog

7. avriis'] mut. in ccvrccg (comp.) C 2euan., avrdg D. 8.

Post iâdd. d supra scr. C 3. 9. xvxAos T|, TJ ds AZT] supra

scr. C 2. 10. iariv] comp. B, -v eras. D. 12. to/iaW] corr.

ex TO ft a>v D. 13. Z?] corr. ex x D. 14. A&TZ] A et Fe corr. D. 15. ro] rd D. AZTH] AHFZ D. 16. ^]supra scr. D a

. ^|3] corr. ex ^ D. 17. AET] corr. exJET D 2 euan. 18. Ante Irj ras. 1 litt. D. 21. gW*]comp. B, -v eras. D. 23. lartV] comp. B, -v eras. D. 24.

TOt-ovtov D, sed corr.

33*


a [_' d' EyyitiTcC) cc teal Jtcc^cc&tjô^LEv EV TGJ

xccvoviG) TO* GtC%G) TG)V y dccxTvh&v EV T& /?' tear

xal T&V

5 EVEXEV &Jtl Tijg avTijg xaTayQacpqg 6 fiev T*fjg

xvxhog 6 ABT4, 6 ds Ti]g xccra rb peGov a

6 AZPH) xal sxfaiTtErco TO df

coGavr&g Tys

diaperQOV , w^Tf, oi&v sGtlvri

J5z/ diu-

t/3,TOIOVX&V rty pev Zz/ rij$ sxtefyE&s ELVKI y,

10 rr\v d ZH rij$ cfxiag didderQOV xccra tbv tov svbs

itgbs raJ3 Ag Adyov r&v avrcbv ha t/3, dIK rovro ds

xccl tv\v EK Gvvd'ysGd'cci, w] ACT. xccl t&v {JLEV

CCQK TtaklVfj [lV TOV GsAyVLCCXOV XVX&OV y

Ag ftjS, % ds TOV rij$ GXL&S TG>V avr&v 977 a,

15 r&v d' E^ctd&v rb fifv TOV Ê^viccxov xvxAov îy g,

TO SE TOV Trjs Gxiag T&V CCVT&V ^|d A/3. ETtsl TQIVVV

xccl EVTccv&cC) oicov E0TLVi\E Ev&Eicc Irj Ag, TOIOVT&V

8XCCTEQK [IEV TG)V AE Xal EF VTtOXElTttl, g, EXttTEQK ds

T&V A XKL F T&V CCVT&V is Ag, ECCV coGavTcog TY\V

20 V7tEQO%tjV, i] V7tEQE%l, TO COCO TJJS SA TOV CMO T^g

AE, JlCCQK^K^COÊV 7CCCQK T^V E, EÔÎEV T^V TG)V

EK xal K V7t()o%riv TCQV CCVT&V la ^, &6TE xccl

1. syytGra a] corr. ex yyt0ra D 2. nuQcc&riGop, sv corr.

ex nuQKfi")]0oiiev D 2. 2. r&

(3corr. ex x& i$ D

2. 4. xca]

comp. supra scr. D 2. 5. /u-sV] seq. ras. 1 litt. D. 7.

seq. ras. 3 litt. D. 8. BJ] B- in ras. A 1,

e corr. D. 9.

y] corr. ex at y C 2. 11. la] corr. ex 1$ D, IK supra scr. D 2

.

13. ylyvtxKi D. 14. fi^] postea ab extrema linea adinitium sequentis translatum D (i- corr. ex cc D 2

). 15. rov~\om. C. 17. oicov] seq. ras. 2 litt. D. Ante t?] ras. 1

litt. D. 18. g] corr. ex Is CD. ds] postea add. D. 20j] ^ B, M C, ^ D, ^ A 1

.

MA0HMATIKHS STNTAEE&S s'. 517

EK 6vvd/

y6d'ai, y ftd, r^v ds K r&v avr&v

id v/3, did rovro de xal exarsgav r&v AK xal KFr&v avr&v d

yifi. dxoAov&as de rovroig xal rb [isv

rov AEF rgiycbvov fypadbv Joftv it, Ay, rb ds rov

AF T&V avr&v %& v($. itaKiv iitd, oi&v l6tlv ^ 5

jifv Rd didnsrQos t/3, f)ds ZH 6ftotojg Aa i/3, rot-

OVTCDV xalYIAT GvvdyEtai, ft xd, xccl dicov \iiv i<5riv

i] B4 didpsTQos px, toiovr&v rjAT tGrai 9^, oicov

dsfjZH didusTQog px, toiovrcov A

'9',xal t&v STC

CCQK itSQHpSQSi&v i\ per AAT xoiovt&v farlv 10

17, oiov 6 AETA xvxAo$ r%, f)tie AZP toiom&v

d?

oicov 6 AZTH KVKko T%. co6re dice ra ngo-xal rb (iv rov AET4 To/iteog [i(}ccdbv roi-

ovrcov fôjifv Aj3 scd, oimv sdei'xftri rb rov ARTz/

xvxAov oiy s, rb $ rov AT&Z rojif&s r&v avrcov 15

od MJ, ?tl xal rb rov AZFH xvxAov r&v ccvr&v

%v ifj%d AjS.ddixro d xal rb plv rov AEP rgi-

ywvov fpfiadbv r&v avr&v it, Ay, rb de rov AF%& vfi' xal Aowrov aga rb [ilv rov A4FK

epfiadbv ôîv td va, TO df rov AZFK 20

r&v avr&v d Ag. xal 6'Aov ciga rb vnb r&v AZ, TA7tQiXO[ivov fypadbv roiovr&v i&rlv i& xg, oi&v rb

2. did 3. tf p$] mg. D 2. 2. xai (alt.)] seq. ras. 12

litt.C._ _ 3. (fcxoAov^r D

,

g add. D 2. 5. if] v- in ras. A 1

.

9. l<s -91

] As B, deinde add. ly supra scriptum C 3. 10.

uvtfis] avr D. 11. ^y] D,_cprr.ex pay A 1

C,_*y B. 12. d]corr. ex ^" D 2 euan. 14. If] supra scr. D 2

, xJ3 D. ABT4]-B- corr. ex J1

in scrib. D. 16. CCVT&V'] om. C. 17. de]comp. postea ins. D. AET] A- corr. ex d D. 18. A0T] A-

corr. ex A D. 19. AJFK] -K postea ins. D, -A- corr. ex

D a. 20. vu] corr. ex o^ D. 21. Is] corr. ex 19 D.

corr. ex TA C 2. 22. fffrtV] comp. B, -v eras. D.


rov AET/1 xvxhov vitoxeircu jny . coGts xai, otov

6rlv to rov 6&r)viaxov xvxAov tyfiadov i$, roiovrcov

rb ytQis%6[ivov 'bito rov sxtefaovros avrijs

etitai /3 Keel sn is' [isgovs eyyiGrcc, a xccl

5 7tl rov ccvrov KKVOVLOV t& Grfycp r&v y

iv r& yr

xcci GfhrjviccxG) GskidCci. KKL 0nv17

rcov

xavovi&v

2. Imtv] comp. B, -v del. D 2. 3. TO] e corr. D. 4.

e corr. D seq. ras. 1 litt. tf']t'' A 1

CD, Ts B. a] ins. D 2.

7. KQIVOV D, xavovt D 8.

MA0HMATIKHS STNTABE&S '.

ij'. Kavoviov fjMov sxhefysoov. ftuou $xie

519

5 Ttlcctovg \

yd;

rtlatov;

dax-IV-loi

it$ oltd ATTf O

10 ~7Tf A

Ttg" o

it, o

nt, I15 itr\

o

Jtn I

7t&1t$ I

20

9 o

9 a

a o

9

25 5y o

9d o

aos o<ro Aaoe o

~ood~A~aod o

aoy A

Tty7T(f

118

x

xy its

it?

aoy o

crop A

aop o

<TOOf

aoa oao i

A xA r<?

a ty

7*17

la x

la ty

I vd

xrj

* nXS It]

xy xj 9y

aog y.S

ooe vdaos xd

aod vdaod xd

goy vd

aoy xd

ao/? vd

ao/* xd

xa xw 10xd /d

xg xf

xw tc

aoa vdaoa xdao vd

a ra*Y

ly a

ao xd

Ay x(i o 20

Ay is

ly a

I? Ayla va

oft

at?

A vc 25

x us

*r\ is

9d

30 9

a|s o

9yxd td

xa xrj 30

9? 9* xd

9 rJ

9? xe? oy

1. y'~\ om.A1BCD. xav6viov filiov]

Tjliax&v D. ^xAf^fcov] -Isiipttov inras. D. Inter lin. 1, quae utrius-

que tabulae communis est, et lin. 2

ins. tov lo^ov xvxlov tfjs (J xtvtgovTtaoodo? D. 3. a' <T] om. D. 6.

H<jQla C. 7. o (quart.)] e corr. B 3

.

12. xt] x* D. 16. TTf/] TT^ BC.17. A] a D. vd] corr. ex ra D. 18.

Aa] corr. ex Ac? D. 21. Qa] -a in

ras. A1. 22. A(pr.)] corr. ex a D. 24.

a] -f e corr. C. 28. a^] a- e corr. C.

31. <r(f] aa D.

1.

om. D, u. supra). 3. a' <J'] om. D.4. Alatovq] B C, aQi&/uoi A1

,om. D.

uQi&iu.oi'] rtlarovgD. daxtuloi] aQi&-SfJ.7tt(0\ ----

D. 10.vd]vaC. 13.A?] A-ecorr.D. ig]corr. ex xg

1 D. 14. /<] ps BC. 16. va]-a e corr. D. 17. Ay] vy B. 19. xd] -d e

corr.D. 20. t^df] tft'un in ras. B 3

, ipe

C, ip D. xp o] xp o A1B C, xp corr. exxg

1 D. 26. a^C] o|n D. 28. aV] agg; D.

29.xd(pr.)] xtC. 31. 9*] corr. exvd] mut. in va D.

520 KAATAIOT HTOAEMAIOr

r-1 W Q<**>> fn (H

.s IS 71"'* ga

r

|* ^1 ? . o ^-^,

< 5J R-

2 ji R M *5 2 OT 8 z* S M

Q"SS eNjoto^toS^^^Vo

1

1-S-

Io

ISi

I-

<*> f

r "0 v ^ sto to to to ^

R- R-3.

"

R- R-

t

I" 5.1:

<J>X

8 S

IS- i-'S

U, JJ-

MA0HMATIKH2 STNTASE&2 S'.

|Slafl ||rf 1 | |l|5^i2

521

d P

*.. -r 1 a * I a$r v PQ e1 n &

S S

j> u. 5

S"0X

*, a- R- *

W> JUyito to

X \J> ^,

44

8 <*!.

_

*8

xdja-^o.w'Bb <JO, 8

? S" ? S-%^.

55. S-

^8

8-Wa- a- a- a- a-

<V In>

0-,

P,

s so P

""

p Z s 3tit-x;7c5r>{ 2 * L!"^

-! "-S pq P g i P ^-.S S ^

o< x s


dt,OQ&G)6G)$ xavoviov

MA0HMATIKHS STNTAgESS <S'. 523

Tovrov drj TCQoexts&siiiev&v ri]v ftv r&v

x&v sxAsfyeav &efaxfyiv TtoLô^fd'cc rbv rooitov rov-

rov sx&fyevoi, yccg rfjs Êi^ToufteVty

rbv Gwccyonsvov dQi&pbv xard rqv v'

rov peGov %QOVOV rijg 6vvyfas &QCCV r&v re cbrb rov

aitoyeiov rov sitixvxhov rr/S xccAovpevrjg

xal rGbv ccTtb rov (logst'ov Jtsgccros rov 7t

rr\v SK rijg TtQoG&ccycuQsGs&g diaxQitiiv rbv rov

ito&rov efaoitioiiev sis i& i&v ^^VLKK&V 10

sxtefyscov xavovicc, xav tftovepxticfy rolg r&v xo&rcov

dvo GsktdC&v ccQL&yioig ,ra 3tccocc%i[ivcc r& rov xkK-

rovQ ccQi&yiG) KK& exccrsQOV r&v xavovi&v v r rots

r&v Jtaoodcdv tffAtdtotg KOI v rots t&v daKrvk&v CCTCO-

l<s xcc6rct' 7ti,ra xal rbv rijs KVCO^LCC- 15

doi&iibv i(SVyx6vrs ?s tb r

xccvoviov, o6cc txvfi

ra JtaQKXi[iva ccvrG)

roGavra A.af$6vrs ri\$ v7tQO%ils r&v tcatf xccroov

xavoviov a7to'y'yQtt[i[iva)v daxrvh&v rs XKI %r]xo6rG)v

rots ex rov jtgcbrov XKVOVLOV xccrfi^^- 20

bdvroi 6vâivr] rbv rov itAdrovs KQL%--

ts vb devreoov povov xavoviov itiitrnv^ r&v v

1.-9-']

om. A J D. 4. iKspsvoi] -ot e corr. D. 5. Iv]ins. D 2

. 6. r&v] mut. in xov C 2,corr. ex TOV D. 10. slc-

otocoêv A 1. 11. fylsfyEmv D, sed corr. 12. fffybjtftW A 1

.

14. catoyQatyccusd'a post ras. 1 litt. D, -o- pr. et -tydfis&K in

ras. 15. ôo^tg] in ras. D. 17. idv] s- postea ins. A 1,

- del. D. ctvrois D- 18. roGav-ta] ra rooccvra D. rr)t

r. ex SKUGZOV D 2. 19. V.OB. fxartôv] corr.

corr. ex lv rto KKVOVLO) D 2. ccnoysygaîLsvov C, sed corr.

21. Gvctiv'ti C.

aVTG) [IOVG) TtaQaXEi^lEVCOV 8aXTvA.COV Xal [lOQl&V Ta

voL6x6îva sfyxoGTa EX&rjGoiiE&a, xal oGovs [LEV av

EX Tijs TOiavTrjs dioo&G>6Ecos

,ToGavTa dcodsxaTa TCEQIE&IV

5 ETtiGxoT'rjGiv rils GEAyviaxijs diaîEToov xaTa rbv

%QOVOV rils sxfafys&g. rots S* sfyxoGTOts tots ywo-

[izvois XCCTK rrjv avtrjv di6Q&G)6iv TtQoG&svrEs xdvrors

TO i$' avT&v, av& av 6 ijfaos sitiKivsiTcu,

xccl

6CCVTES SIS t6T TVJ

10 XLvrjîcc^ oGccxis &v funsGr] 6

[lQLVCCS KtQCCS %0[lV XCC0TOV T&V

TJJS xfofyG)S') t&S f*v EX TOV d' Gs

X&gls fov TE Tijs tpyiTcfafsmf xal TOV Tijs K

60)S %QOVOV, T&S d9

EX TOV TCE^lTtTOV T^S ^fAitfStaS TOV

15 Trjs [lovfis %$6vov, <pcivQGbv CCVTO&EV yivoplvcov T&V

TE xaTa Tag aoftas xal TCC TE^y TCOV ii($cc6EG)v xal

avaxafrdoGEMV aoiaLcov 7to%&v EX TY\S agog TOV pf-

Ta%v Tijs povijS) TOVTBGTIV TOV Ti}s axoiflovs EyyitiTa

JtavGEhtfvOV %QOVOV, EXCC6TOV T&V XaTa {lEQOS EVQ16XO-

20 pEv&v TtaoG&ayaiQEGE&s' avTO&EV ds xal T&V Tijs <^t-

pETQOv dcodEXccT&v EfaEVEx&EVT&v fis TO ETtl JtaGi P$a%vxavoviov xal Ta i$' TCOV oA&v Eîftadcov EvotjôÊv EX T&V

3taQax(,[iVK)v EV T(p y' GEhidiG)) oîoicos $E xal Ta TCOV

EX TCOV EV TOO dEVTSQG)

1. nuQuy.siv(ov D. 2. sdv~\ o &v D, p (ovv) del. D 2. 8.

t^'] t'|S' A 1(" in ras.) C, ScoSs^ccrov BD. &v&' cov] corr.

ex KV& D 2. lmv.ivthai] -t- sec. in ras. 2 litt. D. 9.

om. D. 10. OG<X.Y.L<S\ OGK D. 14. XQOVOV'] 'v D. 15.

XQOVOV] inter duas ras. D. 17. avaKaQ&dosav D. 18. TOVT-

f'drtv] comp. B, -v eras. D. 22. svQioofifv C. 24./i

B et supra scr. D.

MA0HMATIKHS STNTAgESS '. 525

6 [iv ovv Aoyog aiQEt ^r\ ndvrors rov dnb rrjg

s Mteifa&g XQOVOV [i%()i> rov psGov faov

ro5 onto rov pteov p%Qi rov rijg

dice rqv Jiot rs rov r/Atov xcci fr\v 6^tjvrjv a

t&v fa&v TCKQodcov diet rb TOLOVTOV ev avfaoig %QO- 5

VOlg K7tOTA.OV[lVG)V) t^ $ afad"lJ6G)S VXV Ol)dV

KV Kîoôyov a7tQyd(jcci,ro nobs ra (pcd,v6[iva

rb ^ dvfaovs rovg x$6vovs rovrovg

xccv XQI rovg pfaovg dgopovs &6iv, OTCOV

r&v jtaQav^tj&csv v7tQO%cti, rr^v ye

rotfovr&v ctiQ&v Ttccôdov^ oG&v stirlv 6 nag rris r-

rqv r^g VTtQO%ri

on $ xal EMor&s dirjiiaQrypwyv evQfaxopw rr\v

VTCO rovr

l7t7tccQ%ov dfdfiyiiwrjv rov TtAarovg rqs 6A.tj- 15

rijg iirav rcov

tteCovog 81 rfjs xccra rovg rjiittfyovg iiti-

XKri&r)[in,vr]s, aitb r&v ccvr&v av itdfav

arccvoi]0cci^v. 20

haficov yaQ ig rr^v roiavryv catodeiîv wfofyfig

dvo Gfkrjvicixas dia prjv&v y j(>| yyvrnLva, V cclg

rb rdragrov rijg

XQOVOV D. LGOV] corr.

ex OGOV D. 3. yiVfffihu] A 1, ysvsG&cci BC, yfyvfG&KL D. 5.

roiovrov] corr. ex toiovr D. sv\ -v ins. C 2. dvtaotff] -IG-

e corr. D. 7. a.v\ supra scr. D. 8. nsQirL&sG&'cii D, sedcorr. 9. V.OLV] KKV ft BD, corr. D 2

. 10. v7tQo%dv A 1. 12.

alGd-rttr)v] sG&gt D, supra I- add. at D 2

. 13.fr>] supra est

ras. A 1;

fort, delendum. 19. tiari^r]^vrig] -it]- alt. e corr. D.

av ndUv] corr. ex ccvdnaUv D. 22.

Q D. 23. trf'ra^Tov] ^/ B.

xccra rrjv avtyv onto rov

srvy%KVv^ cav xoarrjv [iv

ds rqv v rc5 A' s'rsi trig roirrjs xccra Kd^ntitov

5 rtfoiodov5 6vy%oijrai, filv rc5 TTJV ctvrrjv xccru

itgg tr\v r

rov %v\v [isv 3tQOTQttv eKteifyw yfyovwcu xara rb ccjto-

yziotarov rov BTUKvxkov rijs faAtjvrjs ovGrjs,

10 devregav xccra rb xsQiysiorarov, xcd dia rovro

$ xal KKX avrb rovro

xal I

Ttaaa rb

15 wofaxfG&cu rijs oMQipovs nar' K[Kporoas t&

AA' litl ply rijs nooreoas pia [loioa fyyuGra,) iitl ds

rijs dfvnloas oydoa) [lias fiotpag, &s Kara, ye rovro

^L7tLV ir\v rov nAcirovs 3tQiodov sis

xara6ra6i,s v\\ii6i> xcil d' nolrj

f

[lias [lOi

20 6rlv 6 Ao6g rijs teMpnft xvxhos r%. 7Cira ovds

rrjv did ra rijs 6A,rfvr]s cc

7tol ra

yC6a.ro rr^v itfafarrjv pakuSra yyvrnivriv inl rovrcov

r&v fxfafyfov diet rb rr\v \L\V noorfyav notrcc rb [18-

25 yiGrov djt60rrj^K rijs <S^vrjs ovtiys ysyovsvai, rrjv

1. avxriv] corr. ex roiavrriv C 2. 2. xr\v\ om. A 1

. 3.

L D, e* D 2. 4. feet] L D, f D 2

. Kctimnov] BC et -in-

in ras. A 1,Kdllimtov D. 5. 6vv%QfiTcn D, sed corr.

x&v] ins. D 2. f|] -| in ras. 2 litt. D 2

. 11. cog ye] -g yeins. D 2

. were] &- e corr. D. xr\<i\ supra scr. D. 13.

iyiyvsro D. 15. Ante Y.KT' del. sv D. 20. ovds] suprascr. C 2

. 23. TOVTCOV] -TCOV supra scr. D 2.

MA0HMATIKH2 STNTAgESS '. 527

de devreguv xard rb &d%i,6rov' avdyxq yag r^v rov

avrov d' [iQOvg e7ti6xorr]6i,v 7taQr)xohovd"r]Xvai, xard

[iev rrjv rtooregav exAeityiv dxb ehd66ovog dtadrddeog

rov dvapifid&vrog 6vvde6[iov, xard de rr^v dsvrfyavdjcb ^tôi/og, G)v trp dicctpogav (XTtedsi&iiev [p. 520 5

tab. 1 lin. 10 et tab. 2 lin. 10] fii&s poiQas xai ns^jfTrj-

0vvccyoîvrjv , fog xctl svrev&tv re!) roGovrco

iv riiv rov Jthdrovg itsgiodov ftfO1'

o^ccg cato-

rb plv ovv o6ov iit avrr] rfj rtkdvrj

rats Q ati<porQG)v r&v dpaQricbv Gwayoiizvcus dvtilv 10

[IOIQCUS fafptxAy civi\ jtsQiodixq rov itAdrovg

el srv%ov diitporsQcci, TCQOS rb skarrov

rb itfatov y>QOv6ai, rr\v Siayogdv, eitsi ^'17

iitoiu rfv ditoxardtirccGiv, f]ds itfaovd-

nva 6vvrv%iav, rp> fa&$ xai 6 "Ixxaoxog 15

ttvravajtA.'r]$ov[ievr]v ytcog ^ccravevoêi^ fidvco rw rrig

rcbv dîaQn&v rQirco peêi pices [lOLaag

ov6ar] eitttrjilug rqg

i.fHkiaK&v exkettye&v

rH [iev ovv rcov GeArjviax&v Mfafye&v eitfaxîg 20

pov&g av did ravra yivoiro vyi&g, xa&' ovg exre&eC-

lie&a rgonovg, rcbv eTuA.o'yiGii&v dxQt,j5ovnvcov %fj

de rqv r&v fjfaax&v eKkefye&v didxQitiiv xaratixefad-

1. ikd%iGTOv] corr. ex &ct%gr D. 10. avvKyopEvac A 1

. 11.

lioli>' D. 13. Post ntefov ras. 1 litt. D. 14. laolct] om. D.&itoY.a.6TaGiv C. 15. i'cos C. 18. fTrt'A^îg D, sed corr.

D, ccnoxurcracs cos D 2,

ut saepius. 19. t']

om. A 1

CD, mg. A 4 B. 20. Post tttetysuv del. tniGut-yie C.

21. ysvoiro BC. 23. ^KrGKfUsGrigav D, corr. D 2.

rsgav ovdccv 8iK tag TtccQccMd&ig tys 6htfvrjg

ps&a rbv rpdjrov rovrov

6xil>d[ivoi, yap rbv v 'Atet.avdQeiu rijg dxaifiovg

<5vv68ov %QOVOV, JCQO Ttocfcov r) [ir& noting caoccg '|-

5 E7t(3v iGripeQivag rijg ii<5r][if$QiaS) sjtsitcc, sav

ftrb vitoxs[jivov K^lpcc rijs liti&

sccvfti)

VTCO rbv avrbvr\ yL6rm,fiQivbv res

rr^g 'AteâvdQeia^ TtQoG&acpshovtss rb xccra

sv rots dvtilv [isGrjuflQwoZs rcov

10 COQCOV xctl na&ovrss, ngb TtoG&vr} psra

Qwa$ &Qas xccl nay' sxswois %rt6v 6

<5vv6dov XQOVOS, diaKQivovuev TtQ&rov xal rbv

Gvvodov %QOVOV iv r

rbv avrbv fyyiGra tioîvov ro5

15 fa&s djtb rijs TtEQi rag TcaQaM.v&.si

v roig 'n,7tQo6&v Hcpodov. A.a(i6vrs yaQ x rs rov

rfbv y&vi&v xccvovog xal rov r&v naaaMd&covrti r Kkiyiari, xccl rri r&v cao&v KTtotirdtiei rov

runfiQivov xal hi r& Gwodixfi {iQi rov Z&diaxov xal

20 agog rovroig ro[ivov peyfarov nvxhov xal ditb ravrr^g

itdvror rr\v xara rov avrov 6ri%ov

25 Yifaaxriv Ttccod^cc^Lv d%b ri\g Aotîjg diaxQivovfisv^

2. Ante rov del. D 2. 9. dvci B, Svtt D. 12. rov]

r&v C. 13. v.Uâri\ corr. ex HUpu-ca. D. 15. TtÛd^Lg D.16. dicdapovTsg BD 2

, $LccUc<p6vTE$ D. 18. co^wv] eb- e

corr. A 1. 19. %-u] corr. ex ti D 2

. 22.

ccno] ins. D 2. rav D,

? add. D 2. 25. nccQdJiK^v D, corr. D 2

.

ws] corr. ex GO D 2.

MA0HMATIKHS 2TNTASE&2 g'. 529

did rrjg VQL(3xo^vrjg Ttegl rr\v

rov ^cpdiaxov xccl rov dice rov Kara xoovcpyv

y()cc(pO[ivov {LEyfarov xvxAov ycoviccg rr^v

cog rtQog [lovyv rrjv xard ^xog itdgodov 7t

xccl ravrri TCQQG&SVVBS Ttdvrore rb 7tifidM.ov rotg TCSQI- 5

%0[ivoi,g 'bit avrils ^^>dvotg faqfttQitrblg rtj?

r&v jcaoaxL^vcov dvo

r TtQ&rr] rov xard xoovcprjv 6r){iiov

xal rrj [ird rijg 7tQo6&rixr]g rcbv I^^BQLV&V 10

d rr\ xard [liJKog povrj itdkiv Jtt,fldA,A

L [ird rov rotiovrov pfyovg avrobv^

ft,o6ov xal avra pfyog 6rlv rijg

?,xal rotg ovroo 6vva%&st6i, rijg oAqg xard

pijxog itaQaMd%G)g [looioig TIQO^Ô^V itdhv rb do- 15

dexarov avroov, av& ov 6 r\kiog 7Cixivirut,, xal roc

tg &Qag i6rm,Qivag x rov

rcbv 7tol rqv Gvvodov rijg GfAtfvrjg dv&pd-k&v G)Qiata)v ^dftov, xav [iv tg rd 7t6îva r&v

^cpdi&v 17 xard pijxog TtaodMal-ig $ yivo^vrj' dfdffya- 20

( jiv YCCQ v rotg fpTtooGd-fv, nag r^lv ^ roiavrr] did-

^ xoiGig A.a[if$dvr}rai,' rd yiv ig rdg &Qag rag l6riyiQi-

vdg dva^f^,v(jt,va poQia dcpk6vrg dnb rcbv xard rbv

5. ravrrj] corr. ex ruvt D 2. nt.pdUov~] corr. ex TtfidHov D 2

.

6. atmfc] corr. ex ccvtois in scrib. C; CCVTU!> D,

g add. D 2. iiii-

jtaQcclLa.CQs D, corr. D 2. 7. rovrear D, comp. B, TOVCSGT

I D 2.

13. #] corr. ex v D 2. IOTIV] comp. B, -v eras. D. 14.

xat] supra scr. D 2. ovroog CD. Gvvax&fiGL] GVV (a supra

add. D 2) fji8g lotl r itQcor ffitiGi D. 18. Gvvodov] corr. ex

cvvofc D 2. KvaiiccMav D, sed corr. 20. gcodicav] corr. ex

ZQJÎKK&V A 1 et A 4. yiyvoptvr] D. 22. rd] corr. ex

rd<s A 1.

rfjg Gvvodov %g6vov

[loioobv %K)Qig exdtirov rov re [itfxovg xal rov

ithdrovg xal ri]g dvcoâ^Lag ô^,v rag v

rijg (pawoiiwyg Gvvodov axgifatg nagodovg rqg

5 v^g, avrag $ rag &$&, eGope&cc svQrjxorsg, o6ai,g

rsgov -Y] (pccivoiitvr] Gvvodos ysvritisrat, ri^g catQi

eav de elg ra 7tQorj'yov[ivcc rcov tydC&v f)xara

g r] VQ^^vr]^ rcc(i

rcclg xccra rov (xxQifir} rys Gvvodov %QOVOV10 7tQodiaxXQi,iivai,g nagodoLg xd<5rov rov r

xccl rov ithurovg xal rfjg avG)[iaMag, rag $

, oticcig vtirQov i] (pcuvojiwr] Gvvodog k'tirai rijg

ndfav ovv xara r^v rrjg q>aivo[ivrjg 6vv-

odov rcbv l6r]^Qivcov WQ&V axb rov

15 GrccGiv rti,6xil>d[ivoi, dia rcbv avr&v (p6dov^

xocorovr] 6A,7Jvr] 7tccocchA,a66i, itgbg rov dt' avrijg xal

rov xara xoQV(pr\v ^rîBiov/

yâ<p6^vov [ifyitirov xv-

xhoV) xal aq)^6vrg aitb r&v VQi0xoîdvK)v ryv r&

avrGj aQi&[i(p 7taQaxiîvrjv rov ^LOV jtaQdhha&v enro

20 rcov Aoiitcbv G)6avrcog x rf}g ror jtQl rqv r&v xvxh&v

ro[ifjv voi,6xo[ivr)g y&viag diaxQivovyizv rqv xara

Tthdrog ag itl rov yf^bg oo&ag roj ^G)dtaxc3 xvxhov

aQakha&v xal ra 6vva%&vrafig ra xara rov Ao|6v xvxhov

25 riitfpara, rovrfarw d&dfxdxig avra ttoiiJGavrsg, rag

,sav psv rj

xara xhdrog

1. Ante alt. tfi<s del. r D 2. 5. evQiOKOvreg BC. oaaig]

(xlg D. 11. >tca (alt.)] oin. D. 13. TIJV] supra scr. D 2.

TTfe] T D. 15. TfOG D. 16. 7l(XQC(ndai A 1

; IlKQaMd&l D,corr. D 2

. 24. XK] TO D. 25. rovrtcriv] comp. B, -v eras. D.

D, corr. D 2. 26. yiyvo^vccg D.

MA0HMATIKH2 STNTASE&S S'. 531

Ttgbg tecs ccQXTOvg i]TOV did [is

TOV %QOVOV Tijg

TOV xaTccfti^dôvTcc acpeôvîsv OÎOLCOS' sav $i]

XCCTCC 5

nAaTOS TtccQccA.A.cc&S &S XQOS ^^rî^Qiav ajtoTe^YiTca

TOV %G)dlCCXOV) XUTK TO SVCCVTIOV 1tQi {lV TOV ttVCC-

Tag K Trig itaQaM.d%G)s ^tOiQCcg ccnb T&V

llVG)V V TG) XQOVO) Ti]S (fKiVO^VYlQ Gwodov TOV Tt'ka- 10

TOVS IIOIQ&V, 1t$l d TOV XaTCi

OVT&S %OllV TOV V

Gvvodov TOV fpaivo^Bvov nAccTovg a^t-0-ftoV, ov

zfe V ^LCCXCOV XfafyG)V KKVOVitt,

<xv tivvîtCTtTri Totg T&V TIQWTOV dvo 6kidCcdv apt^- 15

V <56&tt.l TOV r\MoV (pÔ^V ^ ^g [l60VCC %QQVOV TOV TTJV q)CaVO^LVr]V GVVodoV JtSQi-

%OVTCC. X&llVOl, OVV T7]V 7t060Tr]TCl T&V JtCCQCCXt,^l-

VG3V TG> TOV (paiVO[lVOV TtAccTOVg KQL^^tp dct-XTVÔV T

xai [lOQL&v Tfbv T Ti}g ^7tT(b6Ktg xal T&V Trjg ava- 20

xa&aQ6cog x^^S f'l XCCTQOV T&V xavovi'cov ftc>ofaoiiv

KCil TOV KTtb TOV UTtOyflOV XCCT<X Tr]V <pCUVO[JiV7]V tiVV-

odov Ti]g dvG}[iccMag dgiftubv Ttfg 6&ijvr]g tg TO Tqg

dt,OQ&c6<}(Qg xavoviov, xal TCC nccQaxi^vcc CCVTO) Qy-X06Ttt 06CC CCV ?}, TK TOGCiVTCC kafl6vTg T^g XCC0TOV 25

T&V CC7tO''aVG)V V7lOY$ 7t00^r00V CCLi

2. tov] TOV avrov B. 6. jrpog] supra scr. D 2. &TIO-

reJLrjTai] D 2,

ccTCOTsteirai A 1 BCD. 7. rov~\ -cbv uvrov ED.9. 7tQodia-AXQt,[jiEV(ov] TIQO- in ras. A 1

. 10. sv] s A 1. 15.

di;o] -o supra scr. D 2. 16. fo] supra scr. D 2

. 23. r" dio^-D. 26. v7iQo%fig] -o- in ras. A 1

.

34*

TOV ztQCOTOv xavoviov xaTt,krj[iiivoig xal Tovg

x

&p' O<JK

r\ rti,6x6Tr]6ig serai Kara TOV [i6ov

5 %$6vov rijs exhsfystog. rolg d' sxarsQag rijs

TtttklV TO 1$' KVT&V,

O.V& G)V 6

)xccl Ta yv6^,va Jtgbg TO

OVTOV fÔpSV TOV %QOVOV XttTQaS TijS T

10 xal Tijs ttvaTtArjQcbGfcos, &g iar}d[uac; pivtQi

%QOVOVS TOVTOVS 7titfvitflai,vov6ri$ dice Tag Tt

xecl ovyl

15 Tijg av&iiccMag T&V (pc&T&v, natf v xal fjt,%ovg aito-

T&OVVTai, X^QiS MKTfOOl T&V 7tQOXT&l,[lVG)V TtCCV-

TOT xal cog 7tl TO Ttokv avitioi cU/l^'/lotg, ov$

v, si xal fig

ovv TOVTO TO 6v{i7tTG)[ia dia TO

20 yuv6&aC Tivag iv rg <paivo[ivr) Trjg

7cdvTOT T&V 7taQaKkdt>G)v VXv

Tivag cpavTa6ia) i [tydlv Idtog ig Ta 7t6îva dia-

ka{ifldvoiTO xivov[ivrj. lav TS yao TIQQ TOV î6ri^Qi-vov 7taQodvov6a yaCvriTai, xaT bMyov dva<pQO[ivr]

25 xal 'ka<56ov alel TOV Ttao^rjkv&oTog

1. KKVLOV A 1

,corr. A 4

. ^ccTEilri^^vr]? C, sed corr. 4.

D, sed corr. TOV] TO D, TOV D 2

. 6. t^'] t'^'

A^BC, Soodârov D.f

KV&' G>V~\ corr. ex &v&" D 2.

^

13.

ylyvitui D. 20. ysWtfOm BC, yLyvtcftai D. 21. $)GTtQ\

-EQ e corr. D. 25. tlaGGov alet] HO.GGOVK D.

9-drcog C, sed corr. TtccQcddccovGa D.

MA0HMATIKHS STNTAgE&S '. 533

bg fag dvccToAag fioddiov (pKivsrcci, TTJV sis *& eito-

a(5i,v Ttoioviievr]) dv r [isra rov fi<?t?^/5@fc-

vbv TtecQodsvrj, xarci(pQO[iV'r] Ttukw xat' okCyov xal

jthsov aid rov jtaQshrjhv&oros 7tccQccMd66ov6a agog rag

dv6{iag bpoicog fiQadvrsQav ity tg ra sxopsva [isrd- 5

ficcGW (pCiWlJGSTGCt, TtOiOV^VY]. TOVTOV {ISV OVV VXSV06 TtQOBLQrilLWOl, %$6VOL TtKVXOTS [1%OVS fGOVXCU T&V

aTih&s ovrwg A,ctiif}avo[iVG)V) ineiôvog d' ccfel

iv rccts V7tQO%ats rcbv TtaQccMd&coi&v fyyvtfym rov ^TJ^QLVOV nagodov avdyKri Kal 10

rovs ngbs rd3 yL6runfiQiv& iLcckkov r&v wfafyf&v

vovs j$QCidvTQOv aTCOTffaiG&at,) xal dice rccvr^v

altiav, OTCCV plv fig ccvryv tyr î67i^QCav 6

%Qovog rilg xâ4>cog imtitttri) tors povov faov

rbv r^g fjjuttaGfwg %$6vov rc3 rijg avcatAr]- 15

xal Trig x r&v JtccQaMd&cov rtgorj'yrjTMrjg cpavraGiccg,

orav d ago rijg fj^^tftâg^ tore rbv rijg avciTtAqgG)-

6wg fyyvtegov OVTCC rov ^6rîftQivov pEC&va ytvz-

<?<0m, orav d [iT<x ri]v fiftf^/Spt'ca', tore rbv ryg 20

{jL7ir(b(5G)g eyyvrôv OVTCC rov

ovv xal rr\v roiccvrriv rCbv %QOVCOV

ov

1. figddsiov D, corr. D 2. qpaiVrjrat D, sed corr. 4.

&i D. nccQuhdccovcct D. 1. [j,%ov D. 8. aft D,corr. D 2

. 9. ytyÔjCt^rj? D. 10. syyvtZQcoi BCD. TCCXQ-

6dcov~] corr. ex naaodovav D. 13. TIJV~] om. A 1

,add. A 4

.

15. yCyvBcQ-ai D. rov'] TOV re D. TOJ] corr. ex TO C 2.

17. iv. r&v] supra scr. D 2. 7tKQaM.dCQS D, corr. D 2

;deinde

del. SK T&V TtocQccUd&cov D. 20. otav] o D, o D 2. 24.

in ras. 1 2 litt. D 2.

re

vov xaroag r&v xxi[iVG)v naoodov Kal rfjv Kara,

tor pfaov %QOVOV ri]g Ixfofyscog anb TOV Kara XOQV-

svsxev 6 pv %oovog xdroog

, f]ds TOV Kara xogvcpyv

'a drj iv ro3 TCagakkaKriXG) ua-

vovi ra itaQaKsiîeva r& r&v o ^t^c5 r^g itag-

aHa&Ktg sfyxoGra ajg Kara TO ^yi^rov a7t6(STrjâ

10 Ad/ov SVSKSV ovtirjs r^g (JfA^v^g, nobg o ano^rriâ ra

ev T<p y' GskidiG) 7taaaxiiiva kaiifidvsTat,' svofaxoiisv

ds STtLfiakkovra Taig os ôCQaug S^KO^TK vfi. Kal sitsl

%oovog rr\g rs fyTtrcoo'scog Kal ryg avaTtkriQG)-

og [ii,ag plv cooag

15 t^êQivi]^ IQOV&V de is, rovrovg acpshovrsg plv anb

rcbv bs rilg aitoGTaGeog UOIQ&V svofaxoiizv ralg Aot-

TCaig | iioiQaig ra naQaKSi^sva ytaoaMd&cog %r]xo6Ta

ev T& avrti GeUdiG* ^ &g rqv Kara rr}v ^6r]v itabg

r& iLetirnifiQiVK* Ttdoodov sx ri\g TtaoaMd&og ytootj'yîv

20 QriKoGT&v f Gwriyftai,. TtQoG&dvTsg d' avrovg ralg of

Kal ralg ^vvayo^lvaig 9 poigaig svofaxopsv svmrc3

avrti (JfAtdtco TtaQaxsipeva ra rr^g okrjg xaoaMd&cog

^Kotsra ~vy /.', cog Kal sv&dds rrjv ttQOYiyiqGiv ri\g

Ttobg T& OQ%OVTI Ttaoodov 6vvij%&ai, rcbv avr&v %r)-

25 xodTcbv a L'. rcbv VQ&VTG)V ovv diayoQcov ra rc3

Kal xdroov

3. TOV] corr. ex TO D 2. 7. navovia) D, corr. D 2

. 8. rrjs]

om. D. 11. laâvBTKi' BVQIGY.O^V\ -i s- in ras. D. 13.

xaTf(pog 6 XQOVOS Halma. 14. &coQov^Bvoi D. fi&>] seq.

ras. 2 litt. D. 21. 9] in ras. D. (IOLQOIS A 1. 22. ofoje]

a-Or/jff D. 23. vy /_'] ~r [_'A 1

. TcqoijyrjGw] -r\- in ras. A 1.

24. TtKQodov] corr. ex nccQctdovg D 2.

MA0HMATIKHS STNTAEE&S g'. 535

X rov rij

aoag fatffteQivifai) cog vnodsdewtcci) rb 6vv-

ayopevov dcp' xaroov jrpotftbôftfv oixsi&g xarQG)r&v iifa&g xal dith&g s^rj^svcov %Q6vcov rr\g re

Xal '

rtfe dvK7t^r)QG)CfCDS^ tb {lV [ISi&V TG) 5

a rr^v iyyvrtqav rov [isGrjiifiQwov itaQodov, rb d

rci Kara rrp> iyyvriqav rov ogftovrog. dr\lov

\ on nal r\rcbv XQOXSIUBV&V %a6vcov V7tQO%rj

ysyovs y L'->&' $ zyyiGra (nag agag

iv otic* ra rooccvrcc %t]xo<5ra iLtd&g r\ 6krjvrj xti^tb?- 10

e x 7tQO%toov xal rb rag

^sav -O'fA

ig rag Kara [iQog KaiQixag Kara rov iv

rotg 7tQO&vvrra/

yîvoi,g VTtodedBiy^vov fytXv rgonov.

ia'. Ilol rCbv iv ralg Kksity<5i TCQo6vv6G3v. 15

'Etp%iig d' ovrog rov xal rag yivoîvag r&v iiti-

<5Korri<5e&v 7tao<5vv6ig iitiGxvit&v Gvvfararat, plv f]

roiavrrj xardîîg x rs rijg avr&v rtbv

nQog rov dia [ifa&v rCbv tydiav xvxkov

KOI x rtfg avrov rov did {ifacov Ttobg rov doi&vra. 20

rovrcov d' xdroov iv xd<5rc) rCbv ilxfoiJtrix&v %oovcov

av xal aTteQi^Ttrov itaod0%ot, 7tol rdg

4. EiJirnnisvoav] -co- in ras. A 1. 6. TOV (ieor](iQivov^ ro-

et ptai}- in ras. A 1. Ss\ om. D, d' supra scr. D 2

. 9. y^-

yovsv D. &QCCS] {IOIQCCS D. 10. 17] postea ins. D. 11.

Supra TO del. a D. 13. rag] rd C. 14. TtQoaGWTsrayÊ-votg D, sed corr. ccnodedeLyiisvov D. 15. ta'] at B, om.A 1 CD. 16. rov] supra scr. D 2

. 17. &ri**eTefr C, sed

corr. 18. xataZ?]|u/i/>ts D, p eras. KVT&V r&v] D, T&V dv-

rcbv A 1

,T&V ctvrav BC. 19. TCQOS rov] supra scr. D 2

. KvnUov]v.vJC D. 21. Iv] supra scr. D 2

. 22. nagdoxoi] corr. ex

D 2,et similiter saepius.

evaAAayrfv ,si' rig rag dt' 6Aoi> rov %oovov

yevr]6o[iBvag itQoGvsvGsig nsoisoyd&o'd'ai, -fo'Aot, îtdvv XL trig STtl roGovrov rtooQorjGscag dvayxaiag rj

XQrjGi'iJLrjs VTtaoxovGrjg. rijg plv ydo rov tydiaxov agog5 rbv oQôvra 6%&fea)g Q-scoQov^Bvrjg ex rijg r&v dva-

rsMovrcovrj

dvvovrav ccvrov Grjiisi&v xccra rov OOL-

ovros STfo^s ava'yxrj xara rbv rijs fafafyf&g %QOVOV

dicKfoocov 6vv%cbg yivopivwv r&v dvctrsMovr&v xal

dvvovrov [isQ&v rov fydiaxov xal rag i)7t avr&tv

10 aTtorsAovfisvag rov doiôvrog ropag <5vv%(bg

GXfavr&g d xccl rijg xobg avrbv rbv

7tl rov di d^(por0(ov r&v xwtocov rov rs rij

vyg xal rov rqg Gxiag T) rov rjMov yQayoiiwov [i-

15 yfarov xvxkov ndhv dvdyxrj did rrjv iv rc5 %oovq) rijg

fxtefyEKtg rov xzvrgov rijg (Sekrivrig ndoodov xal rbv

di' d[icporQG)v rcbv Xvroc3v yoatpoîfvov xvxhov rfjv

&<5iv ah&qv al JtQog rbv tydiaxbv â^dvsiv xal rag

Vitb rijg ro[iijg avrcbv 7tQi,%onvag ycoviag Gvvsi&g20 dvfaovg Ttoisiv. avrdoxovg ovv 6o[i8vr]g rijg roiavrrjg

rcbv ennsriâGiav nvdxal xard rb

Q6roov r&v Ttobg rbv ooiôvra ^BCOQOV^BV

cpsosicbV) dvvarbv {lev etirat, xal avro&Bv roig ye rb

25 ywopsvov Ttd&og vit oiluv Aa[if}dvov6i,

1. s^ccJiJiaijv D. 2. fvrtfofVag corr. ex sviGoisvas D 2.

6. rot;] r corr. ex r D 2. 8. dicccpoQcov] corr. ex dicccpoQcao D 2

.

D. 11. ytVfff-frca] A 1

, y^vtcO'cti BC, yiyve-14. rf| ins. D 2

. 16. TOV~] corr. ex r&v C 2. 18.

as. D 2.at] a- in ras. D 2. 19. VTIO] corr. ex ccno D. 20.

$ T^S D. 21. novaov x&v\ in ras. D. 25. yivonsvov] -i-

in ras. D. ûidvov6 D. rfttu.cafff'ftm -act- in ras. D 2.

MA0HMATIKHS STNTAJ3E&S S'. 537

dice t^s wi d[ji(porQag Tag xhfafig dva&G)QiJ6G)g rag

r&v 7tQo6vv6G)v Lxavrjg iv rolg roLOvroig

rr\g xa&' 6/lo^()tav, <bg s(pa[iv, dia-

o[iG)g de,f

iva pri TtaQsArjhvfi'otss Gzpev rov

rOJtOV, JtlQa66ll&a Xal JtQOg XV\V TOLCCVTrjV k'tyoSoV X-

rivag rgoitovg cbg Ivi iidhiGrcc 7tQO%iQOVs.

T&V [iv ovv 7ti6xoTtf6a)v ytaQ^tjâ^v xal

3tL6r]na6La$ U&KS tr^v xs rov XQ&TOV

rfj &Q%ri rov <Uoi> %$6vovxal riiv rov 6%drov fÂftjroi/rog, ijng & rri <XQ%?J 10

rov rijs /Ltovijg %QOVOV ytVfrat, xccl rr\v rov

iv ra [i6a) %QOVG) rijg

ytVfrt, xal rfjv rov ito&rov

iv r vA.o /

yG)rQag re xal

[i(pari,xG)rQag 7taQiA,ij(panv rag acpooiôîBvag vjto re

rov [i6r}npQivov nal r&v rov dia [i6G)v dvarohcov r

xal dv6G)v L6r}[iQivG)v re xal &QLV&V xal %i[ioivG)v 20

rijg rCbv avi\i&v ^fjg diacpooag ^nlv av itokkolg no'k-

kaxig vjtaxov<3&q<5oiivr]g, dvva[it'vr}g d' ovv^ l' rig

j3ovAotro, xal dnb r&v xxi^vcov rov ooi&vrog ?&-vitiv fycpavi&o'd'ai,. r&v plv ovv yivo^dvcov vitb rov

3. dicdrjinpews D, (i eras. 8. cog] om. D. 9. yiyverat D.11. yiyvsxai D. 12. rifr l*Ae/^fl9ff] om. BD. 13. avev]

om. D. 14. rov 16. o/lot;] mg. D 4. 14. oJiov] A 1

,

6'Aov rov BCD 4. 16. rov oAoi;] etiam in textu D. TS 8x-

?)g IH- in ras. A 1. yiy^frat D. 18.

-A- in ras. D 2. 19. r&v] -&v in ras. A 1

. 21.

a A 1. 23. Post oQLôvrog del. royf ndvrors D. 24.

corr. ex cov C 2. yiyvopivtov D.

v ropCbv rov bat&vrog rip plv fioosiov

axovG)[isv aaKrovg, iv\v de vonov ineGyuflQiav^ rCbv d'

dvarofan&tv xal dvnK&v rag {ilv VTCO r^g dgp^g rov

Koiov Kal r&v Xrjk&v yivop&a$ rov OQiôvrog ropdg

5 Ttdvrore rb faov rsra^r^ptiQLOV aite%ov<jccs r&v V7tb

rov nsGynflQivov yivo[i8VG)V faqtiSQivrjv avccrokrjv xctl

rag d' vnb rrjg KQ^S rov Kaguivovxccl dv6iv, rag d' vitb rrjg ciQ%i]g rov

XSQCO %LHQt,vfiv avatQ^v xccl dvGiv, r&v {iv Kara

10 ravrag diaGraGscov xara xhl{ta dia<p6$G)v artorsAov-

ds ri\g rav TtaoGvsvGscov aitotpa-

,orav J\XQI Kara rwog rj nsrat,v nvcov r&v TCQO-

OQCDV dfixvvrjrai,.

roivvv ri\g xa6ror rov ^cpdianov nobg

15 rbv bgCôvra 6%e6G)g itko'yi,(5diL&a Kara rov v roig

Tta&roig rijg Gvvrd&og v i

jtoddei'yiivov rgoitov rag

ywopdvag itl rov doi&vrog iv raig dvaroAatg xai

dv6<5iv VTtb rrjg do^g fvbg xd0rov r&v

ILOQI&V djto6rd6i,g (p*xdroa rcbv ditb rov

20 vov yivQ\iiv&v ropCbv xa&' sxatfrov r&v ditb

Boov<5&vovg xfoiidrcov, <p* cbv xal rag

'a, Kal diyadil>aiiv Kara rb fv&fcoorjrov avrl

xavoviov KVKôvg r\7tol rb avrb Kvroov iv rc5 rov

voovpsvovg Kal 7tQiB%ovrag rd r&v

1. tr\v\ corr. ex x D 2. 2. a^xTov?] -%- in ras. D 2

.

corr. ex r D 2. r&v] post ras. 1 2 litt. D. 3. Post

A&V del. tag ^ vnb r oQifrvtos D. tag] corr. ex rd D 2. 4.

yiyvoptvKS D. roîas rov OQI&VTOS B. 6. lGJ]pEQt,vri D,corr. D 2

. 7. rag d' vnb rfjs &QVls T v KctQulvov ftsQivriv

avccro^v nut dvGw~\ D, om. A^C. 9. ccvarokriv] ccv- in

ras. D. 16. anodsdet-y^vov D. 17. ln'i\ A X

D, vno BCD 2.

20. yiyvopivcov D. 22. xca] x- in ras. A 1.

MA0HMATIKHZ STNTASESS g'. 539

dt,a6rtj[iara xal rag 6vo[ia6t'ag' eiteitK TCKQCC-

sv&eiag dvo dia itdvr&v r&v xvxh&v

ycovtag aAA^'Aatg, rr\v [ilv sregccv xal

<bg xoivrjv roprjv rcbv iTtntiS&v rov re OQi&vrog xal

rov farftLSQwov, rr\v d' srsgav nccl OQ&JIV &$ KQivriy 5

jv T&V srtiJtedcsv rov rs OQL&vros xccl rov[lECirjii-

rtaQ6r]neiG)6(xn&cc Kara r&v ngbg rov sxrbg

rtsodrov r^g {isv Tthayiccg y^Kîlg farjusQwiqv

rs avarohriv xccl farjiiSQwfjv dvGiv, ri\g $ OQ&iig CCQK-

rovg re xal iisGrnifiQiav. caGavrcog $ Tta^cc'yQKiâvrsg 10

dia ndvr&v ndfav r&v

xal xara rovrcov v [iv rotg {ira%v iitra

rag VQr^LVKg ua& f'xatirov Klipa r&v

liiG)v ano rov <5rjiiQt,vov dia<5rd&ig 7tl rov OQLÔV- 15

rog G)g rov rfragrrjiiogiov [toiocov ovrog 9, iv $ rotg

rb Ivrbg r&v xvxAcov iteQaGi rotg

WYIV avarohfiv xal

rolg dl TtQog ratg agxroig frsgivriv avaroMjv xal

VKv dl r&v [ira%v d&dxarrjnoQia)v 20

ra%v xd<5rov r&v r06dQK>v diatirri-

ahkag dvo 'yQa^dg 7taQ&ijxa{iv xal xard rov-

rov rag r&v olxsicdv dcodxarr][iOQiG)v sttl rov batôvrog

a7to6rd0ig rov i6rîQivov rijs ovonaGi'ag fxdtirov xara

rov |co xvxAov iti,'yQa(poiivr]g. 7taQ6r][ii,K>6d[id-a dl 25

xal rt$l ri]v p&fiifliviiv yccftfi^v rdg r

5. 8'] 8e B. 10. Post xai del. G in scrib. D. Ss]om. BC. 11. iGJi^givfi^ -Gf]- supra scr. D 2

. xar'] -x in

ras. D. 13. dtccGT^^KGL B, diaGTi]^K6i\ D. 14. Ante T&Vdel. Gr^si D. 17. TOI$] comp. D, ut saepe. 18. ^Gr\^-PQLCCV D, sed -v eras. 19. TKLS] roig C. 22. xara] V.K C.

23. otuEiwv] om. D. 24. xara] TOV nurd C, corr. C 2.

rcbv TtaQaMtflcdv xal rd fooiaicc iieyeftr] xui roc r&v

nokcov %dQ[iarcc rrp r&v poofiordrcov bftyfayfo dnb

rov psftovos xal 7tQi,'xovro$ xvxAov rtoirjGcciievot,.

OTCCOS # xai tag avrcbv rwv 7ti6xortJ6G)v TCQOS

5 rbv did [lEGov tpawoiievccs TtQodvsvtisis xxsi[iva$

ycoviccg <p xd&rrjg

rijg TOfttj^ rov re

xai rov di' a[i(porQa)v rcbv ddrj^coîvcov

QKtpo^vov îî(Srov xvxhov, Kdl ravra$ iit-

10 ekoyrfttiL&K xa&' xd<5rr]v r&v vl daxrvhc) x^ 7tt-

rr}s 6hvjvys, iiti

a rb ccvraQXs r&v xara rb [itiov

yivQ\Ltv<av xal cbg xaQccMtjAcov nobs ai'G&rjGw

ovticbv r&v v rats 7ti6Korri66i, 7toi(pQicbv rov rs

15 diet ii6cov rCbv %G)diG)v xvxhov xal rov Ao|oi> ri\$

j plv avrl

rov did ii6cov r&v ^cpdC&v v&Zcc i]

) l(p' tf$ rb rov Ât'ov xvroov rjrb rijs Gxias vno-

20 Xfa&n rb A, r\dl dvrl rov Ao|oi) xvxAov rrjs 6Atjvr}$

ri P4E, xal rb ply F (?^tov, xcc& ov rb xwroov

xccrd rbv {i6ov %QQVOV yCvwui rf\$ x-

jrb dl z/

9KK& ov ndhw h'tirat, rb

orav jtgoir&s o/l^ btfafaty j no&rcos

1. Y.KI to.(alt.)] corr. ex KCC D 2

. 5. fisaov C. 6. rovr-

comp. B, -v eras. D. ytyvofisWg D. 7. e/^ft&w?] D,wv A^C. 10. r&v\ D

2,rto A X

C, x&i B, t8T D. 8a.v.-

l~ D, SciwvU31 D 2,ut saepius. 11. naQodcav] nago- e corr. D 2

.

13. yiyvoîvav D. 14. S7ti6ytOTi](>G D. 18. fv&si&v C.

22. TOV] TO D. 23. xatf' ov] -AaQ^ D. 24. KQO)T(DS (pr.)]

T mut. in TIQWT D, corr. D 2.

MAGHMATIKHS 2TNTAEE&S '. 541

)TOVTBGTW orav h'tio&sv (pcc7tTr]Tcci, TOV

Gxiag xvxkov, TO $ E, xct&' ov yivtxui to xw-

TQOV CiVTijS^ OTCiV 7tQG)TG)g

aQ%7]Tai, sxhsiiteiv rjTO

6%ttTOV KVaJthrjQOVG&CCl,

TJrot 6 ijfaos % xalf)6-

)TOVTSGTW OTCCV f|-

Xttl

KalAE. 10

OTI lilv ovv CCL ILZV vnb BAP xal ATETOV (JLB60V XQQVOV ItSQlfyovGai, TCOV xkefyG)V

TCQOS cd'6d"rj6iv, rjd' VTTO BAE 3tQi%si

iiti TS TOV TCQ&TOV fxAewrovrog xocl TOV

dvcc7tA,r]Qov[ivov , fjd' vnb BAd rr\v iiti TS 15

TOV 6%KTOV exfofaoVTOS XCtl TOV 7COG)TOV ava,ltkl]QOV-

(paveQov. dfjlov d' avTO&ev, OTI, xal i\ pkv AET&S X T&V XVTQO)V K[l(pOTQG)V TG)V XVX&G)V

, fj$ A4 tr\V V7tQO%rjV aVT&V.

VTfodfi'y^CiTOS VXV X^l^l<S^ XCC&' 20

7J1/ V TO) fteVfi) XQOVG) TO ^L^V Tf}S dlK^LBTQOV Tijg

xal tdTO TO A XWTQOV TOV

&6T ity ply AE TCKVTOTE dia TO [i6ov vno-

TO rijg Gfkrjvrjg a7t60Tr][ia 6vvccy6d'ai, {LOQI&V

$ AT foCnovtiav avTijs TCO ^fifost, Tij$ 25

dia[iTQOv T&V KVTCQV Tg ji.titd ovv, O'LK>V

6. r/]om. CD. 8. &nr(ov\tcovrca A 1

,corr. A 4

;anrrcci D,

corr. D 2. 11. Post on eras. TO D. 13. slciv] comp. B,

elti mut. in stci D. 14. yiyvopevriv D. 15. rj6' 16. ava-

nlj]QOv^vov\ om. D. 15. RAA\ BA- e corr. A 1. 19. rrjVj

om. A 1. 24. TO] supra scr. D 9

. (LOQIOJV] (JLOIQ D. 25. TW]corr. ex vvv TO D 2

.

v\EA vttOTivov6a 2,ft x, TOIOVTCOV

xal f) AT Kara TO xxi[ivov rijg

&og 7g ji? xal oicov i<5rlv aga fjAE

TOLOVTCOV xali\ fisv AT h'tiTai, %a v~a, v\

d' iit amijg5 TtSQKpeQEia TOIOVTCOV |/3 ft otcov fatlv 6 Ttsgl rb ATE

ogd'O'ycaviov xvxAos r|. &6rs xali\

vitb AET^ rovr-

0ri,v<fi_vjtb

BAE [EucLJI^ 29], oi&v piv tfaiv cc

ogfi-al T|, rotovrov stirlv |/3 ft GLOW d' CCL d ogfrcd

10 itakiv xccl r&v GsArjviax&v sxfafyscov tvexev

TO A TO Trjg Gmag XWTQOV, &6T^ 7td TO [i6ov d

Tr}g as^vrig ajcd^r^â, T&V avT&v ccd 6vv-

TYJV fjiv AE sv&elav 1, TJJV dl A4X^ |Lt,

Xal xA,MtTG) fj 62,1JVY} XCCTK TYJV T&V Irj

15 Acov Ttdgodov^ &6TS TK> YULIGEI Tr^g dia^Tgov jtdA.iv

EkaTTQva fivcu rv\v AT T^g AzJ, xal xaTafafasG&ai

T&V avT&v 1, o.

7tL OVV, OiCOV <5TIVYjAE V7tOTWOV<5a, ^5C, TOi-

OVTOV xal ^ pv AT yivtrui x o, y d' in avTijg

20 JtQl,<p(>ia TOLOVTCOV 1$ tft OiCOV fttlv 6 7tQi TO ATETOiycovov ogd-oycbviov xvxfog r|, fl'rj

av xal fjvnb

AET ycovia, TOVT&TIV ^ ^^6 BAE, OLCOV pvai

ft OQ&al T$) TOLOVTOV L& t/3, oicov d' aC d ogftal

1. 1^] x, %- in ras. B 3. 3. Igl corr. ex g D.

EA D. 6. yÊT] corr. ex ,4E ET D^; deinde add. ycoi/ta D.

7. BÊ] corr. ex_^BE D 4

,BE^ B.

^J3] A 1

,Wo BCD.

8. ToiovTtoV 9. a] mg. D 2. 8. #'] 5f I)

2. 9. TOLOVTOOV

Jia a] etiam in textu D (ooa). 11. V.KVXQQV ,

in ras. B 3. ware -f add. D 2

.] -f add. D 2

. 12. anoGTri^K, ra>v~\ corr. ex_

D 2. a-urwv] supra scr. C 2

. 13. Ante del. at A 4.

14. ^xAftTrf'rco] supra -ftadd. t D 2. 15. Ttuqodm D, corr. D 2

.

ro5] TO C. 16. xca 17. TWV] in ras. D. 18! AE} EA D.

19. ivfTcci D.

MA0HMATIKHS STNTAEE&S S'. 543

TOLOVTOV ft AS. aGavTcog fo', sxeidr} xat, oiav etirlv

% Ad VTtoTivov6a QX, TOLOVTov xal % [ilv AT yi-

vsrai,jits, ^ ^' >jr> avrijs JtSQitpsysia TOLOVTOV pd ft,

oicov 6rlv 6 Jtol to AT4 OQ&oycoviov xvxkog T|, /'^

cfv xa^ ^ vTtb A/iT yewfa, tovr&nvfj

i)itb BA4, 5

oicsv isV i6w at

avrov di\ tQoitov xal titl t&v aMcov

rag jrÂtxdr^rag r&v ttccGtiovcov

jtl rijg piug r^îdrcov ov0r]s 9, fiff&v xccl 10

TO rov bîôvrog reragrrmo.Qiov vn6xsi,tai,, drd^ccîsv

xavoviov Jtl Gxfyovg [isv x/3, Gskidia ds d, (bv TO [iev

TOVS ebqitfxoii&tovs avrr^g rijs Kara

sxksfys&g, TO ds dsvTsgov Tag iv Tatg 15

sxhsfystii, yLvoêvag y&viag k'v TS TGJ TOV

jtQG)Tov exfafaovTog XQOV& xal iv TGJ TOV 6%aTov

,TO $ TQLTOV Tag iv Tatg

&viag xaTa T TOV TOV

XQOVOV xal TOV TOV 6%aTov dvayt^ôv- 20

,TO ds TTaQTOv Tag yivopwag y&vtag iv Talg

6hr]viaxatg itaKiv extefyedw xaTa T TOV TOV

xA.i7tovTog XQOVOV xal TOV TOV TCQWTOV

[ivov. xai i<5iv at diayoacpai TOV TS xavoviov xal

T&V xvxhcov TOiavTau' 25

1. Ss] S' D. 8. xai snL] add. D 2. 9. Za/*j3avovTg] A 1

,

Hccfiovtss BCD. 10. yaviccs] corr. ex ycovt D 2. $n~\ el D,

mg. 10 cog inl rfjs fti^s D 2. offcav] corr. ex oV D 2

. 11. TOV]TO- in ras. A 1

. 12. ds<?]

corr. ex j A 1. wv] corr. ex co D 2

.

13. 7iQa>Tov~\ a B. 15. dtvrsQOv] & B. 16. yiyvopsvccs D.18. TQITOV] f B. TO.?'] supra scr. D 2

. 20. rov] om. B.

21. TETKQTOV]^ B. ytyvoufWg D. 24. at] at' Tf BC.

544

if} '.

KAATAIOT HTOAEMAIOT

TG)V TtQog rag

cc'

MA0HMATIKH2 2TNTAEE&S '. 545

iy '. 4iaXQl6ig JtQ06VV6COV.

"E%ovre<s ovv 7toodt,axXQi,[ivovg, bv vnedefeapev

rooitov, rovg %o6vovg xd0rrjg r&v ^XXL^LVCOV iiti-

Grjiiao'icdv xal anb r&v %Q6v&v dyAovdrt, ra xar* avrovg

avar&Aovra xal dvvovra ^,orj rov dia {leGov cato re 5

Tijs xarayQcc<pii$ rag XCCTK rbv bôvra &<3t,s avrwv,

oTctv pv xar avrbv rbv di& [ifa&v y rb xwryov rijg

^roi rb cpawopwov &$ itl r&v rjhaxav tx-

irb axQt,p$ &s till rav 6A,rjvi,ccxG)v, rr\v pfv

xccra rb nycbrov fxfatxov rov qMov 7tQ66vv6w xal 10

h'n r^v xara rb k'6%arov Ixtefaov rs xal avcutArjQov-

[ivov rrjs 6^v^g fôîfv anb rijs avrov rov rors

dvvovros xara rbv bgitflvra O-g^tog, r^v $ xara rb

6%arov avan^rigov^vov rov ^Mov xal In r^v xara

rb itQ&rov Zxhetitov re xal avajiôov^vov rijs GeArf- 15

vrjs an' avrov rov dvarMovro$* orav $ ^ xara rbv

dia ii6G)v y rb xvroov rijs 6^tjv^g^ A,af$6vrg x rov

xavoviov rovg olxetovg rrj 7to66r^n r&v daxrvAcov

Ttaoaxfipwovg r&v ycovi&v aoi&iiovg 7tQo6xj3aAoviLv

xal avrovg anb r&v xoiv&v rop&v rov re bgôvrog 20

xal rov dia jig'tfaw, av [iv f$OQi,6rQov % avrov rb

xevroov rijg 6e^vrig^ enl plv rov xo&rov IxheiTtovrog

rov iiUov xal rov e6%drov exheiitovros rijg fcAtjvrjg

&g 3tgbg agxrovg rijg dvnxijg roiiijg^ enl de rov 6%d-

1. ty'] ri B, om. A 1 CD. 3. TO %QOVG D, rs %QOVG D 8.

5. jtifff D. 6. frte D, <s

ss D 2. 7. y] D, om. A a BC. 9.

qiu, D. 11. inhtiitov ri\ corr. ex enteiitov D 2. 15. rfjs

Aijvr)s~] -TIS osl- et -v- in ras. A 1. 16. avarttovros D, corr. D 2

.

17. f] corr. ex j\v D. 19. ngoG^KUov^v D, corr. D 2.

546 KAATA. IITOAEM. MA0HMATIKH2 TNTAgES> g'.

rov dvan^r]Qov(ivov rov Âtov xal rov ngcorov dva-

7tA.r]QOV[ivov rijg 6eA.tjvr]s &S rtQog aoxrovg rijg dva-

roAlXijg) Xal TtuklV 7ll [lV rOV TtQ&rOV xA.LJtOVrog

rijg ^s^tjvrjs cag ngbs5 sal ds rov 6%arov

xgbg ii6qiiflQiccv rijg dvrwijg' KV d vori&rsQov r

rov dia iifacov rb xwrgov rijg 0^t]vrjg^ itl plv rov

fafaovrog rov i\Uov xal rov 6%arov %-

rijg Gfhrivrjg &g n$bg ps^\$$tav rijg dvri-

10 xijg roîijg^ 7tl d rov 0%drov dvartAr]Qov[ivov rov

j]Mov xal rov Ttgcorov avait^Qov^vov rijg

&g itobg [i6rjii(lQiav rijg avaro^Lxijg^ xccl

\i\v rov Tto&rov zxheiitovrog rijg 6A.tjvrjg cog Jtobg

aoxrovg rijg avarofaxijg roîijg^ rtl d rov 0%drov15 avccjtA.r]QoviJivov rijg 6hrivr]g &g xobg agxrovg rijg

dvrwijg. xal rb GwiGrKpsvov x rijg roiavrrjg dioo&G)-

6(og pfyog rov QQi&vrog sô^fv^ cp 7toiij6rca rfjv

itQoGvfvtiw, ag k'yapm, bho<5%Q6rQ< ov ra $%6[iVKr&v cpcorcov iiQrj rag xocbrag xctl rag 6%drag r&v

20 exteofv xal rcbv d

1. rov r}Uov &vccn1H]Qov[i8vov~] supra scr. C 2. 2. rfys (alt.)]

supra scr. D 2. 4. Ante rfjs (alt.) del. rf)$ dvTiKfjg D 2

. 6.

vorimreQOv] BD 2, vonoregov A 1

C, vorsidrsQov D. 7. dta (is-

c&v] -ice ft- in ras. D. 8. xca 9. G^r\vj]g] mg. D 2. 16.

Jx] corr. ex t-' D 2. 17. w] om. D, 6 D 2

. 18. bkoGxsQSGtsQOv]ult. o in ras. A 1

. In fine: Klccvdiov Ilro^BâiOv jwa'ibj^cmxTfc

cvvrdêcos ? B, KKcrvdiov Uro^f^Kiov fta^Tjaartxcov ? C, rAogrov gxrov D.

PA

4404A2

1898v.l

pars 1

^tolemaeus, ClaudiusClaudii Ptolemaei Opera

quae exstant omnia

flfe

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