notes du mont royal ← prcfiiot fit, alibi altior , 5l extre-ma non obumbrët omnia media, dicctut...
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Notes du mont Royal
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lEVCL ID 1* S
; E LEM’ENTORVMi GEOMEIRIC o RV M
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r ægézèæuéæasae
Domino D.NICOLAO rochvm;
REG: A sizerin-ricains:h Coufiliis, Libellmûmquc flip-. - ’ plicum Magiftro , Vicecomiti ’
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pli; Mimi, corporifia: mi dans( quo: hac loco mmmemomn pu-’dor mm non finit) Regi, "guignepalpita) o’m’mrâu: gmtiofum , a-
mabile»; omnibm. à» qui hi: op.-ubiliu: efl,Dn prapotentigutqm,iceeptûmque reddunt. Paremi ve-rb me quàm fit obflriëîa nom"SOCKETÀS. qui"?! i3 amabnl’u-
nicë. quahtum ipfidzbut Pan?fimfe Caüegium , ’qmm Chrijliiç-pifu’mm Rex Ludouügu, ë nimbus
funum eflë iufiir qui "Mia [un deSzholis nofiri: inflaurandi: axa-gumdo parfit. a: no: Ripa amalumina , in datendipofifgiommlange inumlüo flaquant» mit-nant du: inquart: (à: ah» malta,os? 1guti. animé verbe dedans.film renon pafsim. Tainetfi qui]!primidi): culbuta nofiv-um "topa-7tnti debere plurimum tommemp-nm. qui de par"); vuiùeçfil , d;
’ 114mm: à. infimi: maria: fitfuçgr:"grima,confiantiagnumgerë-En"? fritterieaé "fr-am me:
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h-...,..-- ’- .- f.
t imitstianë du» propofmris,ma-gnan; quiddsm prtjlan uhlan]?mommfaciam, w quipntemarumboumant barn ex. idem 0mm): la.nui: amtmentafingulnëqm in."inuit du; "go Ordimm mafflu!»vniuerfum bœewlè’u’am, 1mm n-
qutu bandits" cerna. En a;M11: optmfazit non guigna moi.51:61; tatin: SOCIETATlSflu-«Un»: ergo te , Idufirtfiimûmqm
Bnianenfium Jntiflinmfntnmcharifiimum , non nobilifiimatuafamilù mon? .fid «in» EcclrfiaGlllitlul damé. ’omnmmtum -, .«du: prndmtinm. planifia: viraun: 1mtifiriaæ tarifai; Ludo-gicu: ch Chrijüanifiimm , w oimitnndum Mm» omniâus "gui -fui Pufulilmxmdmimndum mul-ti: in" pronuncinmn’t .- Vtitl fo-u confidam , mm» in» magnumune 60m": initii: ànitumfuit.
lib]; addié’tiflîmus ,
Gzoncxvs Fovmuuç.
tu: gin": firman». Hum»; ti-
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"-.7; ,-
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N O n vains m0463, [cdplutimorum hominüvigiliis a: induflriæ ,quorum alij ’aliis vi-
xcrc temporibus, dcbctur hic Li-ber. De pofieritate bene meritusEuclidcs, qui en, fiuc Thcorcma-tu, (in: Problcmata qu: à maioçribusaccepçrar,au&iora, 6c me-liori digcfta ordinc rdiquit.Tha-les Milcfius, qui Princcps om-nium Geomctriam ex Æ gypto inGraciam tranf’tuli: , amenan-nit angnlum in fcmicirculo rec-
z mm clfc:Triangulilfofcclis an-gulos ad bafim elfe zqualcs sa:allia nonnulla inucnit quæ in pri-mo.& tertio Elcmcntorum Eu-clidis lcgimus 8; admitamutJ’y-thagoms Samius , qui Mathema-çucz ludum primus saperoit, Om-gis çzianguü dais zrcsanguloç
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duobus mais :ch æqualcs: nuétifquc clams efilztitiis, vbicamPropofitioncm reperi: , qu: ri.m0 Elemento , ordinc qui r:-
efima feptima habemr, v: mu-Ësccnnîboues immolarir. Thcq,dans Cyrenens multi: adinuenotis Geomctricarn plurimum anxitflapelleàilcm. Q1! inuenta àCratiilro expliccr, in que tant:vis en: ingcnij , v: nullum nonGcomctricum Problcma illicorefoulent. Si Laënio crcdimus,Democritus Milcfius, multa delincis , vt voulut , irrationabiliçbus faith , multi: de folidis,nuira de numcris: Cent) illudextra comroucrfiam . EudoxumGnidinm quintum Elcmcntum,quod appellant , de Proportioni- -bus , intcgrum faille, aimie-nife; Thcztctus de quinqua fol.»dis, primus librosfcripfit. 8: de.cimæ propofitionis decimi eleqmentorum inuentor fait.
fixe à muids foliaire: excogigaa iij
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O
in: a: diffipata paûim, mais un;te Chtiftum circitcr 550. Hippo-cratcs Chins in Elcmcnta Goa--menin primus compegit ordi-nauirquea Polka Lco Ncoclidiçaudiror,illa qui: : Tcrtius cicin-dc Theudius Magnes. Hos fe-qu’utus en: Hermotimuœolopho-nias qui ca fait baud paulô vbe-rioraaTandcm Euclidcs Mesa-rrenfis, omnibus , partira à f: ad-înucntis ,pattim ab aliis accep-ti9,vltimam manum his Elcmen.ris appofuit , sanza feliciutc , v:non tantum 031mm.- , feu! vnusPræccllentiæ iure ,Gcomctra fi:appellatus. Infupcr hoc ci lundislcûimoniumfingulare Proclus, vlPappus cæzcriquc Mcthcmaticitubucrc , v: de to , quad de ne-
t mine mortalium ante illum, di-xcrint . nahua»: hapax ail.Ne: folum ocarina Euclidis faitadmirationiæ (Ed çiiam ipfè or-do, uem perturbait adhuc au-,fis cv - [luge 5 gagé ornais 4;;
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monflrationis vin) arque robuçfiltrera: , iPfiquc quodammodoGeomerriz firmitatem illam .
un cetcris Idifciplinis antcflat,are Videur. Scripfir prætena
Pbænomena , Optica . Catoprri-.ça, Mufica, Data, Conicorurnlibros quatuor, a un Porifma:mm. Varan) du; ad Prolomæumquue primfln Ægypti lugeraproducunt Hifloriæ. An lit idemcom Euclide Peau: Mcgarica: au-thore , nos, qui: parum conflit,reminmediorelinquimus.
Porto quemadmodum Elemen-ta appellanrur en . ex quibus cm-pi: oriuntur , a: fiunt , 8: in qu:eadem, cum internant. Conner-çunrur,& trani’eunt; fic propoli-tiones cas qua: Mathematicis re-bus tflicipndis infcruiunç. a: inqu’Stefolui polihnç demonftragnones Mathematicadicimus E-lemenra Mathematica : u] certèquemadmodnm qui-literas 8L :4icmença nouir , libres POICR le:
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3ere, ira qui Gromctri: elemcn-ta tcncbi: , fine laborc PCI’CDI.ter. &intelli cr qu: traâanturinOgticis,A tonomicis, a; a-liis reconditioribus Mathemati-ca partibus. I
croupis
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.1
si:8V CL [DISÈU-LEMENT’VM
g a PRIMVM;z. DEPINITIONE’S;
Ë V . Ï. Punfium tif;min: par: valût;
I R Æ C E .lcgitur a;faim, id cit fignum;
. curn cnim fit omnisF magnitudinis exiguë;
illud quodciterius pingiçur, fi- -gnumcfi illius quad mente con-I:cîpirur -,efl:quc idem quad vrai-Itasin mimera , inflans in (cri-là
p15 l porcgafonusiu mufles."
l l à
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a Euclidi:. o na. Lina: tuera’ i [nigaude ne» la-
’ [Il .Lima talis nulla exifiit à parte
rei5fed fieu: pur-laminât: a: [incaquam ducimus, fignum cil: illiusqpam mente concipimus.si cnimpunâum quod concipimus, m0-ucmur 8L relinqnctet fui vcfli-gium, illud clic: lima, longumpropret motum , non rumen là-tum, quia punâum à que proce-dit,omnis expcrs cit cxtcnfionis.
l i 3. Lima «un»:-----4 termimfimpun-
(.74.Id cil: longitudinis v: longitu-
do cil , principium 8: finis cit:punâum z quia magnitudinemnon confident mathematicusmû YË finitim. Vndc cum infini-tif? [Imam vocar Euclides, in."11151! imam cuiufuis magnai.
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g liber primas. ,
. 4-...
infinis, feu indctcrminatam.4. 136674 lima efl,
*-* que ex æquofiaInternat puma
Il. .Siuc cuius extrema obumbramomnia media, vt dixit Platane!minima earum que terminas ha.-bent cofdem ,vr vult Aubin-ic-des.Cùm enim Hum punâi con-cipiatur fieri linca, fi ex arquainter rua punCta fluat , au: petbreuillîmum fpatium,dicctur t’a.Cia- Si punétum fetatut vniformimon. 8c diitantia à cette ali nopanifia . dicctur circularis -, St inmatu hinc inde titubet,& hic de-Prcfiiot fit, alibi altior , 5L extre-ma non obumbrët omnia media,dicctut mixta. Hinc ingeniofcdixit Atiftorclcs lib. I. de Codatex. 5. iuxta tripliccm liane li-ncam,tres tantnm die yolfc mo-nus,duos fimpliccsgegtugnôt cm,
. 1,
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4 Èutlidis’ .cularcm, curium veto minuit!en vtroquc.
R si Superflu: ive-s* Ü ri: cjl aux longi-
l ’- tudimm latitudi-jyëmque amène baba.
Vtfittxu pun&i producitut li-nea , prima fpecies quantitatiscontinuægfie fluxu lincæ in tranf-uerfum , produci coneipjtur fu-petficics, feeunda fpccics : que:potcfl diuidi in longumlvt lima,-lc prætcrea in latum. Vmbtamconcipe. ait Ptoclus, (upetficiemconcipies longam.8datam,nullo(amen modo profundam.
6. Supnfiriri 4n-
trm extrnm rit
t lime. iHaie dciinitio intelligcnda cit jitatitlim de fuperficie plana vcl
muta, non autan de circulai all
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Liber primas. V 5quan’do enim habet extrcmum,iincam tîtüm habet, non lineas.
, 7. Plana fupflfi-I. V au, 54th ex de
profila: interh-tct "674:, l
miaulai de linea- méta, ca;dem de plana fupctficic flint in,tclligcnda.à A 8. P142114: 41mm
4- Mgælur a? duermn [irradiant in
plan]? matir?) tangon-.-itium, ânon in dinâ’um
hautin»), altrriur 44 41.4un»: inclinait).
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Hîc ciaufæranguli explicantur:Materialis , fun: du: lincæ qua:fe mutuo tangunt Formalis , cilaltcrius in alteram inclinaùm. ., . . ., A ü.)
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6 EuclidisVndc fequitur primo, uôd in:duælincænon itafi: de eut tan-
’gcte, vt iaccant in direâum , idcit vt vnicam reâam eonftituâ:Iincam; (Ed airera dcbct in alte-ram inclinari.
Sequitur 1.. quad anguli quan-tiras confiait in maiôri vel mi-nori linearum inclinatione. nonin longitu dine linearum.
chuitut;.non effe neceKc , v:aux litiez poli: contaâum pro-’duâæ fc mutuô feeent, v: vulcPelletarius; id enim tannin! en:vetum in angulis teétilincis: fedfuflicere , vt il: tangant a: mutuoinclinentur.
Dcnique fi angulus ille fit infupctfiçic plana , dicetur plantas.In ornai veto figura,licet quem-libetangulum tribus litteris ap-pellemus , ille tamen fenaper in-telligitur , cui media: chataâerapprngttur.
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i huer primas. -7’ .g A 9. Cam un»;. comme": angu-
lum [mm "a;fuerint, affiliera: q:-pelhmr angolais.
si «raque curua,cutuilincus:ficutua altera,alteta «en, minus.
la. Cnmmerà re-dît: AB. fiflf n-
ô" "1’th CD.qum ,en: qui fin: (Marqu-ABC. ABD. doguin,que!" intcrfi fiait, re-tins efirvttrqw qualium
l engaina»: , ée infifimrj realia AB. perpendicula-
m avatar du: mi in:fifiitC D. Il
il A üij
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1:4:le 1 ’.Tune anguius vterquc,.dicîtur
arquais, quando rcâa 11.3. nonmargis in C.quamin D. inclinati’
mgd autcm Gizci dicunt zaï-fle’lo: Latinè redditut perpendigeularis; frequentius tamcn «un:leur Mathematici verbo Græcqguam Latino,tnaximè inOptica:vade apud ces nihil vfitratiius,quàm "a; x4346: , imo Latinefeddllnt Cathetum. ," A u. thufùf ulula:
’ EBC.efl,qui mgr.., 13571350133 . ’v’’- N’empc quia reâalEBi. magis
eccdit àfu.bie&aca.quàm pafpendiculatis Ali. i i i’ A i: 31.151!!!" il!!!
l qui mi-t- B D narrait?) ABDç; fermium equuad 411:fait" a? (maternant. -
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l
lLiber primas. q i
Talia [ont , punflum,linea, fu-ïerficies: trempe punaum lineæ,inca [upcrficici . a; :fupetficies
tarpons. , It4. Figum et? que [lib911.7149 , ml fiib 41:40:?bru termina, ÇQIZIPNIJCGIÏ
. xi Digit fub silique; trempe quiaçitculum a: cliipfim , miens tu?minus, hoc en: [inca circularis icom ptchciiditzad rc animas 7e;rè figuras,Plures fcmper termini
requiruntur. iPorronotabisdebetc terminas;
quantitatcm,quæ figura dioitur;ambirc a: comprchenderc , nonveto tantiim Çârîninarc.Yndc fe.
ituri. uo me: nu la ira-iâge en: fiâtîyctim punâalii’ieîj
non ambiant, fed [aluni termi-nent. Sequitur z.quod fu crfieiei-infinitz ne! cotpotis in niti;quad dati police, figura. aunant,
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i6 Euclidi: ’i.quia ornais figura dcbet ambï.’ v j,me: eamptchendete figurarum.a. quia tcrminis amblait, termi-nus autem cit cxtremü rci. (me-
a .mode vcro id quad habet fincma: extrcma . en: Infinitum?
r à 15. circula: (fifi-Œ :guraplanafib «v-
. [ne lima A. B.C.’comprebmfi, que wu-Il" perybùia : 4d fait»:ab «me punfia,eomm que
in!" figura»: film pif-u, aman ardente: ne:DA. DE. DC. agitait:inter fi finit.15.00)!er «ont; rirtulipar: film illnd appellatur.
Theodofius Sphçricorum lit".fief. 1.8: aidera habct,dcfini607
ll
j.
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Liberprims. If’ ne verdi 5. fic polum defcribir.Pains circuli in Sphçra,efl’ pun-’
d’un: in fûperficie Sphçtç. à que
omnes reâç ad circuli pcriphe-riant tendentcs , (un: inter le.çqualesÆx quibus colliges intercenrrum , sa polum hoc tantûmJe difcriminis. quôd cenrrumconcipiatur intra figuram poli-tum : Pains verô in fiiperficicSphçrç.
1 7. Diane!" 4143A un: cirrnli a)? re-
dît! quadrant A.qupar [011711771 D. «40474, de
terminant ex 71mg; par-mi circuli feripberiaA.ô B. que é bifiriam [en
i ut circulant.Hic tria obiëruabis r. omnea
. Diamcrros eiufdcm citeuli elfe’ squales inter [gains :319me .
![Page 23: Notes du mont Royal ← Prcfiiot fit, alibi altior , 5L extre-ma non obumbrët omnia media, dicctut mixta. Hinc ingeniofc dixit Atiftorclcs lib. I. de Coda tex. 5. iuxta tripliccm](https://reader034.vdocuments.pub/reader034/viewer/2022050300/5f694a06c3c3e71d2542056e/html5/thumbnails/23.jpg)
si Emlidi:dieratcs ex dcf. r5. fine crurales;2.03.961 fequitur ex Leil: uôdlicctilh cireulo poflînt in. niteduci reâç non tranfeuntes parAçentrllm, fait; tamen mais pergrenant-n duâç , et in petiphetia
. terminait; dicûtut diamctti,quiacum fait; fin: arrimes çquales in-ter fa, detcrminatçquc longitu-dinis, au; veto inçqualcs fem-pet a: inecttç : diamant fol:pardi» metiricirculum. Menfuracairn cuiufque rcj,aitPtolomçus.in Analcmmare ,"dcbet un (tatadinerminatâque," non indcfinita.Varie non cit quod mirentur t);Îroncsfi in feminino genci’c po-natut à Mathematicis. Idem e;nim cil: Diameter quad linea di.nictiens , sel in duo çqualia di-uidens. .
a Jri- r. en. Dîamerrum bifariam (ca.005 caté circulum, quad ira deman-
fiffl Tilde: apud Proclum.Con-"m. vip: animoportionê- femicirculi ien il? 9932:3". romanche": u
I
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. Hà" primai. xidiameter En vtriufque bafis. sicircumfercntia vna congru: pe-nîtus circumfcrentiæ àlteri, ma-nifcflum efl: illas du: portioneèà drainent) flans, elfe inter fi: æ.
males , cûm neutra aliam cxce.En. Si vcrô’ cireumferemia un:non congru: .cum alter3,fed valextra cam cadat , 1:1 Enta , volpartim intra , partini extra: tuneteâæ duCtz à centre ad circum-fcrentiam «un: æquàles a. noücrane.
- " . 18. smicirm-la: un»: cflfiï
. gara que came-mtær fixé didmm’a AH.
ôfib a lima ADB:gaz mfiflur de circulépripberin
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14 Eutliditx 9. Segmentumû czrmli a? figura:
714.: citimmrfibreflué tirculipcrifherid.
Pcr reâam hîc intellige on-nem non dimetxum , nifi itemvclis femicirculum dicere (cg-mentum.zo Reflilinm figurxfàmqu [ab 1767i: man’mx- 3
un. w,2.1. Trilmrz quidam glufifi tribu.22.. æadrilatme mûgaz [a]; quatuor.2.3. Multilattrz 41mmque fifi Planta: 9:43»:quatuor "671: campa":bmdnnmr,
t5
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nier primas; q, ’ 2.4. Trilaterum, A par" figaramm,,l aquilatem trii-i . galant a]! qnadm’d la";
! ânée: «gadin.
’ A 25. Ififieln an-a c tîm,quoddtn nî-
mm 1246:: aequ-IiaAB. AG..
2mn, fi , crus Græcîs en,7nde compofitum honni: qui.æqual’xbus cf! cruribus : rpn’yum
’ hormis; quod êtribus lincisdu: z Halles baba, quibus qua-filcmi usinfifiit.
e 2.6. Scalenum Yen)A A 2mn! m’a inæqualit
’ 4th bien.Ttîmgulorum la: [une fpg.’
des ex latemm ratione petitæ..chuunçur au: g: manqua
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i3. . radiai; udifcrentiis omcrgemcs. t
27.1!d’lneçetidm ç
fiùcmlanmrum fi-
gulum guident "1’412qula»: eflquojhaba raffinaangulum ABC. .
A . 28.JMÉlj!guniÊ
k a? mimi baba:E c obtufimwgn;
lum. A 13C; Â 7B.MÏs 10’: de obture a: hcbcî
le dictent, propriê de ferro;cuiuàacics cft amura: 1nde aîyCAwJ-eun quad obtufum angulum hâ-bet ÂÏBÀQÎN 7min) Ex".
19’. Oxygouiù’mà
Z 5 ra quad ne: aru-m lute; dugazon
Net.
gururumà refiun-
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1.55" prima"; riNet. In ornai triangule cuius
duo quæcunque latex: exptefsêl” nominanmt,folct tcliquum Iatus;. àMathemzticis ,bafis d1c1,fiuc’ inud in fitqucum infimurn oc:r’ capet, (me fnpremum.
30. æddfild;un»): au!!!» ji-gurarum quadra-
.’ tu»: quidê’ e14 quad qui.
; lutent») :flé-refluugulù’.
f E 31. urina [une.. . lmgiorfiguru tif,
l
que: ’rcfldngulu
Ï quidam , et tequila"!r mu efl. I, 32..R110môu.r «F’ g S :0»,un æquilaleè
m quidtm,fid rt-gfluugulu par: (fi.
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18 . . Emlidig-’ Pî’uêo: Gtæcis rota cfi , feu
quiddam 1’0th formam habens,àradiceie’qu,idc& ;uod y-çum circumago g apu Mat -matîtes tamen eût): dicatur fi-gura quadrangula, a: latetibusconüans æqualibus, (cd non ç-tiam au ahé , qu: Vt apparu"nihilha etcommunccuxjn rotà,’ 1a: ad mçtum timolgrem 91m4 1(us inepta en: , multôquc adhucmagisjmên’ïù: figura 3H: de 1glus. piroxime, Rhombo fimilis. à
alim vttamque figuram . à; udiâam à fimilitudine. 51mm ha;be: çuim Rhombo pifcea d
, 35. fibambuide:, I www que dune
jà, d" lutera ,. à: ,4115110.; gaula iutqrfi ’blêmi, tuque «quina;(Il: (un: «45?ng-
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3:
A
.Ltber Primm. V191,- 54. Frater ba:
P v H .. d aux niqua qua-drilatcræ, Trupes
au apptllentur. dT’arfitqun ciscfl-I’nenfatvndc
diminutiuum 13-41141 .gm men-’ fula,abaculus;hi9capud Maximad maticos 7è Tam’cm figura:
quadrumane quæ- menfas ali-quatenus roFemnt: EH; veto Tra-pezium, vel ifofizeles , ne! fa;-
n lenum , veldirrcgulare.MA 3 5 . Parallglqunïa,
refile , que: inenduis-[114m en:
fleura, étpraduflue iniufiuitum ex 12mg; par:n. in mutmm mutuà iu-adam.
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go EuclidisA6 hoc v: duæ reflue dîtântul’
parallelx, non fuificit vt profil-»à: in infinitum non conclu.nnt.Sic cnim du: refît; in Han!"-uerfum pofitç media te alignaa&non f9 tangentes , dicctenturParellclz,quia nunquam concur-rercnt. Sed requiritut gratterez."flint in codent plana.
Pofiulata;
1. J’eft’uletur à *
, H quauispunfla A.ad quadui: pun-
fium B. raflant [imamA B. duit".
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Liber prima: atu 3 c zÆttermimtuuz
j "au: A B. tua? continuum ratifia ’13;! freiner: in G. -sa; 3. Et gueule au: ’d ne, é- interuullou circuit? dçfiribcre;PGômunes nOtioncs (en
, Axiomata.à. 254e aidan- 44.144111;x. à interjêfiut uquuliu.1-1.. Etji aquuliàu: qua-Àa; [i4 udieéîufiut, totajîmt ’
quuliu. .f3. [fifi 46 qudibu: 44gradin 4514:4 fi)", que re-linquunturfimt tquuliu.5. Et fi iuuqualibu: a:
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xi limitâtI gadin udiefiufiut, tata :-finnimçudiu;5.. Et abimquult’âu: 4.- quint 46121:4- jittt. ,. reli-çuu- fiut inuqualiar.6o E t’quteiufd’ë dupliriu; ..
inter junt æquuliu.7,. E bquu’et’ufeïtm dînai-z
dia,iuterfifimt Malin... I8.-. 2544. magma"! fiât?mutua, iuttrfi 47144154.
fiat. t1d cŒqnæcollata, ita compoé” .nuntur, vt pais parti rcfpondeat.8c tqrminus termine , æquah’aflint. Lineæ autel-n 1661?. 8c æ;-qutles congruungvti 8c-anguli.a. Et totum-pdrîe’muituj
64:
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’ Lib" prunus a;10. Et 0mm: mît? angult’
taquait: inter fifint, u.Si in dllfl rap
3,467.44 A B. C D.
c "au innéJeux interivrctàé-ud en];
du». par": angula: Bf P. E- FD. duobut. nais:.y ruinure: ficiutigraduflu,;. du iliu "au in infini-7v, 1.qu cuinçidcnt. inter [àl «du: fartes, in quièus:I; fun: anguli dudit: ratifia;
. ruinera. ’Scîo principium ho; obfeumng
guibqfdatn , 8: à Gemino a: Pto-. clo teieâum à numeto princi-
piomm : mm non debet tu:x?’*q°1à.n°fi9ël!ïê 99mm: v
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iî Euclidi:bu: reîici, qnod ynns au: alter ciaffenfum neget : opottetet enim8c nonum ex un etc. hm cnim(ont aliqui P ilo ophi adco rub-tilcs vt ncgent totum [un partemains. His a: illis fufiîciat dicc-1c Euclidem czterofquc cames ,hac emmi: et fol: terminonlmnorione, cuidcnti: cenfniffe , a:cxifiimafre fenfu communi carc-ce, qui ca ncgatct. Ne fi; alu;remaneat, illud demonfitat Cla-uius pro!» 2.8.1. 1.
12. Dru "674 filtifimnon camprcbendunt.
Id et! ex- omni patte conclu.
fiant. d
PM-
4-.-
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F
si! tu: La 44 I il;MEÆÆÆÆÆâï; PROVPOSITIO 1.
.- -. . d Mou”Super dura "tu "la Âterminant A B. ,C
A A triangulurn a:. v qutlutcrum A B
- o
il t P » C, conflituere."; PRaxîs.Ex centris A.&B.fpa; a V ;E tic A B.vde(’crilzu:a duos cîr- [MF f
, culos,&:çx pûâofeaionisCÀuc a Î. ’
1’ métas CA.CB.:Dico. triangu- b 54 iun AB,C. eITc æquilnterum. l. ’ "fifi Ï
1 n Probatut Reâa AC. Jouant c x5;t eftcteé’tæ A118: BC. cidem: .- ct- T’f- i
go tafia: ÀC.BC.zqualcs cidemAB. æquales fun: dinter fr. Er- , 4go Triangulum ABC. en: e z- d ,5. v,uilatetum. Qlæd eut facièn- 4:93, 4
. nm. ’ .e. H-. Mi
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M020d G reflue BEL aqua-
E F16M refiumAG.c ponere. Ia l PRax. Inngatur a A0. Superfifi: ipfa AC. fac b triangulnm z-b Il. quilaterü CD A. centro C.fpatio1’"!- BC. duc c circulü : latus DC pro-;oê: duc d in E. centra D. rondo DE.d z. duc maiorcm circulum z latuspas, DA produç in, G. Rcâa AG. a-e Inc qualis cit retira: CB."IF- Prob. Reflet DA. DC. (un: ,12è? e z uales. Reâsx DE. acqualis.g al,- frc aDG. g Ergorefl’a AG. re- ..4x. (la: CE..Rurfum , rafla r CE. .æqualis oit mît: CB. h Erg’o
I l monftrazio,vtbcnc nota: Clauius
5.6 212m. Euclidi:PROPOSITIO Il,
( n tmi dutum pun-(B Hum A. dans
AG ipfi CB. chnque au-tem alii ponantur cafus,eademfemper cri: conflruflio 8c de-
cx Proclo.
s;
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Lib" printm. 2.7PROPOSITIO 1H. â
M ,,--, Dais- dunbm cil-1A8 refit) incquztli-IPMJ’
Ï bu: A. a" BC.de muiari B C ’rninori A.agitaient refilant BE. dura-I
1 hare-; PRax. Ad datum punâum B.- dans reflet A- xqualem re-a r.
&am DBJpono. Centro B fpaJ’H’P-cio BD ducob circulum ,abfcxfrab ï-BE,ef: æqualis ipfi A. yin.
Prob. RcâaBE. cfl: c æqualismf,ipfi B.D. qua: ponitur d æquahsd a:ipfi A. Ergo abfctflâ DE. xqualismfln "î tcfl e dam A. Cage! cm: fadent-:4: , -
5mm? .l J
;.
i
ca; a
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fié Èltrn..Éuciitiis i.PROPOSITIÔ IV.
a ’ i A - Si duo triait:D
Thtfïl; .1 c g’dfi A’ à. D’un. E H4 duolnteru,.duo-s
in: [attribut a4-q’udltu imbattu. ururnquenitrique hoc dt AB.ipfi DE. ï8c A C. îpfi DF. hulmtntqugd
MguloJA.âD.lutcri6ut il. L.lis cantentat’, annule: : sa vlufim B C. Itafi E F. aquaq ï;le»: kebab"! , (y triungu- Îjlurn A B C. triangule; DhF.aplatie m’t , à reliqui un- .
. 3141i. reliquis dngltli: 17144; ::le: crut marque vtrique,hoccf: angulus B. angulo E. a:angulus C.angulo F. æqua-lis exit, fub quiâw 47114111 .(citera A13. lpfi D54? AC.lPfi DF-fivbtmdumur. A
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Liber primas. 3.9Rob. Latus A3. lateri D1558:
, lotus AC. ipfi DE a; angu-Ius A. an ulo D.ponnntu:çqua-lia: ergo 1 fuperponanturfl con a 37i ruent ; ergo 605365 B C. bnfi’lx-F. bougran. Lineæ cnim mon
fibi congruunr, quatum extre-rna congruunt : alia; non ex .
. æquo [un panât: bintcriacerent.b D’fDeinde finegas; earum ma ca-4’da: vol (apr: EF.in G. vcl infra.in H. ergo du: reflz EGF. PIF.fpatium comprchendùnt , quoden: contra n. axioma.Bafcs igiturse omnia latcrà magnant; Ergo’& anguli, cum anguli non En:aliud, c quam inclinationes ipfa-c par;mm linearum . que fupponuntn:congrnere..0mnia latera Br an-guli congruunt , ergo :otumtriangulnm tori :riangulo cf: æ-i unie , &c. (Mgr! en: deuton-
arandum. - lc in.
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flan:
30’ 15km. EurliditPROPOS 1T [O 5v.
au 1 "W-A li Âge. quid u.ml un: lundi A
B .C ÆCÂÏACB. ainter fia: (nulles - épro-
çg Mai: quitus 1;:-lix AB.AC par: in
D. &Ë. qui fin Iufifimt angult’ CBD.
BOF. inter]? cquclexfimr. Iszynratio. Exlmeis A3. AC.
D
i
produâis, accipio zqnaliaBD.lCF. Be duco trôlas Cl). BF.
Prob. Triangulorum BAF. CAB.vnumlamsBA. VniCA. a: altcrumFA. arteri DA.a:quale en... Et insu;
5. Ex lus BAC. vttique et: communisærgo’him- b Angulus A85. æqualis ’eû angulq0 fat. NCD. ô: anÊqus AFB. angulo ADC.
0
b4.Prof.
a; bafis BF. afiCD.zqualis. Ruth:in triangnlis ECD. CEP. lotus CF. la-teri BD. cf: æqualç, 6c lattas. F8. pro-bamm dt zqnale ipfi DG. 8c an.gulus D.angulo Requin .Ergo b an.-guli CBD. BC F. infra bafim si: zqua-les ô: Anguli BCD. CBF. æqunles.qui fi tollantur ex æqualibus ABF,ACD. relinquenr angulos ad ba-fim ARC. ACB.zquales. uod en:demonfirandnm. Thales Ëertur lu-:orhuîus propofitionis.
("alunant 0mn: triangulum :4q u1Iaternm . et! zqniangulum: i
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bief Primat. o ai:PROPO’SITIO VI.
A Si triangu’li AB .I duo nugul’i A B C.
"*’ c ACE. æqunlc: interfi fuerint , â fil: qualifiaunguli: fibtcnfu lutera AB.AC. æqualiu inter [è arum.SI negas: pars vnins BD * fiat -
zqualis altcri C A: hoc poli-- to; triangula DBC. ACE. fe ha-
ben: îuxra quartam -, mm IatusBC. commune, 8L lateta BD. ÇA."æqualia. 8: angnli DBC. ACB.zquales. Ego a: totum triangu-
. lum æquale exit toti triangule,hoc en: totnm parti.- quod repu-
nat. b - .Corail. Omne trianguîum manifangulum,cfl: æquilaterum.
C in)
Thon?
a g"Mr;
bM-Q
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A .4- Æ-æ-o-u-*51; ’ filent. Euclidis ,’PROPOSITIO VIF.
c D Super nuira!z "(in AB.duu-’
A]; " ’15 bau ci de»; re-a: D. en. Afc. BC.[6&8 arquais: au;i due 1’886
BD. opaque vtriquc. hoc ca:
B D , non confliruentur Mluliuarcâ’ uliudpunfium ,i put;
D. ad enfuient parle: , "film.tçrmina: B.&DA . hul’entel, et?duulzmj initia dufljtàt refit). i
Rob. 03a poffint duci du:. ialix ,.ducantur in D. Ergo
triangulum CAD. .2 en: Ifofcclesiçrgo b anËuli ACD. ADC.æquaàles. Rot us rriangulum CBD, et]:Çfofceles. linge b anguli B DG:
y
1
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NIl
Liber primurî o 5gBCD fila: æquales , cûm tanner!«gurus CDA. pars anguli totalis’ç DB. probatus fit æqualis totalîàngulo ACD. Ide’mque flaquerai:incommodum v’bicumque [tama-
tes. Nam fi ponatut pnnéturn in;en triangulumin D. v: in (ecnn-il: figura, (mais AD. BDF.BCE.8c DC.fic dico, Rcfiæ AD. -AC.’Ponuntur zqnalcs, ergo.anguü .ADC. ACD. (un: æquateszfimili-
’ ter BD. B C. ponnnmr arquàles,ergo anguli infra bafirn EÇD.Inc. fun: 3 zquales , ergo anguàlus PDC. maint en angulo ADC.quemàdmodum ECD. maiorefl:
ù ino AGD. quod repugnat.Denique non potefi: (tarai pas;
(hlm in patte aliicnius liner. exdans, alioqni par: effet ulnairetoti,conttag. ax, ’ U I *1:: r " ’ . V.t
- lur punëtnm verfirs eafdem par- ,
r
1’103.
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fi.
. Elem.EuclidisPROPOSITIO VIH.
s. A D Si due Man:G nid A. D. duoFZÂËËAÏ’ item , A B,
l-”A AC, nimbusE S. luteriburD E.u c D F. æquulia
hantant,ultcrû’alterifinèmnc
ctium bufim, BC, bu]? EF. e-qunlem : Et ungulum A. un-gula D. arquaient hnàebunt,fié aquuliêur nib) «hum.
tu»). v tPRob. (En; fi congruant (a;
tcra , congruent a: anguli:cum a angulus non fit aliud quàminclinatio duarum linearum.Quod .’1 quando (uperponcnrurnon congruant , (cd trianguliEFD.apex D. non cadatin A,(edin G. ergo tune du: refit: dnabus
,rcéh’s æqualcs, (ope: cadcm refis
DG . ducentur ad aliud pluraux,ronfla præCCdentem. l
.4... , -
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Liber prunus. 5,5
PROPOSITIO 1X.’ A ’ Dutum ungulurn Wh .4’
Æ rcüilineum B A C. .V bifnrt’um fleure.
P Ru. Ex lateribns dati angulii BAC , fume: rcâam A l), 86 a 3.ipfi zqualcm A E. lange DE , 13",;confiitno b triangulum æquilate- b hmm D EF . duco rcCtam A F, Innquam aireto diuidcre bifatiamangulum A.
Pxob. ln rriangulis DAEÆAFJrcétz AD. 41E. (un: çquales: A11;cômunis en: ,ôc bafis DF,bafi EF. oçqualistb ergo anguliPADÆAE, gus- . - A(un: çquales. Ergo angulus BACI FAdiuifus en: bifariam. mg! fa,
r cicndnm eut. A A
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22». r-
a î.
in].Éni-
35 - Hem. Euclidig
nipponne X.Durant refit») ter;
J. ,1! minutant G H. bifi-An’ .i9 . rtumficnrg.Rax. Sapra rcûam GH, ’ con-
(titan triangulum zquilate-mm GAI-I. cuius angulum A, di-uidob bifariam , a: docte redanAF, dico rcâam GH,diui(am bi;fariam.’
Prob. Triangula GIA, HIA’, f:habent iuxta quartam ex confitu-&îonc figùræ : ergo habcnt barres:GI, IH,. æqnales. Ergo refla (3H;ëiuifa en bifarênm. If.
.....-
n- l .1
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. iiberfrimuii l 4 g;PROPOSITIO x1.
’7’ .Pnb.dA Data rafla DE. 4.Agpnna 1. in a. dm.ad refit): unguiab
mon lingam 1A. excité". ,Rrax. Ex lihncaDE, ï purifié ,Ml, (umo a partes h’inc inde æ-l a 3p
goalele, ŒginDEfi’ Conflituo E”?!triangulum zquilatctum DAE. à on;puné’to A,ad punétum I, duce re-
&am,quam airera perpendiculà- I
rem. . . . .y Prob.La:us Dl, c en: çqnalc 121tcri IE, adams dDA,ipfi A5, 8k a 23’;latus AI,comrnunc. cErgo angu- Dellfi AID, A!E.crunt çqualcs. f er- c 3’go reé’ü; ergof AI. PerPendicu. 1:3:
loris. Dm"
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’38 Item. traduis
PROPOSITIO XI I.
DE. à tinta pun-n. A. quad in au
n F C non «fi. perçcndi-Il ’ ruinent refiumlimum Al. ami.
un.Raz. Centre A. duce circu-lurn , qui (ccct rcflam DE; à
(tâionibus duce tell as DA,EA,a diuido DE, bifariamin La: du-
I’rop. ce rcâam A1. quam dico Fer-pendicularcm. ’
b n, Ptob. Latcra AD. AE, b (un:tuf. l çqualia,: latus DI,çqualc latrriC 5x IE.& AI,cornmune :dergoanguli
G
3m35 AID. AIE,(unt çqualeslncrgo te.rawl Chu-1go A[,efl t perpendicularis.e m. Hnius propofitionis autor fer-Def. tut Oeniprdes Chius annis ante .
.Chriftum circiter 550.
l.
bob. 7 Superdutum n. Jfiant tnfinitum l
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b
- Liber primas. ’ 3a
PROPOSITIO xm.Cùm rafla A13, 13.6
vcl EB . fipru re-c n D &um-CD,confiflen:,
un trio: fruit : au:duo: raflas BC, ABD , dutduabm "au equule: EBC,E BD. fuit.P Rob. Reflet EB, cum mâta
DC, au: farci: vrrinque çqua-les auguré? a: 1 confequenter re- au."(rossant non farcit: (mon farcit, Plizb excitcrnr ex B: perpendicularis mmBA. Quoniâigitur angulo ABD, .çqualcscfiznrABI-LEBD, Si vtrif- ° 13.que addas teâum ARC", erunr d’2duo reâi ARC ABD,çqualcs :ri- A3,.bus angulis ABC, ABE, EBD, ’
nibus ctiam anguli EBC. EBD.aux: equales a: confcqucntcr hi
t duo (un: acqualcs duobus monsur.
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in. o Élu».. pRoposmo’ xtv.
ML A x ’ Si ad uli-F que») reflua.
C. G .AC , (à: in c4A. griffu»: C4144
fifi): DC, C E, mm 4d cuf-drm parte: duflæ , cg: quifimtdrincep: ungulus CD, ACE.»
duobur refit: æqualerficerim;in direfium "un! inter ra-(tu. hoc cf: DCE; en: vnâ
liner: refila. ,. . . x-" ’ Rob. Si mât DCiC no
à? z. Piaçcn: in direânrrrf 3Eracer]:un. CF; aurélie quçplam. Ergo an-Mp- guli ACD,ACF,valent b duos re-g?" Clos. Ego r pars cf: æqualis loti.
”’ Narn prlus ex hypothefiA C D,ACE. valcbant duos rectos.
D
’H [47-
,u-M wl
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Liberprimua 45PROPOSITIO XV.
Si du "au ru;Acfi AB, CD, fictntfèa inuitem, 21231410.;
4d vertical; A E D, CE B.«gade: inter fi fiaient.I)Rob. Nam angulo fine AED.
fine ,CEB, addatur angûlus n n;v medius DEB, 2-exit çqualis duo- pop,"4 bus métis , b ergo anguli CE3, b 3. A,
AED, film çqualcs. ldémque fie: J3” n
fiangulo AEC, vel DER , adii-ciaxut angulus AED.
Thalcs Milcfius futur aufio:huius propofitionis.
00:01.1. Duç redît; femmes (et;mame. efiîciunt ad pundum fe-
. dionis,quatuor angulos, quatuor nais çqualcs. I* Coton. 7.. omncs anguli cire:
idem punâum conflituti æquqlcsfana-quatuor Icflis. ;
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à le.Plàp.
l Excupfl.
i If.Trop.d 4. ahop.
e u.If").
IF a: 2km. Euclidjsl .Ï PRO POSITIO XYI.
tu, . ME y Trianguh’
G w. A B C, mm 14-:PC un RA; produ-
’ 370 in E; exter-gm: agaçât: EAC, ’Utrolihe;
fntcrma’" appofita Ç,jvçl B,
àmu’ar efl. . l ’Rob. Latus AC. a llaifccemr in Rducaux: EG..in vt BF. fit aqualis
IF Jung: geai AG,.tunc triangul:A G. GFB’. habem fa iuxn 4, mm la-tus b AF.zquale cf! lateri CF. a: la-tus FG lateri FB.& angulusAFG,è ân-gulo CFhçqualïs; Jet-go 8: an n-lum GAF.angulo BOF. çqnalcm a-bcbum, ergo angulus totalis EAC.
. . , ,- 4extemus mulot dt luterno 8: oppofi-to ACE. Œodfilatus AB. vbifccemrÀin L idem flet, 5c probabxcur angu-lum externum DAB. maïorcm cireangulo ABq. [1go cum angulusBAC. c fit qunlis anguloDAB. cri:angulus EAC: extexnus , maie: que;ibctinterno a: orpçfitp hempe ut-
. ’ . . f H gallo C. vé] a. *
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Liber prime".
h 4 4;3&0 POSITIO xvu.’ Trian nli
Il A . SnÀBABC. duo d’y-T”. 1°,
, B C A: I. CAB, vcl ahi quilibet,qmz-guigne modofimnpti , dupâtesrefit]- fient minorer. ’’ Rob.Ptodu&oBC. in D. en"
tcmus angulus ACE).a maion te.çf! angulo A, vcl B. (ad anguliP’W-ACD.ACB, b valenttantüm tiges . 4rcâos,crgoanguliB, &C,intcr- r ’-m’, flue CAB, BOA, (un: minoresduobus rcâis. Idcm dicam de: ’àggulis A, a B, fi Ptoducamla-gus, BA. e *
Canin. In omnitriangulo. cu-jus vnus angulu; fuerit «au: vclobtufus. reliqui fun: acuti.
6010114.. Orme! anguli trianjguli aquilatcri a; trianguli Hof-celis, anguli farta bafim (bug ,
ùcqti. .. v. , Dl il
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.2-.:n
:æi
n-«*e z
’44, Elena. Euclidis
PROPOSITIO XVIII.
T” ."HA Tridnguli ’ABC:main: 14m: A C,màiarem Anguille»:
l" B c A3 C,fit6tendit.
h a. SI negas : Ex maipn’ latere Ac,3,1L . :facîAD,çqualcipfi AB, ducI; s; retîhmBD,b crunt anguli A312,PM- ADB, çqualcs. Eû autem angu-c ,5. lus ADE, hoc cit ABD ,cxtcmu;hop, a: oppofitusnngulo C3 ergo ma-
ior. Muho, ergo maie: en: marlisangulus ABC, angulo Ç. Mie:item cft angulo A. nam fac CE,
.v p"; çqualcm ipfi CB,dcrunt anguli’ e :6. CE8, CBzyçqualcs, c 8: angulus2. Proi- CEB,hocelhEBC,maiorangulo
j’y A,fcrgo angulus ABClmaipr au:4*" gulo A;QJ5. D.-
Ile
9
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Eh-n :4,’--.- -..
Liberprimijl z;PROPOSITIO x1x.
Tfianguli ABC , ne Ilaurifia lntuerA C, ficb
c "Mini coagula AB C,filatendita r.
San’gas, mus AC, erre maîlrslatere A3, (in: çqualja: acrgo e 7:
anguli B. Br C, fun: çquales.con- "Hun hypothcfim. Si brus, A3. di-cas main-latere AC, b ergo an- l, A.galas C,mai.or cri: angulo B,con- rap,un hypoth. Idem dicam dclate-te BC. Ex quibus fic dico lugusAC,.ncc minus en nec çqualç la;milans A8, CB, ergo mains,
9 in
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:4; 151m. Euelidg’g ,
PBQPOSITIO X39
mm Trianguli AB C,
g 231x.b s.Prop-C 9.Mx.
d l 9.210p".
du lutera pu,ta.AB;n - 4C , gnomodaamquè
fitmfita g relique C , fient:e mai 4.o "e(Rob. Produco CA, in D, fic
Yt AD, fil: çqualeipfi AB, 8Cproinde:CD, equalis ipfis ÇA,AB, duân refila DB,fic dieo:Re-a: AD, AB, fun: æquales b ergqæquales anguli D, a: DBA. c Ma-ior ergo vtrolibet cri: tolus au-
Ius’DBC , Ed hune angulumubtendit mus CD, hoc en: CL
413,d ergo refila Cl), hoc en: ÇA,A13, major cil quàm 13m; PC,
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[fief primas: ’17
pxoposrrxo xxr. Â .Sifieper trià’guli ABC,
E 11’301!!!" 8C, 46 extre- 11;. x ç
ne "tintants du: refit BD, Aà ’ DC, interiu: ennflinul
funin, In cambrienne?lieur? tringuh’ dauber [attribueA8, AC, minores guident errent.ruiner» 11034533114»; cantine.bannir! en Ingulus D. maie: crieangulo . ’ ’P gob. la pars. Produâo BDrin E, t 13
in triangnlo BAE,duo latere 3A, "à »’
A5,: union fun: tertio DE, ergo fi Iladdltur commune EC, un: 3A,Ac,maion (pian: 3E, EC. Bodemmodoin triangulo C150, laxeraCE,.Emmener: Tunt tertio 8D, ergo ficommune adam:- DE, erunt CE,en. msieu quem BD, DC, rad A8,Ac,prob*ara film: anion quem BE.ganga main: quam BD, DC.
hob. 1.. angulub BDC, externuvsvb. mais; emmerno 6c OPPofito D 1’15;l5C 6c h1c main: angulo A. interno P151,-Qr oppofiro, malte ergo maïo: an- 1*galas BDÇ, engluer A. P, ï
x
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mon
s 1oP"),
a-Il.
. Je.
a; ’ 21m. m1541:
PROPosnïo xxu.c Ex tribu: mais
*e’ë-"--q DF,FO,GH,qux4 I [une agonie: tri-
n FLKGH la»: daignais A.B. C. rriangulum
FIG. confiture. aporie: 4mmdu: quomaduunque fumptru,relique efli "miam: a grenaient .emmi: trunguli duo huer» qua-moduungue film)!» relique [unemame.PRax. Daris reâis ARC. fume
ipfis ordine :qqales DE. FG.6H cenrro Efpano FD. du: cit-eulum Dl. 8e cenrro G. [patioGH,duealium HI, muge danscum interfeâione circulorum inI. lineis Il, G1, a: faflum efiquod perirur.
Prob. inïriangu o FIG, radiaF1. aequaliseftbip IDE. bond!A, a Gl,ipfi 6H, hoc cit C,8eGFJPE ë. r
PROPO:’r
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flûterPROPOSlTIO xxm.
V c :Ad ddramrefldm 2:6?-ÂSAB AB épüffum C in ’
ï D e4,datü,dmo aga].à: refitlmeo DEF. .4-
"gaulent 473311414») reëlilmexm
G CB. Confirme".Vme in rcârerI-I». En duo
1 piéta Henrique. para D. 81 F, a:; amenât: DE. rqnëesï nm J fia; . 11;;A iriaqgnlum CGB. abens laiera Prof:
aequalia lateribuslrnàâguli EDF,
lingule fingulis: hoc facto man-gala Ce habenr iuxra propofirio-enem 8. ergoanguli E. 8: C. cum"squales- Husus prorofirioms
) éqrorfergur oenipes (litige, ’
Ë"-Ë
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....4..e .....-.-.. e...«- - .
ème .14-æxpu- 4-..-... ..
5.24,... ..
12.1s.
a 1;.Pro].
fui.G î .
d t’y.
Piaf.
’30 Blum. Euclidir
PROPOSITIO X X Ï V.
4 Si trii-I A galantn A B C.IÂGBAC: duo 14-
E 4 rem ,ËA B. A C. duvète: triangult’
DFE. [Junker DF.DE. c-qualia babuerir, ABJpfi D F .d- ACQfi DE magnum ve-xa A. mainrem un la D.lmfim BC. bafi F15. maton»;habelzie.
D reââ FI). a: ad ,unéh’r in en
«hmm I fiat angu us FDG.fx-quahs angulo A. a: lama DG. lpfiDE.hoe et! ipfi AC. fir aquale,b&cô-fequenrer bafis BC. bafi FG. mugi-tu: reâç GE. GF. angon DGE.DEG.c squales erunr. Ergo (crus angujusrEG.maior quem DLGJmior etiamen! quem DGE. a: muho maior quiFGE- d âme "a: GF. 8: hui: aquilinpo. une! en quem en
î
l
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Liæerprihzmg ,3:
PROPOSITIO. XXV. i4° ’D i Si duo trian-c A gala A BC. 7m-
DEF. du Inte-m , dauba: lareribur eqmzliuhabnerint,alrerum airai h oc
, CR A8 ipfi’ED.&AC.ipfiDF. IMfim on?» BC. bafi EF.
l maierem hubuerint: à angu-lum A. angulo D. main-cm ,habeèunrjîrb aquifère: refit):
contentzm.Rob. (Lu-igfiangulus A. noneIÏ minot angulo D. exit vel
zqualis,vel minonfi æqualisaer- . 4,gobafesBC, EF, erunt æëuales, Puy.quad efi contra hyporhe 1m. siminot :cum bren A8, AC, fin:æqualiaipfis DE, DE, bafis EF, 6 1la maie: erir bafe 80, contra hy: Pr".20th. E a;
B
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7.?!"-
17: J
fi tamtam; h ,PROPOSITIO xxvr’î
(9’ A D Si duâ tria" g:1341:4; la, tigrer arguée;
l, dauba: argalisagnate: habuerinr ,I altcrllni4km; gamin» [aux wu’ 14-.teri aquale,fiue quad «un:eqnalibur Mythe ,fiùe quad’vm’ 471441114": angulamm [1’46-
radiner, à reliqua latere,teliqui: [affiliai agnathe ha-belmnr, airera»: «lamé "li-4
91mm angulwm reliqm’ Angie-f
la.PRob.Gnt in triiangulis AVEC:
DER-anguliB, a: C, æqualecangulis E. a F, fintque primo la-ura BC. H ( (in: adiaeenr :51
ulis zqualibus)æqualin. Si lame;D, non eft æqualei fi BA. fie-
; go mains, a: fumarur V G farinai:
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Lié" primas. 5:r lis igfi BA, mm duüaFG, Duo
lacera triangulorum GEF, ABC.quualiafunlt, 8c anguli E, 8l B,æqualcs contenri inrerlarera ae-
ualia . a Ergo anguli C,8(CFE,zlotæqualeç , quod cire non po-;efl: nana angulus GFE, efl: par:ipfius IDÉE, qui saurins poneba-ru: ipfi C. non ergo 03E, main:eh quem 3A. Sed aeque minor,ahi: lateri 8A3 cadem qu: priasapolicarerur demonfirario. Ergoæquolis. age triangule DEF.ARC, le habent iuxra 4. a: liner;hteribus . a: au uli angulis cor.refgondenribus ànræquales. I
Sint chiade larera A B, DE;fuBtendentia g une; angulosC. a: EPD, inter e æqualia ,dicoInter: C5, CA, ipfis FE, PD , en?æqualia . a: angelot); A; angulq
af.”Prof.
D, æqualem. Si enim huas EF, fit,’maius latere B C, fume monEG,æ;qualem ipfi BC,duc reâamDG. quoniamigîtur Inter: AH,
5 V l : . 1 a * h
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x a ara-ca «gamay-437:4. C.
e
34 2km. Eurlidit Ia!) A D B C, fun: arquant44mm DE, no, a:
FB CEGFanguli 13,3: E, (uneæquales ex hypoth. cri: angulusC. anguln EGO, zqualis. b fgi...tur 8e angulusEGD,anguloEFD,erir æqualis,hoc cf! encrons in-ternas: oppofitotquod CG: ah-furdUm. Non CR ergo larus EF.mains latere BC.fed ne ne i fi:minusveftwrofrendir en cm: -monflzratio applicara. lareri BC.ergo cit ei æqnale î ergo trian-gula ARC, DBF, fe habensiuxra 4. cum lotusAB. ipfi DE.a: BC, ipfi EF, 8c angulur B.angulo E. fit zqualis a: coure-quenrerbafis AC, bafi DE. T113.les Milefius autor huilas.
x1
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g;11’501";me ’ l 5;
PROPOSITIO XXVII.G 3 si in du; re-c Drains CD.n.m
rafla EF. inci-B
i a de»: angulomlrernq: AGI-I.DHG. que!" interfifece-rit : Pauflela emm inter finife.PRob. si non (ont parant-1re
3 eoibunt tandem pur: in]. en;a: fier triangulusGlI-l. coins an- D’fe .
ulus externus AGI-I .erit b main: papi ’Interne a: oppofixo GHD. (mita-men ex hypothefi erat æqualis.similirer demonütabitur, fi di-santur concurrere in K. Ergo non(encartant. Ergo font ourdie.la.
’E iiij
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S.
n"...- 4..- Ce...749° surje: N’SN x «en
3,5 . FW.3ÇUÎair 3PROPOSITIQ xxyirr. Î
il 3541.19. A C t si in dune-l I. .rt . fichu A* "En E’F. inti-
de»: , externum’ ungulqng
ÂGE. interna à oppafiraad «file»: porter ÇHC. c-ègalemfererit : une interne:Ü ad enfler» parte: AGH.QHC. dualms rem: trek):faneriez paiaflela en)? interle jet-ça. "
Robatur r’. pars. o AnguioACE a raquons cf! anguluè
PGH.2nguîus CHG,æqualis p03nirur angulo AGE. I- ergo alter-ni.B CH, GHC. fun: aulnaies.c ergorefit A13. CD,funrparaIle12. ’- J
51,.
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me? MW"- .rz"troba’tur 1*. Ang’ulus 156A.
cum angulo AGF, d me: duos dl oicâogangnli AGI-1,6110, po» ’4’;
honnir agneler duobus’reCfils:Ecrgoanguli EGA, GHC, finir 9 Io
. squales. Ergo reaæiAB. CD, ""5?
rem hûius. ï
’ Ex ramena: arreliuius propo-fitionis, con neÎ fufiîeienter deirritât? massifiai ÂËÎÊWËÙ’. C
A.
flint pataud: En priorerri gara
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i
15910..A
i a.. P"?-6 18.
Puy.«à.
fi Item. Eaelidis r
maronne xxrx;ç In parallelar
A l 72343143. CD.* refb: EF. inné-
dans : à. alterna: unguis:BGH. GHC. qui". interfi fait: é externat»; EGB.interna d’appofito à 4d en];dam partes EHD. quater»;à internas ad "fait": par-te: AGI-I. CHG. daubas r91au cavaler.
PRobarur r. pars. AnguliDHG. GHC, g valent duos
mîtes: anguli Item DHG.BGHJ’ valent duos mélos, er-go anguli BGH, GHC, (un: æ-rivales.
Ptob. 2.. Anguli EGB, BGH.[valent duos recto; z anguli
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Liber prima. . à!3GB. GHD, b valent dans re-êtes , ergo angnli 15GB. EHD,fume aequales.
Prob.;.’Redæ A3, CD, po-nuntur parnllelz 4 ergo neque
iverfiis A. nequc v’erfus B, con. ’entrunr,ergo mm verfusA, quamverfus B. angon interni ad eafdêpartes flint «galles. duobus re-dût: fi enim ex aliqua parte ef- , "I.sêt minores, ex ca concurrerent. 1x,
Corail. 0mm Paralleiogram-mum , habens vnur’n angulumremua. en parallclograrnmunrrdlangulurn. ’ I ’
. 444... A
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. 4- ..4..-.,,,.,.L.E,.-w:-ü.«e ce.
. . 4.: .7,
je EKmÆwMg?ROP05;TIO Xxx;
nm. 5° Il 2’09 eidemi -L l Ënüe pe-C rolleidAB.Cp.
â intérfifimtpargllele( 1 I:P Rob. ln [un tres "site: in e9-
v dem plane petites fi au;F613 GH. angulut AIL, saqua;lis cri: 1.5;qu ILF.aquia (oural-terni ; a: angulus externat tu,enguio LED. interuo a oppoâ-toge ergo inguli AIL, LKD, (unealeqlurles:c ergo «du A8, C12,(9259253513 ’ q" ’ " Au
:3959. Ignv311:0: . :1 i5;
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h iilierpririturl ilA ÊRÔPÔSITÎO xxxr;
A CG 23 data Film. Pietroi Ai En G. dm re-c” d A,” a: (3D. put;
lehm refrain lineam AB.düg
ji ivre.
’ (Un darda-r CD. du: re-Ciam CH, vtcunquel,& an- -: z1 l
1110 GHD. 3 conflituatur aequa- En;isard G, nempe angulus HGA, a";
5 crie refit AB,’ ipii CD, parant- hop,a, qui: anguli alterui AGI-Ï.
Dm. tout aequaies’.
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171.11.
à gr.
hg.
6 29 .Prof.
le Item. Euclidie vPROPOSITIO xxxn.
A!) Trianguli A B C.on: latere BC. produ- ’
p &a in E externman- Adu: ACE. daubas inrerni: ;
éoppofiti: ABC. BAC. e- -ïqua!" efl: é trianguli , ne: 43interninnguli A.B. C. duo-z Abu: refit: eqxalerfimr.
PRob. prima pars a Dueaturex Caca: CD. patelle]: re-
âæ A8. tune quia rafla AC. ca-di: in parallchs A8. CD. anga-lus A. aequaiis cf! alterna ACD.Et quia BC. cadit in eafdem. an-gulus ECD. encrons b aequaliscil inrerno B. Totalis ergo ACE.aequalis cil duobus huerais koppofitis A. 8c B. .
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Libr primas. 65Prob. 2.. Angulus A C B. eum-
cxterno ACE: valet duos renfles, , n;(cd angulus ACE. dînequnlis dt Prof,angufis A à B.ergo angulus C. du.cum nngulis A. et B. valent duos P"!-redos,ergo tres anguli,&c.Huiuspropofitionis autor fertuchthn-garas Snmiuseircn nnnum anteChrifl. 650. -
C0701. r. Cranes ne: angulivnius trianguli.funr nequnles tri-bus cuiufeunque akerius trinn u-li (1mn! fumptis 5 a: quando uofun: aequales duobus,erit 8: reli-quus relique.
Carol. z. ln triangnlo lfofcelereaangulo, nnguli ad bnfim (un:
. femirefii.’ Cent. r. Angulus trinnguli æ-
quilnteri en: vnn renia duorû re-&OIÜ,VCI du: renia vnius rem.
Seb. Omnis figura reâilinendifiribuitur in rot rrinngula,que: ipfa eontinet Inter: , dem-ptis duobus; a: nnguli trinngulo-rum,eoni:tituunt angulor figura.
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Muni-enfilée
monisme xerii:75-3 Ai 3. AC.c D que goualera.- pour?
v, h Ida: AB.CD.adeafide»: partes caniungunt :,. cripfie agrafe: âpqralieleflm.
i ikeb. Duc xeéïam que.10. datas AB .CD. jaugent? tune"7’ nngulinlterniDABQADC. erunt
nequales :larus AB. ponitur 26-.qunle lnteri CD. lntus AD. c115
r coninæuneb ergo baies AC. DE.ç, 4- font aequales. b Ergo angon5:1” CAB. ADB (ont «quarks:c et:l; 7’ o reflet AC.DB. [ont Parallé-
, "p. fan. V -
èfiorôsr
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Liber primas. . ï;PROPOSITIO XXXIV. "
A Pamfldognmmoruwfinition!» que a: adver-
c n fiélaternAB.CD.-AC.30.6! nuguli 11.60. B (’3- C. e-qualiafuht interfi. éàiamanrA D. il!» bifariàm feus.
PRob. Reâæ A13. CD. poulin-tur parallelæ , n ergo nngulus
BAD. nngulo CDA. St angulusCAB. nvngulo ADB. funtaequn-les, cum Emalremi. Ergo man-guln ABD. ACD. habent duosàngulos aequnles alterna: alreri,6: ipfir commune lattas AD. ad-.inca, berge 8c reliqui anguli B.8: C. (un: aequnlcs, a: reliquat ln-tua, A8 ipfi CD. a BD. ipfi AC.erunt nequnlin, cum aequnlibusangulis, trempe alternis oppoatanneur.c Ergoi rrinnguln ABD.
. ACD.:equalia inter le.
tu»;
a 2.9.Puy .
b 2.6 .
P"?!
e 4.Prop.
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. T1ùvvv-m-nm .311. n, .
a?" 25 2V
"ç; :310». Euclidi; ’
ruoposrnp xxxv,AEFPEA FER Paralltla - h
Lu c n "ont": A12,A E T 3 FD. fiper e4-u D de»: bdfi CD.
(9’ in irfiz’em parallelir A3.
CD. confiture . in!" fifi"!qqualia.
D tribus modis poreft contint;gere, fi Vt videsin 1. fignrafic
dico. Reâæ AH F8. (un: çqun-les. quia [ont h aequnles na:CD. Reâz AC. BD. font nequn-lesungulus CAB. d aequnlis efl:nngulo DFB,externus interne aoppofito,ergo rriangulum CAB.aequnle eft e triangule DE!!! nd.
il dito ergo eommuni PCD. fientpnrnllelogrâmn AECD- 55(1).-
nç unlin. h’ ai pina: tua: Mil?r fun:
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à,
La" primat. (7nequnles vr prias: f demptn îgi- f 5:tur’oommuniFE. erunt nequales 486Aï. E3. Redç AC. En (un: w,f.aequnles: nnguli A. a; E. fun: M;
nequnles,iergotrian ulnÆAC. f1 29;BED. film: aequalin. n dito ergo 177°communi trnpefio EFCD. parnl- in;Ielogrnmma AECD. FBCD. e- ’
tout l aequalin. l bsi v’tin 31. idem repeto. me:ABP. B. fun: m aequnles ipfi CD. "a::ergo &interfe: ergo re&n Aï. g r.
çqunlit en: reâæ EB.Re6tæAC. Mr.ED. flint r aequnles,nnguliitem ’ h15.3: Arum"! æqunlesœrgo un- P;Euh ACE. EDB. font ,nequalin: 12",:
rgo fi ab vtroque rouas trian- q 2,.guium .EGF. relinques acqunlin P"!-trnpezinACGE, a: mon. qui- 53-,busrfi nddas commune trinngu- 07”lum CGD.facies parallelogrnm-[on AD, DE, aequalia.
Eïi
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var...
31.15.
. f4!. M-6 3;.Il»).
Cl.
h plenhdfiüçrueront-to xxxvr.
a H B Perallelvgrom-122. maAEJ-lD fi.-c E F 5° perequalilmlm-
film C 12.. FD. a. in iifdengperallelir A3 C D. confirm-24, interjêfimr quadra.
PRO!» Conneânutur patafiolo-. gamma mais CHJB a que
erunt nequales et Parallelæ. Ho:patito, parallelogrnmmum Ali.aequale dt ipfi C8. 8c parnllelo-grnmmum C8, ipfi HDJ ergoParallelogrnmmn AE. HD.fun:agonira.
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Liônpn’mm; v a
BRÇPOSI’I’IO xxxvn.
A E r Tain" :414 11.17,-gzàA cm: w... tr «de»: 641iCD. du”: Àiiflem paralleli:AB.CD.canfiitut4,fimt in!"1è agada.
PRobJPe: D. dans DE, pa- t 3!-,. rallclam "(120.13.51 DE. iyfi "a.CF. parallclogrnmma AD. C8; Il 1;.5 «un: acqmlia z (:4 goum di- P"?-
. n - u t 54.mucha fun: mangula A C D. P".7ICI). dergq Ma alangui: 4C1), 4 .
ICD.fuqc acqqaliq. 4;: I
r a;
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7d En»; EnduisPROPOSITIO XXXVKI;
B Tfiangulæ lACE. BFD. 1k.
c l: F D1)" æqtmlilm:bafilm: CE. FD. a" in iifiiep:p4r4lleëi: A8. CD. 17144154film inter fi.
[643; IA a
- a, 1311on , nucaux: EG. para;32",; maya AC. a: PH. ipfi un,65°. b cran: parallclogrumma CG. f
I Mm. HD. aequalia.cHorum dimidiq3:. fun: triangula ACE. 35033::’ ”- go funtîntuië: nana. 117- . -- - 71-»:U439
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fiânflîmm. à
r10 pqsnro xxxrx,.1 1441M très»; n. ’
.. gaz? A B. Q aA 3 C fitperea-7 Je»! 54]? BC. a". ad enfilent ’
par" confirma , in. iifdemfun; parallelisHoc en; AD..èflparallela BC.
PRO!» Si ncgas AD.ipfi BC. cireparallclam Jfit A2. cui mâta 331.!
* BD.produ&aoccurratin E. DU- ’° ’
a: ergo man C E. b triangula b 37;ABCÆBC. cran: æqualia, quod Trait,"fieri naquit g mm triangulum ’ I ”DBC. poncbatur squale m’an-
! gulo ABG. (aga fi dicasAF. 8cBC. CIT: parallelas,cadem repe-tctur demonftrazio , a; requiem;5.09m 85 Raglan elfe æqualiq.
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76. go.
I
7:. E10». Euclidi:
Æqzmlia trié-
A gui; A B C.B c: m DEFsfilper a,qùaltbus bzfibùs BC. EF. (a!ad «Idem fumes. confinu- ;
4 t4, in iifdem [nm pamIIelig j
PROPOSITIO XL; ,
l
ï
4
AD. BF.
V PRob. Si negas AD.. îpfi
1"];
BF. cire parallclam, fit Ac,cui occurrat En. produéhin G, ITune duâa GF. crunt 1triangu-laçGEE. ARC. æqualia: pone-banmr autem æqualia triangùl:ARC. Dit. ergo totum GELa: par: D217. cidem niangulq 4304m3 agqualia.
PRO-f.
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imrprbnià: fibRoposIho XLÎ;
v A En, si parallelogrmix . WinmhAE.CD-cahi-l mumm, cum trian-. gicla FÇD. bafim CD. b4-(jam)? a» à. il’fdeinpànllelir
AF. (.1? faufil. : radiale-ë’rammm’n tri! duplnin
rianguli.
A: PRob. bueaiurÂiaxhcrcrÀÎ). 3Trjangula PCD. ACD.a (un: 1734;.
a &qualm 5 , Parallrlogrammtim Pro!"I .ÇEcht duplum trianguliACD. ’ fi, !
t ergo a manguÇi F615; ,
m5!
Ë
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74 Elem’ Euclidü lPROPOSITIO XLII,Ray Ddta triangule)
fruit: 4711418 p4-
ne.Prof.la u.a z .
. Pro;d gr.Puy.
e38.
B E c rallclogmmmnm ’G C. conflitucre in data flai-Iineo angulo D.
An manguli ARC. Bafim BC.dxuide a bifanàm mE.du&aque
RA. b agami pet A. mâta AH. pa-nlIclaJPfi BC. A d punchs! 3.: fa-âo angulo GEC. ipli D.zquah;edu-catut ex C. mâta CH. ïyfi EG. paral-lcla ,Îtuncfigura GC. cri: pataude-gramma,cùm luus GH. ponçant pa-xallclü ipfi 15C. 8K laïus CH. Jpfi EG.
muni autèfi: lalc,quale pentu: , ficI’mbalur. Triangula A 8E. AEC.
[une æquajia; triangulum AEC. et?dimidium trianguli. ABC. 5U dimi-d’mm parnllclogxammi B C. (bye! ’
j, eadcm bafi EC. cuniÏiIuti: ergotrinngulum ABCÆR g æquale pan]-Iclogrammo GC. baba amen) pa-rallclogmmmum ex conflruâmneanguium GEC. :cqualcm datolugu.la D. quad Pclcbatur.
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Liber primat. 7jPROPOSITIO XLIII.’
1A? ,3 lelagmmmi,cô’-
, HIC: 4 l plemenm un?né c
metmm faireparallrlagmmmamm , interje film agnathe.
N hac figura, parallclogram-I ma circa diamcrrum (un: , 5K.HZ: complementa verô’ comm,parallelogramma AG. GC. hçécomplemcnta dico elfe æqualia.
Prob. triangula B A D. ü C D. g 44; lfun: 1 aeqm’lialtémqne triangu-
ln BKG. BFG. 85 CE0. GHD.Ergofi ab aequalibus triangulîsBAD, BCD. collas acqualia , né-pe BCG. ipfi BFG. 86 GHD. ipfiGE D. complcmentz G A C.qu: remuent. erun: aequaha.
r. Gii
Omni: paml- n. 52’.
A J que cira: 454-.
(H
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7 6 E101». Euclide?
- Ara I JddamnddùF. de" niaisai.Pane- .Æ lABCAqualepnd.tu n. :1 Maman CM.311. N npffîzanivdau n-
gnlo "511m" D.8 41-. CÇnflirue triangule ARC.il æqu-Pnfn le parallelogrammum C G. ha-l’ .1- bens angulum GEC.zqualem angu-Pnp. la duo. D. tum produc B C. in K.t in fic vt CK. fie b tquahs data: F. petit.1(0). «germe lu. punch ipfi CH. on:
carrens CH. produétz in l. Deindey ex I. ducazut pet C. diamerer 1C.l occurrens reâæ CE. produâz in L.
de par]... ducaux LM. parallela ipfiEX. feeanslx.produ6tam1n M. me-
- ducanirque HC. in F. dico parajlelo.summum CM. cire quod petirur.
Prob, Com lememn GC. CM. sûrd 9L 4 çqualiazcôp cmenrum GC. cf! e z-Pur- qualc triangule ARC. ergo &côplç.4 41- memum CM. habct autêhneam (K.P"P- e zqualê dal: F. à: angulum GNM,Jas. çqualem langulo HCK. qnifæquzhspn!’ en angulo GEC. qui ponitur çqualis’ dam angulo D. ergo parallclogrâ-
41mm! CM r çqUIlc CR trmngulo ARC.a? hlbfl un"!!! C K. cqualem du:F.&nngulum GNM.:lqualem du! .D. quodperebntur.
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Liber primas; 77PROPOSITIO XLv.A 3- na K llDao nih-nn AD.:-
Wh Pi",- ProbJ;A! zlogrammwnED. coiffi-were a in «tuc n HI Dreflilùna «gala F,
D Iuide reâilineum in rr’xangula.J fac par1llclognmmûEI.çquale
tçIngulq BCD. in angulo 11. ç ualiîpfiF. fuyralams GI. a a: parral clo-grarrimum G D. çquale trianguleARC. habens in l. angulum G10.zqqalcminfiH. 8e flâna: et! quad
perm". b a:h Pxob. Rem EH. KD. g, eidem Gl. "up.xdeoquc’Se inter te funtcpaullelç c 3°.&4çquales : angulus 61D. eæqullls m".en angulo EH]. r angulus 5H1. cum d ,4,angxilo Hic. valent, rings rcôtos. er- p,’30 &anguli 61H. G10. valent duqs g 29,naos: ergo glincç HLlD. iaeentm pubdireâum, fimilirerque ES. GK. 55 f".cum æqualibus HL FG.çqualcs 3d" Profi.ditzfintlD.GK.totç HO. me. flmt 14..zquales.ergo figura ED. de yaralle’ Pro!-logrammum cuius Pattes flint çqüa-les partibus dari reâil’mu a: angu-llus a. zquzlis ça) F. egqibtc;
À ’ An.
444:P",-
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78 V flemzuelidis
PROPOSITIO XLVI.
lm" c n D412 refiè B.qyadmmm A . C,
A 5 dEfirilzçre.
km. X A a: BRenge perpendxcu-lares ÇA. DE. aequales ipfi
5B. iungaturque reâa CD.& fa-!) to. (hlm cil quad pentur.
A ruan-
:18 ’ 6th ergo raft; AC, BD,funr°P3-3 [à rallelç. Vçraque d en: acqualisr wifi. ipfi A3. ergo a: inter (e :c ergo a;ï ’ W AB,& CD parallelx, fimræqua-j P"P- les: trgoAC,CD,DB, (un: ac,. ’ quales, a figura dt pataude--. f I grammaxumquç anguli A, 8c B,, r4.r fiat Rôti , ferunt etinm oppofiriï1 P9” C, 8: Djrdli Ergo Ah D C. cit.5. quadraçurn. 1?. *
Î! D’fl Prob.b Anguli A, a: B, (unttc-r
.-.4e-. ..
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Liber primas. 751,943110st xpvn.
In 7257m;- T”’ 3’-
l’ gulotriangulo
B A C. qua-d’un"): BD.
eD l quad 41menB C. riflant V "
au alun; BAC. fibrendeme ’djm’bimr 5 agende (fi. qua-
dmti: BG. CH. que Éclat:-ribm HA. AC. réf-hlm anguolhlm BAC. cantinemilzm, de-firi «mur.PRob. Ex punCto A. duc: rc- 4 si.
&am AL. parallelam ipfi BE. Vive
a:iungereâas,AD,BI.Tri2ngu- .laACD,lCB, (e babel): iuxta 4,.nam lama CD, ÇA,b funr ac-qualia ipfis CB,.C!,& anguli con.terni ICB,ACD, acqualeszcüm b w.-anguli 10A, BCD, fin: b rem a: r -
G iiii
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4:-91’?
in? Hem. Hadith- Il engulus .AÇB,
* commuais: et-o triangqla
ACD. 3121,10!!!Aaçqliah’a. c SCJ
triâgulü ACD.en dimidiü par-
rallelogrammi LC, cüm fine fir-pra eamdem bafim CD.& intcçeafdem pamllelas A L. CD, 8ctriangprum [CE , dimidium’quadrariCHpb tandem caufam.d Ergo quadraujm CH. fifi çquq-e parallelogrammo LC,cüm eo.
mm dimidia En; acqualia.hm ducanmr refit AE,FC.
Triangula FBC, A55, fun: ac;qualia , eü fc habeâriuxta 4.. P4;tl’ianguhlm. A 8E, éfi di’midiü par
rallclogrâmi 3L. fifilt trianguhîFBC, dimidiü quadrati BG:crgdquadratucn BG en; çquale paralé
lelogrammo 5L. Totum ergoquadra nm BD, açquale efi qui.draris BG, CH, quarrera: probi-dum- P! Mile prapnfr’zianir "(En
futur Pythagmu Sdmiug. .
E14 T
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Iiberpn’mm r
PRGPOSITIQ XLVIII.
I f I Si quadratum mecl n quçdabCBwno I
huerta» trian-guli C AB . defiribitur,aqua-kfit ü: que à reliqtqi: daubai: .grinnguh’ [4117715111 AB. AÇ.
defiribuntur quadrant) : un:r gala: CAB. contentmfib re-L
liquir dauba: trmnguli [mari-f ..à ba: A8. AC. refilerai.
- Rob. aducaturex A, ipfiAB. gui. . ». rap,. perpendxculans AD. lpfi AC.
æqualis, iungaturque-reâa D8.’1 bée pofito fic dico biAll ulusq n.DAB.re&us en, cergo qua rani D’fi’ !ï refit: DB,aequale en: qùadraris aile
ÇÇÉÏaÇgm tu. AD, vçl 4g (a
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d t.As.
e 8 .1),”.
h Elem Endidiru Iam quark-arumB xpfius CE. e’x hy-C B poth. æquale cil:quadraris earundem CA. A B.d ergo 118:2 CB.BD. lime aequa-les. Ergo triangula CAB. ADB.habent tria laura aequalia , e a;an ulos qui aequalibus lateribnsre pondent ac ualem.Ergo fi au-
ulus DAB. re us en, cri: etiammétas CAB. cüm lateraDB. BC.fin: aequalia.
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l
-.’.r.m.mmêrlE v CLI DI s. ELEMENTVM n.Î; .D 15 FINITIONE s.
h I.C P4 ralltlo-D .i grammurn r5-
i r flangulum Ar - BCD. conti-
i- A B neri dicitur ,J716 tituba: rem: AB. BD.que "mon angulnm A30.comprehendum.
,, Vemadmodum in circulaX cognita diamerro , cou eius4.01131 cognofcirur , fic expreffisl dual-rus lincis qu: angulü refli Continent in parallelogrammo
re&angulo , (tarira tata cirrequantitas intelligirur, niminlmladrudoalongitudo.
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h aga. x.i444.
34 Euclidi:i’ I * iobfÊrua 1. u-Ç 1’ ma parallelo -
grammum dici’ reaangulü quad
vnîun habet an-
". u un: rcâum. siA E filin: vnus dt m-ans ab cum: ô:xclîqni "en.
obferua 2.1nfequentibusnomineeranguli,Euclidem fcmper intel-ligerchnarallelogrammum rafla!-gnlum, lice: vis no minis id non ex!»-
ac.8 a. Geqmegrqs 0mm: parallelo.summum qxprunere duas tanninpomimndo literas , quç pet mame"
- tmmopponunmr.Vt appofitum a-ullclogrammum 2p ellaxîc. AD.
4, Cognitis lalelïî u; reâapggli.inueninfims arçafn ça .multipliça-gagne numeri vmuslatens in numc-mm altcrius lateiis cires eulndemafiglxlum. Similxtcrquc ensuit: ne:reaanguliôgvno lgtexum. mueniri.alternin lama fi dluidaçm’ mimer";érèç pet numerum brens dag, quiz;gym gain) en; lams quçfinunt ’
î
1
Î
fiç!
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iihrprimur; ifIl.
Ômhi:- FA A ’ paranth-
i . grimijimflG . «nuançant-H lilial tarant
È E .1, que ciras’ diamant»: illimfimi P4751-
Jelo’gmmmorum, cum dauba:y complememè, gnomon voué
i Il".g IN parallelograrhmç 415. pi."
rallclogrammum G E cum’duobus complcmcntis GF, EH;vocctur munir, quad Latlnè nm:
i marri fana: , du: cnim (refit!!!le. nabis exhiber;
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86 Élu». Euclidü
PROPOSITIÔ Î.Un. c D r si ingéra; :111;
F u I[Kg fècnurqne ah: -
G - .m :pfàrum A B .«
- in quotcunquelèguent»: AE. EB. "aurign-lum C8. comprebenfian [2:6dauba: "81k A C. imitahoc cil G. 8: AB.f:&Æ, 4:-qtmle a]? rufian Il: CEPS.-guœfirbinfiflâ A. Ü ganglibetfigmenramm A15. E3. Vcomprelacndnnmr.
Rob. ex punais A, 8c B, cri-gc a perpendiculares AC. BD.
un.. à 3. L àqualcs data: G. 8c ducatut rcÇta1.18.1. CD, ficque fiat b «x [intis C A, -634-h hoc dt G. 6c A B. reflangu-
hlm CB. Rcâam AD. vtcunquc
.4-.«.-.7.-’s--æ-g--..-... --*I -
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LtôcriPrimm. 87diuîkîn E. a: fiat d EF. pataud:a æqüalis ipfi AC, crunt CE,FB, dn îxcûangulaa Nam angulus FEB, 051;.refilas env quia æqualis ipfi A, au.8: confequcmcr f reliqui anguli f18- hrcâi. a: lama: latcribus oppo- 334°”fitis zqualia. Han autcm duorcâangula CF, BF, fimul fumpta(un: çqualia torah BC, hoc dtpartes toti.h Q. E. P. b m”
Idem pater in numeris, par: 6.8: 1.. diuide 6. in 1. 8c 4.. dicon.numerum produaum cx 6. in2. çqualem cm: duobus numcris4.8; a. qui-fiant ex multiplica-lion: duorum in duo, a: in gnan
mon. 4
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a Élu». 2:43.123 u
PROPOSITIO
i Si rafla huaiE G PIF ÀBJêflafttvt-Ltunqùe para ing. 56 D. ERe;
- annula C»,.A C D B abîma. com;fifehenjîz [hé rat4.AE.hoc cfliA B. (à? qudIibètfigrizentbrnnâ
-* AC. CD. BD. «gadin-fiant,quadra» AF: quad à taraiAB.fit;
57... z
1&5 ROB. Ex Éatiqiuaàra-iI u ’ tum EB.cx C, 86D, crigan-MJ macs. ou. annela: a: ne-
quâlcsjpfi AE. En polira. cri:- zcaangulum EC. com rehçn-
in (nm fubtota AEÆhoc A8. 8c75sz fcgmcnto AC. 8: codcm modo" gcétangula GD, Hg. (a!) ton Je
. vcrdf
. Av......----.-......
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Liber prîmm. 8’nuraghe: fegmeotorum. Cum en.go’icétangula EC, G U,HB.Ifint d ,Hautes omncsfuo toti quadrant: "J’AI, æqualcs , arc: reéhnguh.comprchcnfa (à) AIE, hoc cfl:AB, a: fagmcnris AC, CD, DE,21311:4: (ne quadrato lincz A8.œi- .
In numci-is diuîdcto. in 7.8:i. dico 7o. sa ;o. qui producun-tu: ex multiplication: ne. in 7. a:i113. çqualia cire me. quadra:minai La:
d d u’fl-’.’
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go 15km. 2115545.;
PROPOSITIO HI.31!an c D Si reüalincq
(15-: A8. [afin fit,fifi opte-nuque in E.
l Ryôbmgtîmn
CB.fiz& rota A817 vnajèg-maman AC.hoc CH AEJÉ-prehmfùm , 471:4]: cl? reg
I, ’ iflangulo FB. quad fub [517. Aimuni: FE. hoc èû 8A.comprehèndimr, é quad à
Prcdifiafêgmtnm defiri-biturqzmdratq CE.
Rob. Datam A8. fcco vtcun;que in E. ex punâis AEBzcri-
- ’ ,14, guiperpcndicularts AC.EF.BD.”31.1. parallclas b inter fc 6: æqualcs.
Ù 3- h fegmcnto AE. mm duco tafia-n ’’ a” 1’ à punâoC éd D. ur critparal- ,
4 lalafipf: AB.Ho pofitoficdico,
lA
mm ægualisdiffi 4E. crgq’ h
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Liber primas. 9xxçâangulum AD. cil côprehcn-
* (hm fub rota AB, 8: vuqfegmcn-l. torum AC, hoc eû AE; Rutfus
FE. cf! dçqualis ipfi EA. ergo tc-’&angulum F8, cit comprehcn-film fub fegmcntoBE,EF, hoc en:AE. Deniquc parallelogrammumAF.quadtatum eût cum AG,EF,En: d’pcrpcndîcularcs ipfi AE, a:
eidem æqunlcs. Ergo cum te-&angulum AD. squale fitquaodrato AF,& reâangulo PB, pi-te: tcâangulum (il!) tout AB. a;fegmcnto AE,æquale cire reflux-gala comprchcnfo Pub fegmcmis
I AILE-113,8: quadraco prçdiâi reg-
g: menti A15. Q3.P.l In numeris diuide x0. in 7:8:5..., 3. numeru37o. produâus ex to.i in æqualis en: numcro 2.x. qui
ex 7. in 3. producimr; vna cum49. quadrato priotis Paris, 7,
e 53.4;
.. "m7 4...? -.a--- w u
n
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9:. E la». Enduis:PROPOSITIO, 17V.
Si rafla limaau... D r E AB.fe&4fi:w-
cangue, in C.H G K quadratü AF.
quad à tata AA CE B. defèrilvimr,
«gade erit quadratitv HF.CK. que àfigmê’m AC. CB. .
dcfiribunmr,câ’ cireflan alequad [71’s jà!) fezmenti: C. ’
GB. a mprehendimn ncmpereflangulis AC. GE.
.46 .i i Rob.Supct datam AB.fiat*qua-il :x’ dratum AE.duc diamantin] DB.à: ’ ’ çx C.fiat CF. parallelab méta; E.D’f’ («ans diamcttum in G. par quadd age HK. parallclambipfi A B, hoc
i’ ’ pofixo fic dico.Ttxanguli Magma."21’ ra AD An. (untcçquâliaïetgo am
f 19’ L guli ADB. ABD. flint dçqualcs, cr-go ranimai, e cum angulus A. fit
I "Gus. ldémquc dicendum de trian-gule EDB. Kamis angulus DFG te.-
...*..K.m. -
--a--
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, Liberprîinm. ,;ans (en, angulus FDG. ofienfusven .femircfltus, ergo angulus FGD. e .âfemiréâusgefl, cr o lacera DE. F8. g 3:. x.funthzquaha: [e lpfis enam funt bal.squalia I latcraoppofitaDH. HG." 1’34. r,go parallclognmmum PH. quadra- l go.mm! cit. Eadem de nui: quadra- 99’.nm exit CK. ergo HF. CK. quadrauflint fegmentorum AC. C3. ciim l:-tu: HG.fir æquale. ipfi AC. Simili-tct reâangula AG. 6E. commenta:fub (cgmcnris AC.AB. quia CG.GK.fun: xquales ipfi CB. cum (7K. fit
mdratum,& CF. item æqualis re-z Raph quadratum HF. hoc çà
xeâz A C. lgitur cum quadrarumAlain: 1131C quadratis HF. CK. seùàapgu is Ac. CE. vexum eû qua.datura AIS. furie: daram A5. æquo.le cire quadratis fegmcntorum AC.C8. a: reaangulo comytcncnfo fubiifdcm fegmenti’s,bis fumpto. ’
Si diuidax 6. in 4. 8c z. quadratum6. hoc ei’t 36. aquale en (gadzartsyttrium 4.8: Lhoc cil 16. 4. vu;cum numero 8. bis reperito qui fit àomnibus 1.8: 4. in fr Quiriplicaris,
si. au
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,4 Elem. Endüisi ïpnorosrr’ro v.
4P
Si rafla [1.7134
. . En A B. ficttur inPH . a æquliajn 0.01
Ü”. A a DE non Æqflfllid in’ D. Reflnngnlü
LD. fid’ iaægnalibu: tatin:AD-figmemi; AU.DG.hocen: DE. comprehenfitm, and(un; quantum H Fg qnod 45intermedia [émanant CD.47ml: cf! quqdmto CI. quad Yà dzmidm C13. defirzâzmr.
:464. Rob.Super diminua CB.filt,1quav.1.31,1, dratum CI. duâaque diamerro
Bi. agnat bper D; «a: DE. ipfiB]. parallela : Ex eadcm refit: B].fume B K.zqualcm iyfi DE. a: petpunâum K. b agami KL. ipfi A8.
UP’ parallela 8: addarur AL. panne]!’ ’ ipfi 13K. hoc pofito fic dico, rriangu-
45W li ECB.zngulusC. natrum: 8th»ter: CE,CB.æqualia, ergo d anguh’.8. a: B: flint «aux. 15:50 * ferrure; .k -a-»...s..- 444
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Lièerprimur.au. hennfanguli 1E8. 13E. (untz- azur.
uales &femireé’ti e 0b eandem ra- fun.
q. h ."M-Ilo-v-vrv-
un" --
u. -1.
trouera. Rurfus in parallelogrammoDl. angulns DE]. remis cit ex con-firuétionemrgqfanguius BDF. re-ausNunc in triangule BDG. angu-lus D. reaus cil : angulus REG. pro-batus cit femireâus, ergo: 8c angu-lus BGD. femireétus eft :ergo glute-n’ DE. DG. funrzqualia: ergo h re-angulum ID. fui) inçqualibus (cg.mentis AD. DG. hoc cit DE. con-ÇCntùm. Bodem mode dempnfira-
.birur Phrallelogrammum A F. ciréquadratum (apr: fegmenrum inter-inedium H63"): efl CD.nam métan-gulum LC. æquale eft ipfi D L cum"runique fit xquale ipii CK. mm1C. 8: Cpt. (rami (upraæguales bafesô: inter caldera. parallelavs: CG vexaà; GI. (un: àomplemenral zqualia,quibus fi addas commune DK. erunràqualia CK. a: D l. cætera mmtrempe HECG. flint communia. ’i Diuide 19 zqualirer in s. ô: s. in-’çqualiter in 7. a: æ. erirque nume-rus u. ex 7. in ;.vna cum quadraropumeri intermed’u; 2.. quod cit 4.mquale quadxarq dimidïi s. hoc eh-æmnæm ne ’ i
Si;la 1;Def. En;
3.. 54145.!.
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95 Élu». Euclidis
PROPOSITIQ V1.l Si rafla lima I
L . F a]; AB.ficemr 62»E Ifuria»: C. ei-
A c BD que rafla qua- -du»: BD.in re-
. au») anciatur, refhnfulum
t 46.!.b au.
Al. comprehenfim fù tataAB. cum adieElæBD. éfitbndieffa Dl. hoc el’c BD. flint ’1
cum quadrato KG. à dimidia lKH. hoc cil CB.;eguale eflquadra» CE. àlinea CD.que tu»: ex dimidia CB. mmwadiunfln BD. emponiturrauqua»: 11m: lima, defiri-
pro.Rob. Super recuira CD. a fiat
Pquadrarum C 5.. er B. age.BG.gallelam b ipfi DE. l’âme Dl. çqiu-
ipfi D B. ôter 1. age. IL: paral-lehm.
--lr.x---. -x. -LÏ. .;.m.
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. .
31.3.;
î iiberficgnâui 9-;lehm &æqualem 1pfi D A. iungatur-que reâaLA,quo faflo fic ficelie-.&angulaLC.KB. (hg: inter cafdcmparallelas &Tupra æquaics baifcs.b crgoz’quahaÆxdem K12. c æquale 5 3.611:in! complcmentum HE. ctgo critôc 645- h.HE.xqualcnpfi LC. ô: addms com-munibus (il-LEI. gnomon (il). 1C.æqualës cm ton reîtanguloALquod.hominem: fub ton dB. cum 3633611BD. &fub adxeâa D1. hoc cit BD.l’am veto gnomon CD. IC. adicâo .quadrato KG. parfis dimidiz KH. 434J!y hoc ’efi CE. fit squaws quadratoJpfius CD. qu: efl pars dimidia cumâdiunâa. Ergb parallclogtammumAI. adicâo codera madrato KGOfier squale eidem qua rata CE.
In humais. Io. fccctu: bifniàmin 5.8q s.add au: ci numcms 2.. nu-intrus 2.4.. qui producxtur, dué’tocompofito 12. in adiunûum z. .vnacum quadnto z; .quadrato dimzdèis,zqunlis efi 49. quadraro numcn 7!qqiçx dimidlos. ô: adicôtoî. com-
pointal! JC
î-’
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abr
n. 7.
56.zW.
98 EImWEu’didi: iPROPOSITIO VIL
A c B Sf "(in [muK M AB. ficeturw-
H cangue in C.D 1- E quadrata tatin:
F G Œvtrinfiasfig- menti C B. jimul fimpm,haceflAE. EF: «quint [in]:bis fimpw refinngulo A M.guadfiab rota AB. (yfilb di-Üa figmema CB.cantinetur,ou») addito KL. alteriu: fig-menti A C. quadra".
Rob. Super AB. * En qua-dratum AB. fume B M. æ-
qual’mipfi CB, ducanxur CL.MK b parfile]: ipfis BE.AB.px-o-
4*! 4*çBE.in G. fic vtEG. fit arqua-’ bal-pli BM.°hinc critMG.çqua- .
11s un": RE. fiatfluadratum 15E:-,
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Libcr fimndus. 99hoc .pofito : quadrant!!! tonusAB. quodcft A b. cum quadratofegmcntiCB d hoc CR EF. tiqua-
fia fun: xcâangulisAM.MF (qu; d ’1’ îf n: fubrota A B. & (cgmcmo "’5’ 3
BC. cumBM. fi: ipfi BC. zqna-lis; a: in ;c&angulo MF. lauraAIGJ’G. fintæqualia ipfis DE.DM. hoc et! AB.CB ) vnè cum
. quadra") alrcxius fegmemi AC,,4 quod en: KLm’tum videlicct Paz-
abus omnibus cf! æqualc.Diuidc 6. in 4.. a: 2.. quadrazum
totius 6. ncmpe 36. ma cum qua-drato ipfius 2.. hoc en: 4. aqualia(un: numcro 4o. qui fit ex nume-to 6. bis duâo in 2.. hoc en 2.4.vnà cum quadrato altcrius par: ”gis 4. qubd cit 16.
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a 100 Élu». fadai:PROPOSITIO VIH.A c B D Si "El-41mn.
AB. ficemrw-
I K144 Manique in C.refiangulumIB.
É HG F quater compre-henfimz tout AB. Ü’ŒHM
figmemarum BR. hoc dl 4BC. au): en , quad à niquafigmenta Ac. hoc C": LS.fit,quadrdto LH. arquait afi- qua-drato AF. quad à tout AB.à diffa figmenta BD. hoc
x CG BC. rauqua»; 4b 1mn ’: A D. drfiriêitnr.
Roblleâz AB. (ca: in C. adh-ciatur in tcflumBDJpfi BC. :-
4 qualxs. bupcr [ou AB. &adlunâa ’.-. BDJaoc cfl fupcr AD.fiatquadrarum ;
» l D. ç: Punâis 3.8: C.duc tafias bG.cri-Wh DE. parallchs aucgtifquc
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’. Liéufimndm. lot13K. KM. ipfis DE. BC. æqualibui,duc métas K]. ML. ipfî 0A. paralla-las.Hoc yofito fic dico, cires [Leon-Ctituta fun: quadrata qu 2mm. quo-rum, laiera omn’u iPG BC.. film a æ. 4 F;çzalanuûa diamctro BD. comple- ""3 ’ .manta AR-RF. b fantxqualiafunt. 3L3que reûangula fub (ou AB. à; En.hoc dt Fegrnenro B C. Eodémquemode 15. 5G. fun: complcmcnta z-qualia,qmbusfi addas quadrata et; ïqualia 5R. 3K. fient xcââgula duo-bus prçc:denribus çqulliaycum fin:inter enfdem paraHelas a; squalesbafcs : ergo quatuor illüeâahgulafaut fub (ou &vno fegmcnto.0439dfi quatuor illis zeâangulis ad asquadrarum LH. sucrins (cgmentiLS.hoccRAC. il]: omnia fimulfum-pt: cran: çqualia qlmdmtonzl).quost fit fupu AU.
Si6.f’ccenturin4. 8: z. ducaux-Ïcâuatcx numerus 6. in 1. . fient 48 .
a datur quladtatum ipfius 4. ho;CR x 6. flet numerus 6.x. çquaüs qua-drato ipfms 8. qui numerus compo;piçur ex toço c. a: gang.
Il
1. au
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15.9
.-.,.».... Id,
NRitoufi.Ô s. 1.
in j. un». Enduis.PROPOSCITIO 1x.
Si "Eh lista.’ E r A B. [Enter in
Æ. agada in C.A CDB t’y-non squatta.
in D. quddmu qu: 4b incl-qualtbm: [égmcntz’r AD DE.
m. dupât finu , camp» quedimidia AC. édifiantes,dia CD.fivn:.
P oh. Ex C. nigamr CE. palpen-iculam îpfi AB. &zqualis iplî
CA. vel CB.ducantuane reGç ExEB. Deïnde et D. cngatur DE ipfiEC. pataud: (un: En. in F. 6c fiat[du FG. ipfi CD. pnalleh. data.turque reâa AF. hoc pofito: Trïan-guh a lfo.’celis ACE. anguli A. 6: E,funtb çquabs c à: famireâimum an-snlus ACE. fit retins. Idem dlcen-
un de mangulo 5C8. ergo tous:t si. x. angulu En. mans en. hm in triâ-
gulo E F. angulus G. à and): cl
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z;------.A
...v-.-g-----’
C Liàer jauniras; le;an n10 ECB. a ergo reflus . ergo an-gu il; 8c F.bz malesc quia angulus .E.femireâus et :e ergo lutera CE. J 59.10CF.zqnalia. flaquais euam vtrrque l5: a ’cit C 1).: cum CD. fit parallelognm-mum. lgirur fi ab çqualibus CE. C8.follanrur squalia Gë. CD. reüabitCG.fhoc cil DE. ipfi DE zqualis.laça prçparatio. En demenflratio.Œadratum real; AF. s mufle eû Î34Jquadraris fegmenrbrum inçqualiumAD.DF. hoc eftDB. Rurrns quadra-tum rem; AIS. g çqualc eflguadratisA15. EF. m auum AB. çquale ipfis 147-!-AC. CE. arque arien duplum qui.And quad fit à (finish: AC. Et qu:-dratum EF.zqua!c en ?uadratis BG.CF. figue adeo dup um quadrariquod fit ab (egmerxto mçdxo (Æ. feuCD. quare udrata qu: fiant ab
, inçqualibus ’egmem’ts AD. DE. du-
yla (un eorum (1qu dimidia Ac,cab intermedia feâione fiunt.Qodcm demonfirandum.
Druide 1min ç. 8:; 6c in 7. 8C 3.media (câio Lquadrata ,49.&9.par-tiuminæqualium7.& untduplumquadnlotum a; . 8: Parus di-midrz s. 6: redirons a.
l iiil
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’30]. me)». Euclidir i
me POSITro x.En: loi 1E 1.- Si rafla AB.’ ’ par!" blfdrit; (
°in C. tique rl
i
G adiiciatur indirefium renvia
150.4;qu 200:4 ou») align- ra4 A0. câ’ quid! adiunffaBC. mmquefimul :11":de44:14 fun: quadrati à dimidid’ ’ .
. AC. 6" eim quad à sampafim 31. C0 ex dimidia CB. Ü 4d-. * 5:47:35 80. rauqua". Fraude: ’ ’
Icrilyirur. l
.-....-..1.»...C C ...-...-F.m.ux r . ..
PRob. Ex C. çrigatur perpendicu- ’laris CE. squalis ipfi AC. iun. x r
Lgnmr «a * r En. ex E. fiat EF.pI- -.vilain :17 . per o. ducaturOF. f î
"and: r CE. occurrens reâz’gy. in G. iungarurque refit: AC. hgIrrangulo ACE. lutera AC.EC.funt
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. X-Zïj -’Asï:’.«l-” "F";
Iihrfirumffll. A 1 o ygqualîl, 5c angulus ad C. mans: er-go reliqui (animai: itidemque inerranguloUECB. Similiter in mangu-Io EFG. InteralF. CF. fun: cqual’ra.E t angulus ADFJeâusjergo reliquifemirrâi.
Hrnc dcmqnfirarur quad gueri-tur. in triangulo AOG. angulus ada te en: ergo wadratum re53: A squale en quadras re-aarum A0. a: 0G. hoc dt BO.turfiu in triangule AEG. anguluu
ad E. reâus efi conflans ex duobusremit: is: ergo quadraturnipfiuf-me! A :quale eft quadratis AB. 8C
41.1.
BG. E8 autem AE. duplum q. drati - -AC. &EG duplum quadrati F.velr6. ergo quadrant A0. a: BO. duâp13 en iprorum A C. a: C0. anden: demonflrandum. DNumerus la. Fecetur in s. 85 s.cuiaddantur 3.quadraüls9. 8:9. nume-zorum la . 8: a. dupli (un: numero-un quadratèruru 25.15: 64. qui,.6: aunera s. ô: 8 . gignumur.
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106 Ehmludidi:
PROPOSITIO XI.
ms. c Jeunf1DEAF
DM»: 78512
A B. rufianin G 3 a): reflux.gala»: C c5! ’
prebenfu fiétata AB. à [246 «me figue»-tamm GB. fitdcguœle «tarin: dfigmenti AG. quadrant F.
punâum A. excita.1 1315......" r perpendicularem AD. terna-
lem darse AB. eam (ce: bifariamin E duc rcâamEB. 8c ipfi æ un.lem fada: EF. produccudo A.Ex AB. abfcindo AG æqualema: faftum en:
Prob, Supraarme! qüàrirur.
atam AB. perfïccquadrarum AGI a; fupra reâamAF. quadrarum FG a refilant
322 HG. produc in l. hoc pofiro ficnaja. dico. ma: DA. - fada eft bifa-
1
1
1
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Liber flamba. rotriam in E. eique m direflum ad-icâa cit AF. b ergo rectangu-lum-FL quad Faâum cfl; fub ro- b 6.1.; Ita DE. a: .FH hoc en: FA. vna
. cum quadrato madras EA aqua-lc quadrato EF. hoc efiEB [am a î.quadrarum EB. czqualeeft qua- sa:drazis A B AE. ergo gradua.A3 AE. fila: æqualia rc anguloFI. cum quadrato EA. Ergo fi
rcommunç quadrarum AB. touas,reâangulum FI remancbi: æ-quale qüadraro ipfiusABhoc ca;AC. (hgd fi ab æqualipus AC.Il. goll’as commune A]. rema-nebir CG reflangulum fuh me:CE. hoc en: BA 8: ahero regai-eorum GB. zqu de quad. arc GF.quad fit à reliqua parte 6:1.quun; demonflrandum. ’ r
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” ,13: 1:10». Euclidis d à
pRoposmo x11. ITÊJL A r ln amblygonia
-Tri4ngnlo AB C.B DE C quadrant»: [mais
LAC; "galant B. akafiamfibrendemir, quanta late-
d mm BA. BC. angnlum 01ml- ’[am comprehendentium,fipe-a: birfumpto "aux ulo par,latere BC. é’fid: ipfi BD. in
direfhnù ci addite reflue adoccurjùm perpendiculari: ab iA. alter.) angqu acare reden-31:.
0
remexA. être am CB. pro-duc quuc dam ci occurru in D.Qui; reâa CD. diuifa eü v;-eunque in B. , efi: quadratum
PRob. demîzre arpendieulav
ipfius CD. aequale quadraris A
’ I
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Liber famhdm. i’oâtcânrum DE. BC. cum duobusreâangulis fub DB. BC. addaturergo vrrimque quadratum reâz V ID A.erunt quadrata CD. DA, az- P" 47èqualia tribus quadratis on. BD. 1*DA. cum duobusillis teâaugu.lis. atquiquadratum même AC.cit æqùale quadratis ipfarumCD, DA. 8l quadrarum ipfius’AB. cil arquale-quadratis ipfaé-mm BD. DA. ergo quadra-tum rçâzAC. cit a uale duo-bus .quadraris CB. BA. cum duo;bus illis r’eâangulisôupratergdquadrata ina , duobus ipfilinetreâangulis. quod en: «mon:firaudum; ’ I ’
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rio mon». Èuclidis
PROPOSITIO XIII.A In Oxjgonr’o
Tir. n. A; triangule ARC.3 "r. quadrntmn late-
ri: AB. ungulum C: 4mm»:fibîendthtrsfilpemmi à qua-g
dratirlatemm ÇA. CB.eux- 7de»: eampnhrndentium, bi:fimpro nîhùgulo fiel! leur:. (J3. Üfib dflîtmpm interiùs
lima D Cqunmd occurfima .prrpendicularir ab A. alteroangqu azura «demis. d
r iRob. demittc perpendicula-rem AD. Reâa BC. diuifa en:
Vtcunque in D. ergo pet «7, 1,quadrata reâarum BC.DC. æ-Pualia fun: reâangulis duobusub BC. CD. 8L quadraro reliqui
fegmenti BD. Adde vtrifqu.commune quadratum na: DA..
l
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, ’ Libnftmndup a.fie tria quadrata BC. DC. DA.æ-qualia (un: quadràtis duobus
X. BD. DA. a reâhngulis duobu; ,I fub BC. DC. Nunc quadraris "’75t r duobusDC.DA.’æqualeefiqua.
dratum AC. Ergo duo quadra; ifi reâarum BC. CA. zqualia (un: l,1 reflangulo bis fumpro fub 3c,.’ DÇ. le quadruis BD. DA.
’ hoc cit quadrato A B. Ergouadxarnm refit: BA. minus efli A
L”; nadraris AC. CB. rcâangulo1 En fumpto fub re&rs ne. ne!
quodcratprobanduru. ’un
r a.
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in. I. Ëltm.EudiHis v.PROPOSITIO XlV.
E . Datawât’lmea"n83- LgS A. æqualeqim-
QBÛÊ. draium C H!c yl .q r p confirmera.
Plie, 4j. i. fiat reâangulum’ BD. arquait: reflilineo A. D.tcâanguli latera fin: aquaha;en: quadrarum quad Parmi. si.irræqualia,producasùnurrr , puezDG. in F. fit v: CF, aequalis fitipfi CB.feca bifanâm DE. in G.&c’eurro G. fpario D. duc circu-lum DHE. produc latus BC. inH quadratum quad fiat ex CH.cri: æquale reâangulo CE-
Prob. Rcâa DF.fe&a efl: ae-qualitcrifl G. a: non aequaliter .in C. ergo maangulum CE. fubinzqualrbus &gmentis DC CD,,
ils-z hot: eft CF. vna cum quadratome? l. (egmenti medii G C. ,aequalia.:47. , (un: quadrato reé’tæ CF. b hoc
en: CH; quadratum 6H, c aequa-le efi
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, r
Lit" far-mâta. h;le en: quadratis GC, CH. a con-fequenter quadrata GC, CH, ae-qualra fun: reâangulo C E. a:quadraroGC.Ergo fi touas com-mune quadratum CC, remanthâtradratum reâe CH. aequale re-
angulo CE, hoc dt rtâilineoA. quad erat faciendum.
MONITVM.I IN filperioribus,frequeriter 1d-
hrbur numerus. cum tamen indemonftrationibus geometricis[rpe vfui die non poflim; quiairrationales & incommeufura’bi-les quantitates non explicant,Sed nota 1 .Sëper in omnibus r92-poni geometricasdemonfl-ratio-mes 1.Non tecipi quidem deberenumeros in demonflztundisirra-rionalium aut incommrnfurabi-lium quantitatum habitudinibusse afFeâionibus que fol: qu mei-tate continua. cognofeuntur : "g
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Q
114. Item. Euçlirh’:mm nemo negarit in demonflraltionibus quantitatis continu]:maioris lueis gratia,& explican-dæ clarius propofitionis , nosgoal: vtr’ numeris , morio cos non
eceipiamus pro finndamento X3:fionis. Vnde robur (hum non ac-tipi: demonflrratio à momeris,fedlucem tantum.Et veto iis vqu efl:Archimedespropofitm de circu-lj dimcnfione a: poüeum 1.2anMfim groom:
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i Aisneæmæwsâï
.EVCL I DI SELBMENTVM HI.
PEFINIT’IONES. i
F G I. 145734;. le: circu-; ŒC 1; fin: ,” " 7mm1 diamerri
AB. BC. finir quels: : mlVacuum, gaz ex contrit D. 85 -Enta; lime DF. BG. fiant«agneler.
z. R554 circulant: . ranger: dièitur,l ’qlm mm cireu-Ï [nm tungar pute .
in B.jiprodummrin C. air:çulnmnmfimr.
’ K ij
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l1 5 ne"). Euclidi:3. Circulifê un:tua. ranger: d;-
D nanar qui fi fimuette tangenteset in A. 1213m:-
tu "enfin".A 4. In circula
491mm" di- r.Dr fine) centra
. l reflue dirutur,G H cr endi-K un» p p jcula": D E.
D F. Quatre D. adipfiu AB., iCK. duEZe egualerfimt; lan-
gins «tu? abefl? dicitur CH;en que»: trimarperpmdicula-
ri: D1. audit. -ç. Segment!!!»
c , . ,. El û crrmlt,e:-figy-vl .A J; m 7:44:15er- .-:-.--....«a.v
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. -.......- **v-
-.. --..--...-æ--’ *
Lihr tanins: en -[in AB. ce. circuliperiphcria
. ACE. comprehendr’mr.»
. a 6- Segmenti m-û rem engin: efi
A’ B CAB. qutfik"En: lima AB. éçirculi in,ripberid CA. compnbendi:
A un.
B 7. Infigmennautan 47.214114:efl para ABC.cumin egmwti
A C circumferentiafimptumfuerir pâma» quad-l. Pian) B, and ce in termina;rafle AC. figmemum termi-
nant: du" refit wfunin: duc’h.
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418 1km. Euclidi: V8. C1553 cucu
D comprebendmu:Ag’; tu angulum
D A B. rafleAD. AB. ali-
gnant (fumant paripheriamen BCD. iIh’ agui»: dr’cimr
infiflerç.
. ’9’. Seâorcirculi
efi , cumul: ipfimcirculi centrage
CBA C AngulmBAC. lfuerir conflim- i
au: comprehcnjà nimirum fi- Agram à à reflieJBJC 4n-gulum BAC. authentifias. ïÔ" à’peripbefia B C: 46:11;":
WMPM: I
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Liâerætiux. A ne
,. . D 1o. Similiacio:euh figurante
1 E finit J80 A, 5. CF DEquz an-. "gala: B A G., EUH capiuntequalu, autirr
- quibus anguli C B .1. PIED.inter e154»; agneler:
&w-«-J-
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P wm. * w:
. 3P? ,.. -.-.- .
Put!
«unla 11.1.
erra.r w.
d Exronfl.
unà.g Exsoufi.
n a Eh»). finaud sPROPOÇITIO I.
Dali circuli.( RE ) A B C. natrum
A c F. repaire. ’DRaxis duâar’n A C, a diuide ’
bifariam in F. ad punf’tumE. h erige perpendicularem at-tingentem ambitum in B. a. DEbanc BD. bifariam a(ce: in F,
uuâum F.erir centrum circuli.Prob. Non cit aliud puné’tum
in reâa BD.c cum centrum ibi fittamtam vbi linea feeatur billai.Ncque cri! extra reô’tam BD. Sit
l enim in G ducanturque GAGE.GC. in niangons GAE. GCE.Lama GA. Ai. funtd arqualiaipfis GC CE. St CE. commûne.Ergotota rriangulae flint arqua-lizr, sa anguli CEA.GEC. arqua-(cs.’ErgoanguiusGEA refilas:quod me non potefl cum crusPartiaiis 175.4. s fitrcâus.
PROPO.
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fiât? intima I dit
r PROPosrTro n.D Si in pm’pheria a; ï .
C tifcùli ABC. duofi E. 914.2121": parfin
A. à. C. accepta.
l fuerim, "(in AC;"’ âge ad ipfi purifia adzungie; "un, i’ntra Cifllllüm M Car-3
de).
., - Rob. sinon «daguai; caria?.. extra. fitquereaa ADC. Centro
B. la repexro.du’cantur teflæEAÆCz V i" BD. feee’rque en. peripheriarn in B. a Li,: quiaiautem niangon EADC. ( qui ’l teârlineus ad aduerfario ponitur)
ratera EA.E,C.funt b zquaha, c e- a .,runt anguliEADC;ECDA. zquales. 6! 5’ .lm auteur externus ADIE.d maie: m- Def’z
terne DCE. &yer cofequensquam M1.EAu,nrgo ne. au. b àqualrs F8. dia!g mater .erit quant BD. pars quina t 193.tourna. Non ergo me. ex A. ad C.
I fluas. extra circulant cadet z «59’
bitta, L ’
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3.2.
l 8.1a le.dz.
et:(wifi.
in 15km. Euclidix
PROPOSITIO HI.c Si in circula
CBDJefl’dqua-
3 13 dam C E. fer1.: centrum A. re-
fiang quandlm BD. non percentra»), bifdriàm in F. fè-en, à 4d ( angulos) refl’asun: jèmbit .- Et fi 4d "fia:eamfim, bifuriàm qnoquecgmfimbz’r. I
Rob. 11 pars. Duâis à centraI Afiæqualibus rrâis A8 AD.
triangulisABF,AFD,habcntom-Aaillant: æqualia fingula fingu- .11’s:b ergo anguli APR, AFD, (un: æqualcs, C ergo rcCti
Prob. 1.1 pars.Latera AB. AD. .flint zqualianngulus ABD. l a.
- qualis en: angulo ADB. 64 AFB.f 16" °iPfi AH1 E go lama. Bi. FD.
un: æqualia.
.. .-A.-4. .
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j 4 Liber tatin). n;r, PRQPOSITlO 1v..
un
g t Si in circularc ADB; du "il: un;AB.CD.fe [Ein-
, - aicemfcctmman .A, par natrum F .extcnfc , mais
fi fi bifærûmficam.
’ ’ Rob. Vis vt alun tamoul; I par centrum tranfcat 8L afin n: *crgo alter: altcram non us;Ï [acabit bifariam. Vis vt neutra du:Il traufcaLEx centra F. in punâum 05.
IL [cabrais E, duce reâam F3, 36Il ’fic dico. Vis rcâas EA. Elenazquales. b Ergo anguüFEA. EEB;» (un: rem. Similitérqnc vis maisl EC,ED,é(Tc zqualcs: * ergo and
gulus FEC, ’rcâus , quad repuegant, cum fi: Pars geai. FEB. -
’ o
U1
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:24 15km. Enduis
PROPOSITIO VaSi duo ciron”
DCB.ECB. je. f: imam fiant:15.4 , D 1113.86 C. mm:
tri: filtrant idem. natrum. 1A.
PRob. Duâis reâîs AB. AI); fV ha: :mntzqualcs , cêm fin: à .
«me ad circumfertntiam. ko- à: miam AB. AD. cmnt aqua-lcs,cnm ctiam ducantur à centre , ad circumferentiam : Pals coti-:4.
and repugnar.
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.---...«
n
- La" tanin. 13.5pR0posmo v1.
si du!) circuli T53”
) A B. C B. p f:c mame Maria:
. Magdnt in B. n,-.rum "on cri: idem centrant -1D.I. Rob. Duüis DE. DC. lins!’ D A. et! squats fine: DE.cûm fin: vinât: à centre ad cir-cumfcrcntiam. Line: DC. DE;
i, fun: æqualcs 0b eandcm au;,.fam. Ergo DA. DG. crunt æquo.31:5, Pars (on, quad repuguat,
n
L iîj
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13.6 En». Euclidit
paovosmo vu. PA. Si in circuli En»:
c diantre AB. ’iT45 D fitmatur aliquad
,E B N puffin» 6.71m!un fi: centra»: :a
cimdi: (à; panifia G. gal- Î;dam rafla G C. G D. G E. hGN’. in ci rada»; mahatma:- î
acinus guident erirGA. in quinatrum F. minima Vera reli-
. 91446841171770» vero,fim- ! .pendus 7m: par natrum du-citur,propiorGC. rmotiorl 1 gGD. migrainfilum numm’ ;du reflua GE. GN. 45 illq
l punch 6.47144!!! in circulumfl
tadunmdwraqu ( Pattes) nmimine. A n ’
x
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Liber unira. 11.7.l ’t’soinl plus Duâis mon FG.
EU. FEÆN. ex centro F. duo la-tera’CF. FG.trianguli CFG. n maïo-ra [une tertio CG. a: hæc fun: (ça-Ana-
; lia (on G A. ergo GA. cit malusquant CC.
Prob. 2.. Liner: BG. CF. triânguliICI. amnios: fun! tertio EF. ergo ou" -maiotafunt quàm fit linon F13. qu;
,- en: çqualix qui ÈE. ergo fi dematururique communis man (Æ. rema-
Î; nebu GE.maior quam GB. e iProb. 3.Triangula CFG.DFG. ha-
fi ben: latex-a F6. FD.zqualia à: latus- E6. commune , angulusvero CFG.
rosier cit angulo DPGJozum parte: Il 19 t.ergo Janus CG.b mains cri: quam ’ v .
DG. C 4"" »9 Prob.’4. une angulo GFN. 2-ï
e quali GFE.GN. GE.emntc æ uales.Nec à punâo G. aliç duci po unt z?
a. males ipfis GE, GN. cru-m enimv1.4 cm et to ioresei uæducmu et
P P** îcentrum vel remarions, ô: confe-quenxet nuions vel I minores , ouaman partent huias.
I. iiii
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i2 8 E km. Eadiù’:4
r morosmo vin. hin”; A Si extra cir-miam BEH. fig.
matin purifia";’quadpiam A. é
àjmn au admitt-la»: durant!" re-rfla qupdam AF.
lAG. AH. quorum maqua? A Ide,» per natrum L. reliqmq Qu’à w 116:1: In «un»: qui. î.
de»; peripheriam maman g"854mm maxima (cm) que , *par centrai.» L. (ducitut) 4- , r:liazmm vau fimpcr prapiar (ci) quæpcrccntmm L.7émo- e g
flore maior erit. In connotant ;une peyipberiam cadmium 1 Ïflâna»: aubain; guide)» ’ v
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Liber unirai 119 ni114 quai!!!" partita»: A. (à:
. diamnmm BH.» (ponirur) a-ligna» un a: quzpropior cf?minima AB.remntiarefimperminer (Il. D244 un»; Mn-ngm rafla ulules 4b tapin;-flic A. càdçmin circulant ad .
. «maque minima AB. lare-J r
I. 74. ïa Rob. n pars. Dudis mais r. L6. 1.P- duolatera AL. LG, "on
hoc eft LH,amaiora fun: tertioAG. ergo AH, main: en: gnan;
AG. AProb. animera AL, t6, trianiA ’ guli ALG,funt æqualialaterihus 524.:Ê LF, LA.rrianguli ALF; angulus
..autem ALG, major en anguloALE. b ergo laças 46, mains en:
lucre AF. .r° Prob. 3. Dufiis mais LC. Il);
duo latex-a AC, LC, triangwliACE * maint: fun: çertio Al,
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156 - 21mn. Eutlidi:demantur arqua":L B. L C. romanc-bit A C, maior
’ quàm BA. oProb. 4. mû:F l’un: triangnlum
à A L D.- duæ refit:J AC, CL, iunguu.
fi" tu: : c erunt lateribus triangulLminores; demptis igîmr quali-bus LC, LD, remanebitDA, ma- .i0: quam CA-
Prob. 5. Paâo angulo ALE.æqualî ML C. duo triangula in:actant æqualia : «gourera. Al,
. a 4, L AC, æqunlia-,neque ah: duc: po-tcü roda, hisæqualis: crirenim .(une: proflior minima AB. vol
’ tu remarier a: confeqmmcr ° ma.in: val minot.
1
--.---- ..-..-h’..-..- A . .
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k Liber unira. l 1;:PROPOSITIO 1X.n Si intracirm- 11,3;la»: BCD.]hm-ëËè : par»: fit alignai. punfihm ’A. à
punflo "vero ad circula»; c4-dant phare: quant due. refis4114418: A B. AC. A D. un.capta»: panifiant , contrit?» a]!
circuli.
diuififque bifariàm per re-fias AE, AF, triâgula ADF,ACF,.
æ 5 crû: æquaIia: ergo anguliDFA, "3.1AFC, æquales:b ergo real: ergo 4è?in lino: FA,eft circuli ceutmm. "Ï ,
; Rursûs cum idem fit de triangu- elis ACE, ARE, in méta A13, cri:
, circulicentrum. Cum verô non- fi: in duobus locis, dcbet elfe vbi
Êintçrfecant,
î
9
b
É .ï I Rob. Dam: mais BC, CD..
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ï
i
â
Ë
P
Ê.
F
i
l
R.
t
ne; mon. fada?PROPOSITIO x.
, . . Cire-«lmF D C. par plu-
F ra panifia par);
F ï .Rob. me: enim in tribu: fi
in e vis. Circuli BEC. centra G.frouenro , dùeanrur redît ÇA;GC, GF, qu: qui; (un: æqualcs,a: artingunt ambirum circonv-triufquc, punaum G,berit aimacenrrum circuli vtriufque quodgît abîmât!!!) Peu: 5. bains:
kir à
37h51 F B AEF. mu fi;An ont circula»:B c
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Lilmmtim-I - 1;;
PROPOSITI O XI.r A Si duo 5270415ABÇ. AED.a d arrangent jà fiinterim A. à. fimpmfnerim eorum centra
GF. ad eorum centra adian-f fla "En lima FA. (monde-
&4,in contaânm A . cadet cirg
cubain.
Tb. me
PRob. Duâa refit: DE. côiungeue.eorum centra, non inonda: in
contra&um , àrunâo F. centre cir-culi AIDE. dncnrur «eau. &Pun’.
r a0 G. centra circuli ABC. ducaru:t GA. duo lutera CF. GA. I maiora
’ funttcrtio FA. ergo union latere’u ID. cum FA. ID. ducanrurà centrek ad eircumferenriam , dempto ergo
communi F6,remanebir 6A. me;a ius latere CD. en nurem GA. æquo-
lis laren GB. ergo GB. manuscritquarn GD. gars toto.
110.!;
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flux
"110.!.
a; 4 21mm Zmlidi:
PROPOISITIO X Il.
A E Si duo tircnlin ABC.EBD, e5-
3" a tingmrt jà inui-
v
un: exterim B. eque adixngitur ad mm»: cen- -rra,pcr convertît"): trahetnr.
PRob. Si neges: fi: reâa F6.centra coniungens.Du&is F3.
I GBJatera BEBG. emaiora [une. tertio FG quod amen mains
probant ilüswam PC, F8, (un:æqualia, cum (in: àceurro ad pe-
J
i
«î
î
ripheriamzfimiliterque GD G3. .uergo fi illisaddas CD, maius erit5FG,quam FB.GB.ergo GF. non ’
1oit refit: iungcns centras.
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Lib» unira. 3;;É
C
PRO POSIT IO XIII.
Circulm cir- n m
B .miam mm mugitAgc in piranha: pun-
D En), 9mm «me,fine intox; five
AÆÆËÂÈD extra rang".
cÏ Rob. Tan gal enîm in duobus;
.- --- rn-w-vQMML. .4... . I.
Put: A, 8e C, cenrrum*debe- - ,bit erre inlinea, quziunget con- e "4’taè’tnm cireulorum : vtriufque Ïauteur non bpotefi elfe idem cen- .,
"trum. Ergo in il]: refile eruneu duo centra, puraG, set-I, quod
fieri non potefi , cum limez invnieo punâoœoflîr «arum fica-ri bifar’làrn.
14.0," Ve.
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hm;
ùr1.r.bast47.l.
49:5,-
D 7.V43. l,-
igà Fin». Euclidü vPROPOSI’HO XIV.
A In circula C.Al) équin rafle A
(A: - BaD C. æqualxtefB c dxjfan: à centra
E. de toutim dilhintc: àcentrofimfilzi immun aqua-lei.
R65. A;c’entro E; in "au AB.CD. a duc perpendicular’es .EF.
BG. refît: AB.CD. feâzb errant bi;fariàm. muais EA. En. quadratumrefis: BD. c dt crquale quadratis re-âa rurn D G.Gri. Demprrs ergo zquà-filins EA. ED.AF; GD. remoucherefit: Fi. çq’ualis rcâz EG. a; confe-
uenrer reCtz AB. CD. a zqualirer
la": à cenero. r
4.
2
E
y
i
I
r
t
Prolb. z. pars. Ex probatrshquadn- a: 4ta EG.GD. flint zqualia quadraris .E F. FA. 8c quadrant!!! EG.zqualequadraro EF. ergo quadrnrum FA.zqualeeflquadraro 60.: ergo reëa! 3A. squame eft refis BC. Ç
ne:
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d)
.-. .fl...-.vn..........h
Liber imbu. :37 .PRôposmo xvg
In circula ABTIm’ç,
c Dà; 1; C D. maxima
H n .A b r guident efi dm-meter AF. 411mm» ver?) jèm-
perprapiorBE. centra G. en";main remariait CD.
PRob. la pars. Duâis GB. CE,duolatera GB, GE, trianguli
GBE, a maiora [un tertio BE, a: * Nihæc fun: squalia- diametro AF.ergo AB. maior eft quam BE.
Prob. z. Dufiis reâis GC,GD,duolarera GC, GD; (un: æquo-lia lateribus GB,GE, angulus ve-to BGE, maior cil angulo CGD.
’ b. ergo leurs RE, mains laterebzm.CD.
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-- . 64:44;; 14.1.; w. ’
Il). 1;.
US Élu». Euclidi: lPROPOSITIO XVÏ.
il? AAÉ Æ mante dinmetriD .3 AC. 4d reflux
I’ angulas liant,c EF. dgcitur ,54-
de! extra cinglant ABC. à;* in [0mm inter ipfizm E5. àçiTa’M’flfCÏCfltiflm,AHB. alta-
m refit: GA. non cadet: àfimicirculi augite: D A B.
Quark extra? n
muiez erit nenni «ne» angqu -reüilinea : "liguai amen,.EAH. minot.
Rob. x. pu5.5i non cadet extra,cadat intra,vt refit; B A. Tune-
- frianguli ADB.’duolareràDA. D3.on.(a.çg.r
a fun: æqualia; ergo anguli DAË.DE A. b funrzquales . quad effe nonforer! per 17.1 . ponitur enim exigu:ne QABrreausiergo, &ç.
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Liber embu. r35Prob. 2.. Vis poire duci GA. duca-
tu: c in camex’cenrro D. poterieducere perpendicularem DG. duca-tur: tune cum lngulus DGA. fit te-&us,rninor re&o d eritDAG. ac gro-inde larus DG. minus latere DA. et19.!. torum videlxcetparre, quo citabfurdum. A
Prob. a. Vt 6ere; en in: main:angulo DAB. deberet uci reéh inrer mais!) EA. de peripheriam AB.quad hm prohaui fieu non poire.
Prob. 4. si en’un aliquis angululreâilineus candirai pofet mina:3:1;qu EAB. duceretur refis interAi. 8: peripheriam AB. quad vein-dixi fieri non pardi.
Corollarinm.
c "un".
1:75.
Bine eommuniter clicitur reflua rodextremum diamerri neryendicu-larem,tangere cïrculum, ê: in miropunâo geometrice longera: mm fiplate tangue; . adorer: mua oie-calma.
e à!
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à
n
w
i i mai
’14," 313m. Enduit
, PROPOSITIO X VI I:W510 x x 2* J data pygâ.
g J. refila» h-un»: «la jace-
’ n, qua datant hangar cirai-Ium BCD.
-PRaxis. Centro D. fpuio A;. fiat pars circuli AB. ducamr
nô: DA, a ad punâum B. exci-tctur perpendicularis 8E, iunga-turque tafia DE,à panée A,du-(mur méta AC, banc dico un g:-
te circulum BCD. Prob. Triangula ADC, BED,fchabcnt iuxta 4. x. cumlatcraDA,DE. DE, DC, (in: 3 xqualia
i 1M 8c angulus D. communis. Ergol’ef- cum angulns EBD. fit nanan:
fins ctiam cric DCA. ergo 3&3AC. b ange: cixcnmm.
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.Liôer unira. un
-PROPOSITIO XVHI.
A c .8 Sialiqmrefla Un!48. 14!)th cir-
.çulum D C E. à
castra une D44«mouflant C.-
que du»: "tu DC. adjug-à, un: que ddiungitur, DG. ;’ pcrpendiculari: cri: 4d un;
que Gonflage! AB.
"I P1105. Si negac: fi! alia , par:” DE. ergo cum angulus B, po- t 17m
mm": rcâus , minot [caca cri: b m 1* ; angulus C. ergolztus DG. b m:-Iî ius cri: latere DE, par: toto quoi
- cit abfurdum. .î
M îij
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(45 Eh»); 3114513:
mon: 0511-10 xxx; ’
33.172 C j; si circulantE5 C. confit: a:
F «tiqua ramés.» à contât-fa VeraLC. tangenti AB. 4d rafla: hm-gulos raft; lima E C. dut-1Mfit, induêh BC. cri: 00112vabirculi D.
Rob. si negac , fitvbi et! F;1.3., - dnëtaFG. lpfi AB,aeritpu-.-. pendicularis :crgo angulus re-
lu.» nMfl
au: FCB, re&o DCB, cric: na. lis, pars mi quogl si]; dag;:dumî
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F Liber merlus: i4;PR gros [T10 xx.
’ tu circula DFGA.A and» BEC. ad ce»
man E. düpkxefi’ a-guli BAC. ad y21171110-
G riant, «Infini: «de»;t BF c gambada BC. fifi: u-
alarma." Rob. Id aigus peut! modis cô-
’ zingue. Includant r. max AB.4c. métas 33.26. duâaque Afin;cenuum E. duo latex: 15A. E3. «un:
un;
zqualiaaergo angnli EBAÆAB. z. a S. iqualcs: angulus autem BEF. duobué12.413. 281m. en çquahs, ergo duplus 5 51- H"
.anFuIi BAË. Idê duc de angulo FEC.le peau anguli EAC. ergo tous:BEC. tarins BAC. cm daylus.
2.. un; DG. DE. non incluantmais EG.EB. hum lacera BD. En,fintzqualiafanguli EDB. EBD. c :-xunt æquales. His autem duobus,angulus vGE B. efl a zqualis. Exgoidem exit du lus anguli GDB.
3. Triangufa BEC.BDC.fcfc inter-fcccnt,ducamrque reâaDG,Per cen-trun) E. totus angulus GEC. exit du-îlus rotins GDC.angulus veto 6153,uplus cit angon GDB. e159 Id?
quum BEC.duplum en: "1in 15.qu’ guet! en: probation,
3.1.!452...
n......... A ,
hum:
1.-t a 334;.-. r
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144. En). Enduis
PROPOSITIO XXI. -
174.19. A In virgule . AD. CB. qui
in (miam. a. un. merÊMBCfimt
h " ongulé BAC.B D’ C. fin: inter f: 471441
la.Rob. Augulus BEC, a en;duplus anguli BA C. a: du-
*L BhC.BDC.ümimuû
gualcs. .
PRO..-
’ "W plus anguli BDC. b ergo anguli j
a.
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v
l
iàeflwiiul inPaovosmo mm. ’
. y Qadrilzmhk ù üforum in air-3
x A cilla A B C D.h (Î defiriptrm’)
uppofit: 4:3!in DCB. DAB:datcha "flafla: æqkdln.
qub. Diamctris AC, on, du:(in, anguli 3013, ACB, in
:3de ponton: a (un: æqnales,fimilitérqu: anguîi BAC, BDC:ergo totusangulus ADC, cit æ-qualis angons B CA,BAC; fez!anguli BCA, BAC, cum tertio b .4ABC, b valent duos rcâocïergo 3."
l .
Un!)
angulus ADOsa-qualisipfis. BCA.BAC, cum angulo ARC, valcbii
. duos naos. Idem de alüs 093.0...l
,
a n.1
fig; diçgc-onErgoÆo
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14 6 filmai mliû:
, PROPOSITIG XXIILTl. 1°
Sapa adentfi rcfidDF. duo
Î ï figmenm circu-
’ [0mm fimiliaD DlF. DEF. à
inzqnalia mm «rythmant4d eafdem partes.
PRO!» sin: enim fificri porc":DIF. DEF, fimilia fagmcnta,
duâis tcftis ED;EF,ID, angon; 4n°- DIF, D EF,acrunt æqualcs,quodD44 en: abfurdum Fer 16. x.
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al È
7.2,;Lib" radium 147
PROPOSI’ÎIÇ) xxxv.
Super un.
1 n51?A B.
DF. fimilinfi’gmcnta circulo-
ram fine: interfi aquilin. ’
R01). Collocctut AB. firpe:DF. 1 congruent ergo fi non .
congruant fegmenta vcl .vnum 1’ à;
totum extra aliud cadet. quod fificft abfurdum oc: 1.; , vcl cade:panim intra,parrim extras a: fic.circulus circulum (cubain ploctibus [mais quam duobuS, qnodtePngnaIPu Io. 3.
Ni)
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Nu
L ".1
f
"en.
a mè-
14.8 Elcmfudiiü gPROPOSITIO xxvË
, Circuli, A BB D. [agrume
. D data A B D.A defi’ribere cir- î
adam, mine 9j? figmenmm.
PRax. Accipiantur in data. fegmcnto tria puné’ta un. îduflifque redis AB, 8D,: diui-fifque bifariàm a: ad angulos re-âos pcrxeâas CE, CF, panamaG, in que interlccant cric cen-
tmm. eProb. Fer x. g. centmm en: in vtmquc CE,CF. ergo vbi Ein- texfecanr. circuli cnim vains,voicum tamtam porcfi elfe ccn-Hum.
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à Liber n 191’111. , I49A PROPOSITIO X XV l.
In tqualibus, jà à circuli: A B C. un. 1;.
. A, D E F. «gaule: ’ 5il A en ’ 41131411 6.57 H. J.B. a" E. aquahbz’n periphe- Ïria? A C. DF. infiflunr,fiue 4dCentra G. éHfiue ad pari- 2’Phpfidd 13.0" E. comflimti fini.
Rima pars. I’rob. Trianguli. HAGC, larcin GA,GC-, a: an- .
’ gains G, ponuntgrlæqualialate- lagibus H0, HF, 8l angulo H. .cr- 14.! :
e go haras Ac,DF, fun: zonales. la au: ol LIE ’rgo pcriphetiz AC. DF,cmnt I î
ttiam æquales.Prob- a! Angulî ABC. DEFL
ponunrur squales: ,. cr o [e - ,menu ARC, pas, fun: mina: GM-
ï’ a ergo Æqualia a cum redue ACDE, (in: acquales. Ergo cûm cir- 4 .culi ponantu: squales, romane. 0 3-bunt fegmcnta AC,DF,5 çqualia. "4*
. N niU
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T5. :4.
I tu.fi 13.;
c 7.Jar,d le.)
:50 Elemaruclidi:PROPOSITIO xvaI. Ï
In aqualihu: zir-ëæ euh: ABC.DEF. .A Tir-5x , .gangult qua m a;
qualifia; periphe-rii: AC. DF. infifl’tmt fientinter]? æqu4le:,fi31e ad centraG. (9* H. fine ad perlpberiasB. Ü conflimti, mfijiant. ’
PRob. fi non fint aequales , fi: ,alter mmor, puta AGC, afiat:-
que AG(,ipfiDHF, æqualis, pe-nphcria Al. eriruacqnnlis peti-pheriæ DF,fed perlpheria DE
l
i
f
ponimr æqualis ipfi AC. ergo. .AC,& AI, crunl: aequalcsypalstoti z Idem: duc de angulis 3,5: V
1
Eïçum G. a: a, d fin: coma; du.-P Io
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Liber terrira. 151
PROPOSITIO XXVIILIn aqualièn: un;
à) È circuli: A3 C.. - DEF. annale:
A LE F reëÎæAC.DF.aqualeiperipheria A C. DE.ABC,DEF. auferunt, m4-iorem quidam maieri , mina:rem amen: minari. .
Rob. Duâisreâzis GA,GC,H D. H F, triangula A G C, ’
DHF, a flint zqualiaÆrgo angu-lusG,an 1110H, cfiæqualisœr- c i’ r ’f0 yeti? cri: AC, D535 acqui- «a.en ergo reliquat ARC, DEF,
fiant aequalcs. ’ ’
N4iüj
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m; Elpmjytlidi:
PROPOSITIO X X155.
fifi In fluidifia:à à circulis A B C.W- . Ï DE F. «squales
’ A C0 paripheridr A B.C. DER AUBE. quater"(Le AC. DRfizbrendunr.
Px... mais mais en. cc, .037.3! HD,HF, anguli 6,8: H, 1 crût
1 aequaleszlarera etiam GA,GC,., un, Hï, (un: aequalia ex (bo-t tu gomme; ergo haïes AC. DE,
.. exantzqulleq.
tl
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liber tartina. 1533
Romano Cxxx.Datant par... MM»
pheriam A B C.A D c [254" -lzifarlàm
- putain B. I I. PszisJDucatur r43; AC, eam a ma
druide . bifariâm in D. pet’ :pcrpendicularem D B. eritperi.r phcria Rita bifariàm in B. n
Prob. Duftis mais 11:8. C B.4 triangula ABD, DBCIl fe habent 5 13.1.V iuxta 4. I. ergo lattera A B, C B,
(un: æ ualia. la Ergo pcriphcriæï’C au: fuîtendunt (untaequaleg.
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17m7
un
154. Bien». Euclz’dù
PROPOSITIO XX X I.
r 1 In circula AB F 3E C. dugtdfl:f S533 Z ABC.quiinfê-A. D C micircnlo reflux
efl: ’- qm’ lutent in maiorefig-
mento B C A. minorÊreFfo:3 qui une in minore figmenroBEC. maiarreêîo : 4 (je infle-
per angælu: CBA. ex refit:CB. &pcriphcria BA. m4-iarù fignenfi, rat-b guider»mainrefli; minari: durent-[Eg-menriangnlm EBC. qüi exPeriphcria 153.6: reâaBC.minar cf]- rafla.
PRob. r.pars. Centro D, du;&is mais DA, DE, DG, an-
guli D AB. DE A, a cran! æquales: ïitemque angon DÇBDBC. ergo ;
l
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Lihr terrira. mtordis angulus A86, cf! çqualisangulis A, 8c DCB, [cd hisb cit b 3, I.aequalis F3 C. ergo angulus au; ’ARC, e cf]: refit". l
Prob. 2.. Angulus ABG, en re-&us:ergoangulus ACE, in ma- .iore lègmentod en: m’morrcéto. un
Prob. ;. Fiat quadrilaterû BA. ,angnlus A; minot efl: rafla, et-go angulus BEC, in minori reg- Mu,mente ton: maint relia. f. 21.1;
Prob. 4. Angulus ex peripheriaAB, a: mâta C8, eft maior angu-
ilo compofitoex mais A B. BC.tptum videlicet parte.
Prob. 5. Augulus compofituset peripheri: E8, a: rcâa CB,miner si! angulo comoofito et.refila 173, BC, pars toto. HuiusPropofirionis autor futur ThalecMilcfigs annis ante Chriflmm,659-
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Th.:7
154 211m. Euclidù
PROPOSITIO X X I.h 1 In circula A
B F . BEC. angulu:Ë ABC. quiinfe-’*« D C micircnlo reflux
efl: 1 quinine») in union]? -manta B C A. minarËrefl’o:
3 qui ocra in minore figmentoBEC. maior "510:4 é infil-per angtdus CBA. ex toit:CB. &pcriphcria BA. mm»iarù egmmti, refit; quidamrmriarefl;ç minori: autant-[Eg-
memiangxlur EBC. qui exPerripheria EB.& refis BC. .minar- cf! rafla.
PRob. r. pars. Centra D, du.".flis re&is DA, DB, DC, an-
guh DAB, DE A, a erunt zquales:marque anguli DÇB.DBC. ergo
î
Î
î
!
î
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L56" renia. lnroulis angulus ARC, efl: çqualisangulis A, 8c DCB, fed hisb en: b s, I.acqualis F8 C. ergo angulus tu; ’ARC, . CR: reflus.r Prob. 1.. Angulus ABG, eft re-âuszcrgo angulus ACE, in ma- I
- iore fegmentodeft mînorrcâo. WhProb. ;. Fiat quadrilaterü BA.
angnlus A, e minot en: «au, cr- L’un.go angulus BEC, in minori feg- un,mento refl: maior reCto. f. 2.1. .1;
Prob. 4,. Angulus ex pcripheriaAB, a: refira C8, e11 maior angu.Io compofito ex mais AB. BC.eorum vidclicer parte.
Prob. 5 Angulus compoficusex pcripheri: E3, a: retira CE.miner cil angulo sompofito ex.real 1713, BC, pars toto. Huiuspropofirionis autor ferturThaIccMilcfins annis ante Chtiflium.659.
par r.
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156 A En... Enduis
PROPOSITIO XXXIL ï
Sicirculü CEP. h
a . Nager" niqua. a. » D traita AB. à rafla àl E «me»: C.duc4tur’ Aguædam rafla, flan: cirât:-lum DE vel E C. Angnligym ad tangenter» AB. fa- ah:-ciet, mon 49min dnguli: ;
qui fun: in aluni: circuli v. ;Jpartioniènr, id dt angulus CACE. æqualis cftangulo F.8: angulus BCE. angulo G.
, PRob. Duâta perpendiculariDO. cum angulus ACD. fit ,
, reâus . angulus quifieret in (e-. im- micireulo. iHi z effet æqnalis : fi
w veto non fit realia vt ACB. pri-mo duc regain DC, pet cëtrum.derme acçiPe in periphcxia au. v
751-!
i
Ï
o
P
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En" terrira. 157quad punétum pute G,l ducau-
, turque reâæ DE. EG,GC,tumargons DEC.in femicirculobfitv, te us . rehqui duo pur: ECD, 53h!"-A 30C, cvalennmum teflum : fed c 3’" r- anguli ACE, a; ECD, valent etiâ’vnum reÈtum. cum na: DC, fitiperpendicularis : chmpto igitutcommuni ECD,re anebit ACE, 27 .æqualis angulo E , quidl se»
kqnàli; cit angulo’ CFE, ergo 6c.angulus ACE. angulo CFE. a?-qualis. Rurfus, cum quadrilateriDG, anguli in circula oppofiti "2.34.EDC, EGC,e valant duos re-&os, ficut8c anguli ACE. ECB, hm
flçquifvalent etiam duos rectos 8c’ P" î,
flangulus CDE, fit g maudis angu. "un;’lo ACE. remanebit angulus G. 1mm.-dngulo ECB, æqualis.
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US 21m. Élu-litât
mobosmo xxxm.C ÎProf-s. rafla AB.]:ar-
A"D .tionem circnli97:5 defiribere, que -rapiat angulnm353:4GC data Mygale re-
F &ilinco 49m:-
lem. t LI dams angulus fit trans,
A bifariàm in D, centre D, fpatio;DA , fi fiat ûmicirculus AFCB..chiais teâis AC. CE, angulus C,
cr. a. a en: æqualiidato angulo Ë,quia’erit in femicirculo. Siangulus fitacarus v: C,fitquc data reé’ta En;
ad punâum A, fiat angulus D52 . .3.x A332 ualcanguîo C,du&aque
l
Super dan .2
.qualis a! E, na: AB. diuifazl J
and pur: üA. perpendiculari FA,fiat angulus EBA. æqnalis angu-
r r. Io 5A3, lacera EH, BA., c mm:4
l
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Libamm’m.’ 1:9:quaiia: quarre fipunâo E, rpatioEA,fiat circulus, trâfibit pet pun-C’tum B. quo pofiro fic probatur.Cam refila FA,fit diameter.& re- tirer(la DA , ad eius extremum fit ci. W",-
. . . rag.Perpêdlculans, d muge: cuculü: e il. ,’ ergo angulus DA B. e cri: angulocuieunque, qui fierin alterna cit-culi portione, puxaanguloAGB,æqualiszergo portio AHGB.con-
"flirter angulum æqnalem aînguloHaro C. Si ver, angulus fit obtu-Ifus put: H, eadem erit demon-fi’tatio: anËulus enim AIE iPfi H,
«l ,’etit arqua is.
’ PROPOS?" o xxxxv.A du» timide A35, Pub; 6
bi - Il figmnmm (B 4, .5-1: G [italien enpiemangu-
[un B. æqualrm data.
. , argol. nathana Vcarur tangens EF.ad pü- a .73&um A. b fiatangulus CAB, 513-1
:14 A arquons date D.portio ARC,c ca- t ’*’
,yietangulum B. zqualem dam.
l
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0 x,Mo HemÆmliÀü
PROPOSlT-lQ xxxv:, A? in CÏftulb AD
flua.” BÇ. dut n62; AnD CD. fi marna inE.fecuërint,n&ah- v
E galant comprehenh IA [un fut: fipmmi:c bruns AE, E8, 4-A p [egmmtù divin:B CE ,JED , «Mn...
LenÀitur "fiançait;
v Rob. 1. un; AËCD. fixent f:in centre E. rcêang’nlum vnumr
(hui cri: æquales: cum omnes "a:fin: aquales.
1.. 50h C D. iranfcat pet centrantl F. diuidatque.’ radian) AB. bifariâm
t ï. 3 . in 8,3 ac pxoinde id angulos naos.ducatu’rqüe rafla PH;ËJuo faflp, humméta CD. (buta: in squaliâ m F, a;mon zqualia in E. cri: reflangulum vfubmæqualibus fegmentis CE. En:
v cum quadrato (e menti intermediip il! FE.bçquale qui nm dimïdwç ED.
V vel FB.A fed quadratum F8. cf! cz-: "m 1311416 quadxa’ris BE.EF.ldémqae F8,
en
Il qualeefleiquodficb
h
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’ fub CE. BD. ê: AB. EB.
Liâtr tanins. 161cf! çquale rcâangulo CE. En. cumdrue FI. :Dcmpto igmu commuaiHi. remanebit reâangulum CE, BD.çqu a]: quadrato BF.hoc cit xeââgu- .la fub BE. BA. cü porfifixtur squales.
3. luth CD. tranficm je: cenmîF. :câam AB. non diuidathiflriâ in1-2, duâaque méta F8. 8c perpendicu-lari FGJeâangulum fub CE, ED,cumv
. quadrato FE, d exit æqualc quadratoFD. val FB. reaangulnm ctiam fubAE. EB, cum quadrato CE. defi z-quakquadutb GB. adde nadratû.FG. cum quadratum F3. x: çqnale
«plairais FG.fiB. en: tcéhngulumAE. EB.cum quadratis EG. CF. z-quale quadrette FB.hoc cf! rcâangü-le CE.ED.&quadmzo FIE. ergo cumquadratum FILM azqualc uadratis ,FG.GF.1i ab vno demas FE. ab alio AEG.GF. remanebunt æqualic «fian-gula CE. BD. 8: AB. E8.
4. Si neutre: tranfcat En centruma: fi: feccnt vtcunque,ducamr ad in- -terfcâionem E. rcâa GH. nanfienspet centrum z cum refîtangulum fub "m’yCE. ED. e fit æquale ci quod fub HE. Nm”EG. ldcmque Ali. Enfin squale api hm"6E. EH. cran! æquaha reâangula
0a:
A .
à
44;; M;ÀA;-k
e M ALLA.
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.t a: 2km. inti à? PROPOSITIO XXXVT,’
1 l si un! rirm- I* fla? . lumFBE, fur».-xur Punâum al’-
guai A. ab tu,il." thulium auditdu; refit- à b2:
- guida» AB. [un circulum in C.* "la aman ALMMM in rafla"!p.5 totafemme A B. à murin: J
. lqfl’umym AC. intlr Punaum A. à annexant pariplnrùm Guy;-pnhenditur reânngulum. 141ml;prit ai , quodà tungar": 4F.def-çribimrquadruo.
B É’
Rob. Tranfeat 1°. «a: A B parcentrum D. duâa ne «a: Dg,
cum ne. CR.bifariim ca: fit in D.. ô: ci rafla AC. ad’pciatqmcfiangmau, . fub AB.& AC. cohtcntum. vna cumi;- g quadrrnto DC. val DE. a arqua]: dt ci fi.
’ qundà BC. cum AC.nuquam vna "1,5 47.!. une: fit quadras) Scnj quadrntüD A. qÉë’vi- b en squille quadratîs DE FA. «sa
(impro «muni FDJcmanebit au;
3
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v vmnu. .
. 1.15" unira. u;datura FA. zquale raflangulo fubAB. &CA.
z. si reâa AB.. non tranfeat peutçentrurn, centre D. duc Perpendicu-
Jarem DG c hac (acabit rcâam E1.bifariàm, cum igitur "a: El. fit Ce.-âa bifariàm in 6.8: ci 1A.adiiciamrsexit reâangulum (ab AB. a: fub Al.cum quadrato IGI. arquai: quadratoGA. addito ergo quadrarè DG. cri:reâangulum fub AB. a: fub 1A. cumquadratis lG. CD. hoc eh quadraroDl. zquale quadrato DA. fed DA.eû çquale quadraris FA. En. dem-yris ergo çquqlibus DE Dl. rema-neb’xe quadramm PA.çquale même;
. gulo filb A! 6: A]., Corail. r. Hinc fequirur,fià punao’quouis extra circulum fumpto y plu-res refit: circulum fecanres (lucan-11H, reflangula compxehenfa fub ro-tis lincis 8: pambus extenoribusfinà1er fe cm: çqualia.
CnroIl.z. Du: reâzhb eodem pun-âo duit: , qu: circulum tangunt.fun: inter (e æquales.
Cornu. a. Ab eodem [mufle extr:circulum (lampa), duel rancum pof-
c;.g’
fun: du: refit: qu: circulum tan-I .sas"-
OÙ
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:164 film, radiai:Pl OPOSITIO xxxvvÎ’.
I A Si extra circulumËHIFJumamrfii-IL)! âgé au»: aligner! A. :5
’Ü’ coquepunc’io incin-
Œ "du"; radant du"au A17. A B. vcl.AÉ. à: ha quidam AB. [un cir-eulum: i114 au!!!» Aï. intidnrzfit41mm quadfub un fêtant: AB..é. murin: 4jumpt» CA. inter"un": à connexe»: periphc-in» . quai: ci quad du incident: ïAï. dafcribilur: imide»: in; cir-
culum ranger. .. Roba Duc rangentem AH. 8: ad"ï 3? P H.re&am DH.cum ergo quadræ-bit 5 mm AH.b fitçquale reâangulo full
AB. CA. a; idem reâangulum fubAB.CA. ponatur zqnale quadratoFAJinezFA. HA. erunt :quales,la- ’retaiicem PD. HD. fiant æqualia 85bafis AD. communisærga tors .triâ-Pula c l’un: æqualia. largo cum angu-
F 3-! Il? AH D. fit J refius, retins enam118.5. en: AFD.ergo A17. çirculum range:
,20! coron. :6. a. 3.
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èswâac-ææmzèï
EVCL I DI sELEMENTVM 1v. e
DÉFINITIONESJ
f E I. figura mail I lima, in figura
A B refl’ilinm in-* jèribi dicitnr;
D C F cumfinguli,eiu:figura , gaz in-
: firibx’mr , anguh, fingula lau-3
1 U
t
r4 du: que injcribimr Mm;
gum. lV: rriangulum JABC. infini:prum eû triangulo DER qui:an uli A. B. C. tangua: latex!)
D .22. DE. ’9 ü)
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466 un». EnduisË 2.. Simili!" à
- figura circumfi«A B garum drfiribi ,
dicimr,cu,mfm- .
D. c F gala du: quecircumfirilrimr,
Iqtemzfingulo: eimfigunp 4n-guln: tetigerint, circum qui!!!i114 defiri bitur.
V: triangulum DER dicitur Ipropriè defcribi cires triangu-vhlm A BC. qui: fingula latere rmaioris rtianguli,fingulos angu-Çles minons targum. Dixi pro-knpriè , nia vtimpropriè dicarurfigura a iquh infcribi vel defcri-bi,fuflicit , v: bene aduerrir illu-flrifiimus Priaceps FluiTates C5-
.dalla v: nuHus fic angulus inte-rioris figura. qui non tangara: an- .gulum :li ucm,vel lattas vel pla-nü figura: exrcrioris;& eo fenfuintelligendæ fun: propofitiones1479155413, gîta. :5. elemcntorqm.
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Iihrquamuï :673. figura dustu» affiliant,in circula in-
fèrièi dicïmr,
5 cumfinguli, eimfigum, queinfiribimr, unguli , tetigerin:circuhprripheriam.
4. figuramm rafli-linen cime
fi tirculnme defiribi duà çitnr. mmfingula latent du;. que circumfirribimr, circzfi
peripheriam t4ngunr.ç. Similiter à circula: i»
figura infiribi dicitur e un)circuli peripkerin finguld 14-.un: rugit du; figura; in am!infiribimr. I
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les Bien). Euclidi
6. Circulmaux!» cirant:azurant defiriln’
tatar, cum m-arli peripheria,
lingule: mugi: et": figure,quarra circumfcribi: dngulas.
7. ma. in air-.4 Vcula accommoda. lri,fèu coaptnridi-e
mur , cum :quexhuma in circulz’ I
pariphcriafzçerim.
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r Èiber pilum! r- n, . .PROPOSITICIJ 1..
, ’35. . In data circula Ml à
i AB C. accum-r t "radar: "HemBA. requiem date réé-ha. D.» que cirouli diaprer" B C. and.
firgnaior..
V Ali cirçüli ducaà Jiamc;Ë. (rem 86.11 dàta rcüa D. z- qualis fit diamerro BC. fafiot-n
(&quod pairur. Si D.minorfir 3j i.. diametro: habfcr’ndarlurêBE. a. . .
qualisipfi Dl. de centra B. fpan’o.1 E.fia: circulas 5A. iunâaenin à];’VIcâta BA. agent: en":c in circule f) f.
BAC. &daquahs critiPfiBfi. a: du:. gonfchençê’rigfipg . - v fief-fié
au .3.
Î fichez;-
l
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x70 mon. Euclidîo
PROPOSITÏIÛ H.
MM a H. In data circula. AIBJriangulum
n a defi-ribe-ra, data triangule DEF. cfà guinguhnn.
nô.) F, a: rangers! GH. adChu-n A. fiat angulus HAC. .
r, æqualîs angulo E. 8c GKS. au.5 13m 9,10 1:, duéta rafla BC. flâna .
en: quoâ petirur.Prob, Ahgulus HAÇ. tq’lfflîl
un en t angulo B. a: Emilireraagu.lus GAI-languie C ergo a: un.guhfs É. augure la; angu’lus F.angulo C. sa canfequcmer angu-lus D. nnguloA. d zqualâlErgo-
431- t uiangulum trianguîe «primage-lum dcfcripfiin date circula. (
v- *-----v---.---.o.----:-..
1
. f
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b
55:14:44"er H; lPROPOSITIO HI.
D a a Circ4 damnacirculur» A N3. "5-;defirièm m’ait-
L En galant L M O;cguiangulum data "in; Je
. D. F. A.la trianguli huis Aï, pro.
Dduc in (La: [languira DEH a "Jzqualjs fia: ad centraux argalis *C18. a angulo DAG. angulus A f a?13.8; Id pâtît: ABC 5 duces per- m 5.pêdicularesquæ C rageurs «unerame: M0. ML 1.0.8; coëun-ces [mini uiigulnrn confinent.Q1341 cairn commuât parer; unflaque angulorum ad A48: ner-
ue eorum qui (un: ad C eFtre-as: ergo fi imelligarur duci li-
sez AC. cran: duo anguli verrue0. minores duobus redis-:1 ergo a 3..in illàm parrêprotraaz rigenres At. Jconcurrent. fimiliterque du: inalias partes Panna: : ergo fie:
P li
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va. .-r.i
.« «, spufltfite hg. ç
"8.3.
’ quales. hm angulus cm. arqua.- A
un.
1 7. 2. h mammaires. D
dam triangule :-ïlr ,JM I qurangulum , fieprobe. ln quadrilatero CIBM.angûli ad B [&ICJ (un; reflux:-gordrqu! C111. C M B duobusnais fun: agneler: probarur,concipc duci- «612m 1M. duo Il.mangula IMB. IMC. ! h..bent D
" angulos :quales quatuor mais:ergo cum duo ad C, a B, (in: re-fit, reliqui (un! duobus real: æ.
Î
’ H rriangulum du...I dama) circulum. ’Ï cr Œgd aurem fi: 4 *
lis ponitnripfi DE. ngu angu-lus CMB’. æqualis e11: anguloDFA. E cum anguli circa laïusDE. valeant duos fracs: codem-Ëne modoofl’endi porcflin qua-
rilarcris’AIBL. AICO. angulos à tL. a; O. æquales angulls A. a; D. - aErgo cite: darum, au.
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ç Liber quartai, 1.71.Q. PROPOSITIO IV.
1. a I» planning]. "al-4- t AIR C. ramdam. F c alangui»...
I’. Iuide duos eiusIangulo’s B.
a C. bifariâ per reflas CD. "° L’ vBD. a ex patito in quo concur-
rent par: l) p. ducaspcrpendicu-Ilares DE DG DF. ad tria huera 5 ne 12K .dari trianguli, St quiatriaagulo-- rü FCD. Gai D. angulus C. Vnius.
ponitur çqualr’s àngulp C. alte-j. rins,& nuque angulorum G. 8:î, IF, reâus efl,8Llatus CD, com-
» mune: [inca DG."eri: æqualis li-, nez DE fimilncrquf OftendtturV 5 raflas DE. DE. effeæqu’alcs. Po-A "fito ergo centre in D. defcriprus.
Ô eirculus fpario DG]d :ranfibir petr I" Punâg-EGF. 8c quia pet coroll. ”’
F m 5. vnaquçquc lincarzrm AB. ’5* BC. CA. tangtt circulum. me!i PerfcÇtum cire Propofirum.
. r inÇ
y A
6161
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1
e atu 151m. rutilé;A pkobdsrrro v. r3.
. cira 4mm triu-4-- ;ulmpr ARC. rinç-
lum defcribrrr. . 4 ,
vînfcunque du! àniiguli, duo ali- 2;:
que latere pan AB. I’Ï l . BC.: druide bifarùn l:13!!- in a. sa r. h ad qu; jA »’ ’. o yunüa excitab’rs ou,
endxcuhres que coï-tant in D. vel inrr
. trnngulumwel inter- Dn * A ,7 rio lucre , vel au;’ (due: enim En. fieu: anguli pas. BYE: minoresIduohus Â
nais: aga coïbunt) due purent j«au DE, DA.,DC.ch qui 1mn- h
» plorumBED.uAED.latcra BIS. BA..v Tune: malil&DE.cemmune a: an-- (un 321-1. re&ierunt& bafes AD. 4.
l
l
un. ,
p 4A [une æquales baies DE. DG. centraigitur D. fpaçio BD.ducctur cirçululAEBC. qui rranfibiç ber punG: A..B.C. Cire: datura ergo çrhngulum,
DB.zqualen. Eodemque mode;c e- .,
eirculurudefcripfirnuç. D
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tanguent: x7;, pROposmo v1.à
Î n . ’A Inddtuirwlo "i5’ B A B C D. qua-
ê5’ d’un)» defirià
c . lute.7 Vaut»: du: diamerri AC’ ’ BD. feeanresfc ad angulos
a. «fics in centra E. a. iungamur .1 "a: AB. BC.CD.DA. a: hélant ’Ç, cliquai pedum
Prob. Quatuor angulî ad ceu-trum E.ponuntur reâi,& quatuor .liner EA. EB.EC. EDJquales. c 4.xMgr) a: quatuor halés AB. BC. -
, CD.!)A. (un: zquales. Omniaergo quadralilalcn fun: æqu-lia. Anguli veto hi: lareribus r-
7 contenu film omncs in femicir-Il cuîozber oreâiÆririgitur AB.t... CD.qu mm per definîrionem
ï» ’5’ Læ . P m)
ayùt in»
("J-t’y .0 .-
73.3
la au;
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115 ElenEuc’lih?
PROPOSIIIO . V11.
. am datanttrahir r A a -. B D «immun Mm:FI CH bore.
D . vais daubas diametrisACJF.D fecantibus f: ad reâos in eêtre .E. per eorum extrew-afi ducnntur
E N circula»; , 9114-.
’ r
’çerpendiculares YG. F! 1H. HG. Dpoïuntes petitum dahunt quadra-mm.
Prob.Anguli quatuor ad E.ponüeV tur nahuatl: ô: anguli ad ABCD.52.3- ïî ergo reflue FG. BD. Ho. (un: giraf-
lclx, fimiliterqut rem; FI. AC. GH.fiH’!’ l, ergo figura FGIH. en farando-
3 l. gramma Anguîus AGI-Lefheâus:ç 1*. c ergo Angulus HGA. (ü retins. eo-
vdem modo oüendetur angulos F. 1.-H. efi-c rcûos. . ’ I
De lateribus chicoJarus 1H. et!gquale lateri BD. 8c lotus HG. lateriAC. hoc cl! BD. ergo luter; lH.HG.(un! çqualia: ergo quatuor laterefun! æqualia. Ergo en quadratü ou.iuslarera circulum tangunt par co-ron. M. Pr. 5. Ergo cirer énumère.
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W" 1141,11". 1.7” »
PROPOSITIO vm,
Î’ÏKA Ê ’ In «la? 744-4PMtQ.
J (1mn, circula";h - de]? 21’502.I C H -
Atera quadratia diuide b;fariif in ABCD.duc remis "130113. 4 1°. ÜA cames fc m punflo E. oued dico cfl’e
cenrrum crrculi . un r dercribatu:fparïo En. erir que petirur.
*Prob. il aux AF. lG.funrprrallelz, amures: ergo retire A01". 5 (un: La z
yarullclzôzzquales &Emrlizer rcv 3’&ç AC.HG. eudnrrque modo r a; c 34,1,FGJH. ipfi 30.: (un: igitur para":-logramma F12. E1 EH. EG. Nunc ficdico. ReâzBF. FA. AC. film æqua-
I- les,cum lînr medlctares malt-1: fis -
1 W P d rialvcro d’un! çqrxalcs reptç 52.5.4 2D. ’ D3 ergo mât: RE: EA.F.D sîrçquales. ".5.
g Ergo E. et! centrum. exqro fi (En-(le 5A defcribatur cirrulll’! danse:runâa ABCD. à: conrcquente.’ 0m.ni: quadra: Inter: pe: coron. pl-IG. fuiL’a. fcurnanguh ad ABCD. Entre. r uAi. ln du. ctgp,8çc.
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Mi. p
i7! V» llanlmlidù ’
PROPOSITIO 1X;. Cireur dam
à; qudrtmmmir-. Julian Jefiri-C ubac.
DVcantur ’dinmetri .AC. BD.faire: rein prude î. «inouï.
dico elfe centrant defcribendnn circuli. .
Ptob. aco: AB. AD.fnnt:-in!b 3L;083.:
H. r
gay
«pales: aet o a: mêuli A8 DADB.Ang us BAD. citadin,-«aga unguli ABD. ADB. fuutfiuguli femireâi 5 Emilia: quir-
ÂlCDxüfemireàus: ergo om-nec interromprai".d Ergolare- vn EA. En. le. ED’ tqualibtuengoue Moteur. (un: argutie. 1
i
ber yarrialium angulorum :4 f0
l
. Ergo E. en: centrum cireuli,qnifi defcribatlr (purin BA. trenti-biz pet me. quadratiABCD.Çrgo circulant, fic.
l.
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r
r
; k zmrwm; r79PROPOSITIO x.
Ififidu trian-c film» A B D.
’ B D riflant , quadbaba: «arum-
4ue "mon qui 4d bdfimfùnt,(angularum B. 66.1). luttantà. reliqui A.2i SVme refilant qunmlîber A3. qui
36 a diuidatur in C. vt reàangu-hm fub AB.!C. zqmle fit quadras"ôte Ac. mm centro Affine B.du-«un cireulusdn quo 5 accommode.tu: refis Il). fluant ipfi Amiant-turque real A . dico triangulunlABD.fore ifofceler, cum refit A8.AD. fint çquales, a: angulos ad ba-fim B.&D. (lupins reliqu’r A. quad
fic probo. vDuâa reôh CD.: defctibe circu-lum AC D. cire: triangulum BAC.rectangulurn fub AB. BC. zqullcponirur quadrato CA. ergo a: quadure B p, n50 emmi 1mm. k
M...
au. a)
DIID
01.44
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du. 3un
In. I.gîJ
’îzx
in Elena.- Euclilù. ducaux focansBA.
l’eau BD.ab eodgmpunfio «en inci-
c deus in circuluma ACD.d cum range!inD. ergp angulus
CDB. . çqnalis ca ipfi A. in alternefugmemo, ergo commun’x CDA. ad-dïço, duo nnguli 5.6L CDA. æqualesfilm duobus BDC. à: CDA. hoc c8:inti ADB. vcl ABD. Nunc angulustua-mus BCD.duubus imexms A .8:ADC f :qnahs c4: ergo idem BCD. ’en 31.12115 9:; un). val Afll. ct-go un: DG. DE. l zqualcs , cumaquales angulos rubanant. Sed30e ponmu Tqualis iplî CA. ergoCD, CA. æqualescrunt: ergo nnguhA. &(1DA.hzquales.ergo externusangulus 36D. duplus en; xpfius Acr-go eiufdem quoque dupli fiant GBD.4013. cum finguhextcrno BCD. ç.
’ agiles tint, Triangulmu agame,
.-.-. -...-4-,. æw
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e zibaryuntui; un.PROPOblï 10 XI.
E In aïno czrculop! H I EHFG.pcnRA- Pnôflî’ 0
a garum aquita-terfim à 4’111!-
a): alun; infiribere.41a: mangulum Ifofceles quid:que, cuius anguh ad bafim fin:
dupli crus qui ad vertical) à: lpfi z-quiangulus b infcribatut in data cu-«110,13an EFG.Vtcumque angulumad bafim dinidebxf, riàm duâis te.au IF. HG. 8: quinque punas E. H.
e vn
41°.;
6 2.4
v " F. G. I. xuhge huas tandem, a: fa-* aumelre quad petitur. fic probb;
Quinque ange)": FEG. EGH. HGF.IFG. EH; ponuntur zqualcs z r ergoarcus quibus maman; zqualcs;d Ergo ulules refit: sa: æqualesyetiphems fubtendunt. Anus EH; ,æqualis efl "un H3 ergo fi Midas 0 1&3."communem HF. cum: periphenx 439-3»EHF.HFG..æauales: erguôc reliquA
, fegmcnta FG. 15.61. EH. çquaha;ange anguh EHF HFG. çqualcs,ldcmqucdæendum de rgxqms. Hz- t 17-36go pcxngonum zquxlaterum 8c a-gniangulum iafcnyû. QLEÆ. .
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’wd. a - MJICD page
un]. culai: ABCDE. a:1&5.Û Il.
4x.
451.!.
437.3.
Ça. 11m îwdiüsPROPOSITIO X11.
Ilü Cire: doum cirai
ï- m GHnçL. qui.p hum": ùaf’ùul- ’1 c x landefin’bcn.
Vnfi hm: propofitàonen n.1 infcripfifl’empenngonûm da.
cueulmregeriam centrum F. a: no-enbo in petipherie quinqua hue:-
rnm FAI8. au. ni ne nfl’a an-q "il fie... [mefiât I «lucane tangentes qu b un.entrent in punàisGHlXL. àquibusfi dune alise 11th «au GF. Il.fic demonflrabo hmm: aïe quad-petïtur. Et primo quiden quod an-ulionnesfintqunlcs. ln nadri.ont. AFBH. quatuor mg 16v:-
lent quatuor «and!!! cuiuflibectrianguli AHF. HFB. ne: "glui va-leavnt duos (côtes: finilitéxque laquadrilntero 3P. C1. 8C fic de afin:ergo cum anguli A. &B. (in: "en,Magali AHB.AFB. valent duos te-&os,fimiliterque angulelC.C-FB.&fic de anisa Sed anguli’ AFB. BEC.flint daguait! à!) squales anus . e:-go rempli 11.8: Mm gymkhana.
l
l
à
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ne" quem. u;à. que diçendum de anis. largo alunespatagoni angulifunt squales.
j Quart autem latere etiam (in: z-i glana fic ytobo. Quadrant]! F1 e en
squale quadntis nm ipfarun En. ’47’1PI. qulm ipfarum 1C. CF. fubhtisergo quadrant :qualium FBÆC. re-marnent xquaha quadrata «Il. 1C. e:-go na: Bi. IC. fun: zquales. Hun:anguli FBIÆCI. a: contihentil late-ra funtæqualia :ergo f: habentiux-ta4. «magnums. ne. fuma-qualel. iodez: ne modo dicam de .niangulis CFK. FD Gade au: omv
i- mbus. Ergo cum anguh BEC. GFD. f 174.f fin! «pales. k anguli IYC.CFK.(in: eorum dimidîa , z une: cran:unguli llC.CFi(.E:go ca in triangu-hs l!C.CFK.ansulx lFC. PCL ulna-lcs (in: duobus angulis CFK.FCK.al- I ’tu nltcü &latus IC. fit commune, z la...
,2 reluqua litelagemnt æqualia. Erg.’ IC. (2K. fun: squales, a: dînai.
dit lipfiua 1x. codent modo clen-des! B. elfe dimidnm a En: tu. Jefic de alun 5 ergoÂCum Midi: le, .m. oflenfa: fin: zquales , cum: un.bien m. Il. nquaha , fiança. ü...Indus: de nm.
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. in; BimÆuclM’;
PRO POSITIO xut.
in data penne
gava quad efl 2-"Krfuf guilntemm â c-
c K13 qumhgulümnira ;adam mfcribtrl. a
kirfi x... Dal’uidanrutbifatiàm duo au.Àx. . guliproximiB-KE ABCJC-
cïisAF. Bunan, coibum, par!in F.cum uulhusangull medicmvaleatredum. Idem fiatneliquis
Vangulis. Qoniam igitut 1mn-gulorum ABF. FBC. wqualia si:
ce, latcraBA. ce, 8c 8P. communc,œnfl. a: anguli ad B. t (un: arcs,- an-44.x guliBAF, 3cm: ba es A17, cr,
à erunt ulules. Cum igirur amgulIBAE,BCD, ponanrurzqua:les 64 BAF, dimidium fit 311ng3A cm 81 BCF, dimidium an-guhBCD. Hic ergo angulusac
:015
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Liber guru". 18;reliqui in orbem feâi film bifa-riàm. Ducanrur fimilirer ex F. adfingula pentagoni’larcra per-pendiculare: FG, PH, &c. Q?triangulorum GFB,BFL, duo a,guli F GIS, GBF. duobus FLB.FBL, fun: æquales. 8L lamas F8,communc,æqualia etiam r «un: 9 tulatera FG; FL, a; bis FIC, FI, PH, aEure centro E, (patio EG., f
ucatur circulus , tranfibit par,punâaiH. l.K.L. exiflcntia inlatcribus pentagoni, g qua: etiam lrangent circulum , cûm (in: fuper f "m ’
extremitatc diamcui ad refletconfirma.
I.
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1&6 1511m. Euclidi: ’
I PROPOSITIG XIW.
4mm, dru dama par;.A3 gagna!» quad cf!l d aquilflttmm (95,c -ggyiangulfim, cit.-
culum defcribeæ,. d Ngulos A, a; E, a dinido bi.
99-! fariàm «au Art-175;, que:bu. alicubi b concurrent, putain F,4*? hinc 1d reliques angines duce!
- rcâas 137D, EC,EB. qua: on: (à:car: bifariâ probant v; in prao
* aima propofiçioneÆrgo cum an-guli mules ponaruur æquales,
5°! arqualcs crunrdimidii,& cronfc;qucnrcr æqdualol- FA, F13. hrfque,:equalcs 091.4165 na: FC. FD.FIE. Ergo centro F. (patio FA,
Da 512.3, defèriprus circulus. tranfibi: parI augulo; pennagpni , nec vllurn
tins larus Menhir. cum enflai;55.14,3.an un circulürn- d
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flinguant". siPROPOSITIO 5cv.’ In data circule; ,A hexagonal» , d’un.
Æ aquildtcrm a!D aquinngulm in;
firihrc.L S I: diamant AD,cëtro D. fpa.’7 de femidiametri DG.fiar cir-
çnlus CGB. feeans dunm cireu-lurn in C, a: E. pçr centrum G,duâis C17, Elîaiqngantut AB.BC, CD, au. crique infini-ptmn hexagonum æquilateà aequiangulum. d,Prob. Rcdz GC. GD,à centre
6,8: rçâz coma) cenrro D,fun: squales, ergo triangulumDGC, et! zqnîlarerum. I Ergo a: 4,, r "
æquiangulum; Hi ne; anguli, àhalent duos naos: ergo quili- 131- k -- Îbe: eorum et! par: renia duorum ’rcflorum. Similircr ne angulusErgo cum CG ,EGF, a ra: c tu;
52,4;
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tu .Elein. Euclidi:A [cant duos re &ofi
B EGF.crit etiam "par:renia duorum re-
, É’ï-I- C EflommScdillis d a:-d v K D I q’ualcs fun: anguli
. Id verzîcem.--Ergo fox anguli adçcntrum G. fun: squales. Ergoomnes refit: 8c eircumfcrenuæ
a? AB.B au; uibusiufiftum e rua:ï arquais. E ergo hexagonum
æquilatemm. (Lu-9d veto fi; æ. .gniangulum Pater, cum omniumangulorum mediccates fin: clien-fæ agnates a: conflue duabusurtiis duorum reflorum. .
Corail. Hexagoui 14m, qui:affimidiawem.
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I Liber parmi 38jamorosrno xvr. ’
tr la» circula mon!.tA I, quznùugonm dufia « agrainera» à a.ï: pinyin» ,. ùfi .
I l ÇÜhr’v
’ IaNrcribe in data circule perm. a ".1;-gonurn uilacerum AEFGH. 6: b 1.4.
exdè ad pan mAab infcribetrian-guhun æquilaterum ABCJIoc pofirocum remua partes: circlunferenri:t. fubténda: AB. hoc cf! qnin ne un!quindenas, «duo veto pentagonï a- 2.3.5au, AE EF. carnmdcm quindeci- ’marum fabrcndant (ex. si ab i fisAB. EF. fubtendenribus fax. ip unAB.fubtcndenrem uinque tallas,fuguent BF. fubtendês vnam deçà:mamqmnnm rotins. Ergo fi qua- d
a mordccim eiçqualcsin circula dac- hltommadenmr,crit quihdecagonum c va
d zqmlatcrum ô: æquiangulume cul! -fingnh anguli fubtendans anus z-
d araks tredccim laterum quxndeca-gour. ü. F. m in
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ËMÆMM LEVCLIDIS
ELEMENTVM v.
Huius Elcmenti quin ri Via4 truuius autorem pudi-
car EudoxiumGnîdium,quiPlatonem, connin:gus et! in Ægyptunl.
DEPINITIONES.Par: dl magnitude magniJ
. . . . u a .4171de , miner mura, Q nm(Intitür maiorem.
. ID en, qua: aligneriez rampa;malmena ipl’am præcisd con-
fiimir: fic mitas , cil: pars terna-ëii. quiarcrfilmpta fuir «un;que» 4959451355 sftræssrropriè a
l
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Liber pénil"; leiIEEE: a: qui voeamr diluois:l Improyrid verè dia: pars , en:-que aliquotilafumpta ,. "(faunetout!» axait? ,l 1M, aïio dejïu’t;
l fic binarius numerus , en: impro-;m’è diâa par: fepteharii , qui;ter fumprus , defieir: quater au."un! fumptus excedit; arque bupar: dieitur Aliqunn, lmoEuf
I çlides libro 7.non voeu partem,Ted partes, a: benè nia quatuor a
V noneQ par: numeri ex , fed du:j du: Parles remix. la germe fic"
poiler definiri. par: a! même à:li [gnangnan fulminique» digue;’ du reputm,metimr ne! and!)
ï; jam» tartan. lr3, Similirer a: fi drfinitio Parus;d prou: tudieu: ab Euclide, pan;
en": communia: quantitati conti-:, au: ; uæ (012 proprièfecundfim,Ï Philo ophum appellarur Ma;, gnitudo , cûm amen numeroa. [mais que ne eonüiçui partibugà dubium tneminific forte eom-
radius Posviiïcs soufi: («a
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I5 llanîuclidl:a]! "du" pantin", tu mutinerrationnai]: v: fir,in equentibus,parti: nominc vrar,cum in quan-titate continuamm in difcrera;imô breuiratis gratiâ frequen-tu]: "a: numcrrs , quorum ra.men loco porcin quilibet ma-gnitudiues rot palmorum intel-ligere que: mimais exprimen-
We .a. Multiplex «rem"alanguir: merlu" miner.MVltiplex idem dt ne mul-
rum fimplex . quando vi-delicet vnum fimplcx hoc en:par; , mczitur mulrum , hoc en:maiorem quantitatem: fic n. en:multiplex ipfius 6. a: z. bis enimcomme: 6. fuies vero 2.. (et au-:cm refpeâu duodenarii dicitur[ab-multiplex. Æquemultiplimdicunzur quanrirares qua: arquè-multories continent ruas (ub-æulriPliees, vr 9. rcfpeâu 3.8:
n. ref-
I V
i
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k un garum; a;in; refpeéhi 4; qui: prifnà (juan;litas Ramdam rci continu. de ’fimilirer. rerc’ia quarram. iHinIèvides quomodo Pars 8c multi- »
plier fin: relata; Ià. maria ç]! alunira»: que»:
tintai): eiufilcpxgenefzr g maiitem quad :m-fècundûm mm:
final habitudo;C
l Vod Euclide: dixit amihoc Campanus venir Pn-
Ïwnia; menu; alii Ratio.5enfuvâfierohic et! , quando du: quan-"tirareç "enfiler-n generis; vi: duomimai, du; liriez, duç (u criédes, duo fondante enim inca i
, eum fup’erficie , zut lineaalbà.5 cumfimora, vrfic ,7 client gon-Î ferri, cum tint diuer rgeneris) in;
ter [à comparantur; feeundânieapacirar’em hoc efilcxctfrumydcfeâum au: aeq’ualirarem ; ap-
I Mains pîçlçognrararï au: ha:
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n!
x94 . Bleu). Euclidi:birudo mutua.Ratio. Obferuabisveto, requirifemper uas quan-rirare: : nihil enirn aber ratierhem ad feipfum, a: decempedafaiirariè confidente. nec ,nltioncil, minot, au: aequalis.
Hæc porto omnis compararioin capacirare quanti-taris fanda-tur, feeundrim quam vu: quanti-ras aliarn comme: vel accurard,vel ex parte ranmm, vel cum ex-’cella. Si enim vna, panem tan-mm airerius confiner vr bipedarripedam, miner inçqualiras fineminot ratio appellarnr: fi ad:-
uare roram vr Expeda fouge.dam, Æqualiras dicirur : fi deni-que plufquam roram v: [expedabipedam, maior inzqualiras feumaior ratio dici’rur. Cüm aurem.in omni rarione duo lin: retminiAmende»: a: Confcgmm qui adinuicem referment : Ille in novminari un effcrri (blet, hic in allocafu : exem i graria [inca (etPalmwm Mauser trime
.-....----..
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Liber aluna. i 19;’antCCCdens e [inca fez palmo-,mm : confequens, lineç rrium.ExcelTus ameeedenris [i1 rat con?fequenrem vcl confcquais fupraantieccdenrern dicirur Dzfinn-lin remmena». Ratio Renonali;’cfl que en: inter quantitares com.menfurabiles 6c numeris porefiexprimi , vrrari’o’dupla , tripla,a: (on Ratio lrrau’onalr’: eft en qu:
dl inrer magniùdines quarurnnulla elt communia menfura qu:Vllo numero poflir expriminxâ-pli gratiainrer larus quadrant": a.eius dirimeras).
4. Proporfio rjl variorum vfimr’litudo.
Racé dicirur immun , fen-fua veto fric en. Œgmad-
modum comparario capacirarisduamm lquanriratum dicirur ra-tio : ha fimilitudo duarum velplurium rarionum dicirur Pro-portio. Ex gr. Cum tir-nuis fina-
1’141
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196 212m. Euclidü Irio n. ad 4..quæ 9. ad ;.ideodid .cd inrer bas quanrirares elfe pro.portionem . quia cf! Emilirndo
rationnai. . l . . lProporrio dimdirur in Amie.mm’um, Geamtrium , dans.fiant. Arithnretica cf! armada1m mlplun: numrriprr unir.dtfrnmr’nm progrediunmr, v: hinumeri 4. 7. ro. cil enim dilfe-Irenria 4.. a: 7.;quali’a dil-Peren.ria: 7. ,8; 10. bec proporrio dicirurArithmerica quia inuenirur iule: Ahumeras in ordine fuo naruralifumpros parax.z. ;. a. pâte.
Geomuriu a]! fimr’ünulo a.
rionnrn que fit inter ne: , mlplan: guenilleux v: internu.meros a. 6. 18. en; enirn ratio a.ad 6. fimiles rarioni 6. ad 18.nam vrraque ratio eft tripla.Hæcque Fol: cil propriè dia:roporrio, a: quam hic defihic
uclides. . iProprrtio Mufiuejl gueuleme mdjnitmlinn; in "lion.
l
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liôequintur. r97Hun w "de"; fig n’itio prima adune)»; ,, que dlfiremia prime
- à finaud, ml drfl’enntùm fe-rundt effume, vr a. 4.6.- Sun:in proportioue mufica quia ea-dcm cit ratio primi numeri 3. adrertium 6. que! dichrcnriæ primien fcc’nndi,quæcfl r. ad diffam-tiam lècundi 8c terrii , qu: cit 2..
I dicirur vero harmonica quia.eonfimantcs farcit fanas inter
’, quos inucnirur.
fg Ration»): baba" interfi garantira": dicxxmr, quea: W": malnplimu fifi "tu: -
un f taper-4re.
Via ratio cit duarum qu":v ritarum eiufdem generisa trauma feeundrim mcnflrram ha-ï birudo , proprereàquârirarcs que
rarionem habentinrcr le, debenctire tales v: le muruo fuperarc
’ fémur; nam quanriraafiuæ me.
I Il tuï
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me .’rc
h, naLîZ:A e’ 139
, mm vnum multiplices,nunquam"’g lamer) aima fupcrabir.» ,i,:rz’az
’ ., pqnia ira poreft multi liearivr la-’ gais exceder diagon cm, [cd hac
ratio dieirur irrationalis qui: ir mon pour! exprimi numeris.
Ïiiâilinea elle rarionem cum inter
r9: ’ film. 51411515.!tirât alreram,’pbrcfl: cum fupera- i
le. bine iColligirur r. inter lineam a: ’fupcrficiem, inter faperficiem a, Âcorpus, inter lincam finirait). a:infinitam, inter angulumvrcârli-ncum a coneaétus , nullam elfernrioncm ,. qui: quanrumuis ho-
Ï Coll. a. Inter diagonalem 8chuis quadrari elfe rationem,
Coll. 3. Inter euruilincn à rcd’
ca firaequaiiras a: inacqualirar: rau! Hippocrate: Chius Lunulamerefccnrem,& Archimcdcs Para-bolam quadrauir, 8c Proclus in.ter angulos reCtilincos se curai.lineos .acqualirarcrn demonlira-un lib. a. in primun Euclid. adn. mérita. - I
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.4- .r
.1
1.
.156" par"). ’ 199
Ë; In cade»: ration: quart-rium alicantur cf]? ,. primaau! ficundam , à renia adguarana, Camprimæ terri:cquemultiplicia,zàficundz (9’
Ï quarta egn’ernultjplicibm aQualifiunquefir lm multipli-catio, l 01:77;»)un 46 vrroqra, i11cl Mû deficiunt. ’Ull 1m); 4-
v ’ , qualiafianrgwl on) rxcedunt,
fi enflrnantùr, que interfgfiaîindenf. l- Sigqo oflëdit Euclides uo-Ïp mode poflîmus cogne ccrcvanna quatuor quanrirarcs fin: ineadem rarionc. r°. Æquemulri-pliez, inquir, primam quantira-rem a: terriam.z-. Æquemulri-plie: fecundarn 8: quarram..30. confcras multiplicem prima: vcum mnltiplici ramas, accru]: .
l riplieem terri: cum ïlgâlplxc:
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.1... w s
au Ilemjnelidiaçunquc multiplex prima: deficilà multiplici feeundæ, vel acque-
p quartz; &vide,vrrum"quorr’eç «
lis :113"ch excedir, (Han) muki- .1pie: terrine rune deficiarh mini-Vripliciquarrac , vel aequalir fitwelexcedar : rune enim fiid fiat,çerrô concludns , bas lqua ruorquanrirarcï elfe in eadcnlr tarifi-Àçelfi non fiat, nega elfe.
8.6 Il!4. au.A.B.C.D.
Exerirplurn: volol’eirc "nm.la; quanrirares A. B. C.D. fiat. reportionales : If. aequcmulri:flico A.& C. pure pet binariumr2°. aequemulriplico a: D..pu-en pet rcrnarium. v: faûum viades fupcrius. r. confero mairi-Iglicçm primae 8. cum multiplici
cundç s. a: multipliait: renieçlëmml’lüriùi quarrq g.
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liber galurin, riotüdeo non termina multipliant(and: deficere à multiplieiSelma: l (cd multiplicem quarta;
çficçrc à multiplici renia.
a 1,2. un; r8]. .1. a. 6. a. A, B. C Il. ,
. Dcinde’ irerum çquemulriplîî,
ce. 21.3; C. » par: per rernariumâfimiiitcr acquernultiplico B. &D!purapcr fenarium eadcm cfl: ra-tio a: ’quocun’que nuniero pet;guerdiiequemulrxpliccâ ) mm il!deo multiplicein prim’àJ æqua,
; let-â ’cÆIhMrîplïciRcùddi; 8c
a: m tiplicens and: . multîrliçi.
. guarani L?t 1612; :34i4. a 6 ï
, A...» c mon.p Terri» acquemûiplico A, Qi (En? Frbinaxitimguqunuk
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loi Blair. Euclidùri lice etiam il, &D. put: paro onariumscaduerro’ multipli-ccm primae 8. deficerc à multi-pliei fccundae r6, 8c multiplianttertiae n...à multiplici quarra:1.4,. a: quia qualirercunque ae-qucmulriplicem illas’ quantita-’res, femper le baber multiplex .-primac ad multipliccm fegrndz,.7: [chebec multiplex reniant!multipliccm quarrae, id cltlfimuldcficiunt vcl excedunr vel fun: 1aequalcs, propane concludo ef- .ûquaruor illas quantitates pro- gporrionalcs 8c carurn primani in .eadém rarioneelfc ad mandant, Iin qua eü renia ad quarrez). . ’,
- :6 r; r4. a;4. 5 ï 5A F C. D.
l Alrerum exemplum; .Propb-i lnanar. aliacfiquarudr A]! C D.3-.aequemulriplico La: C, par, l
l
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N Lihi quintal: no,-I ta par quaternuium. 2’. aeque.
multiplico La: D. put: pet qui.narium. r. Vidco multiplicem
rima: 16. fupcrare multipliccmËccundac 1;. multigüccm m6tarda: 2.4.. faperari à mulçipliciquarta: ty. quatre concludo du:quaàtitatcs mon cm: in eademra:ione,,quia ficfl’cnt’in cadçm
ration: . quadruplum. mais (il.Perarct quadruphî 4*. Sieur qua-druplum primx,fupcrat unira-g,
[flip acanthe. Id cairn aide-1tu qualifcunque fit multipliça-tîo. 045m lice: dnplum primat:
., fÜPCtCI duplum (cannage: fini.li ter duplum renia: fuyant .du-plumquzrtae. Tamcn non po-
tek inde colligi quad fin: pgoàpardonnes 5 qui: v: fin: pro-Portionalcs oportet in fieri hélaquais multiplication.
SÇHOLIVM. ;’ Æ: flint qm: si verba si
renflant Euclidis nunc ce:
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p.04. 814m. Emlidùenflamment! ad rem ipfam, n64quamv’iudi’calui dcfinitioncm il.
hm poire infernire tyronibus:cum tradatur pet obfcurius. si;itagueilhmaliter cnlîcip. glua-nor glutamate: «(impur eflipop arrivante: , du» prévu enflai1nde tantinet [hundnmflel un;finaud-frauda, en nuis un.fiant 7mm»: in! continuur à1mm. Nam quatuor quantità -tes cfi’cîro ortienalcs, en: pri-niàm it Te gabare ad ftcùndam,fieu: renia f: haha ad natrum.-lacé aute’m aliud nihilc , uàmprimai: ira Je maîomn v: mi-nbrem Tunnel: , fiant renia ma-iorcfl: vel’minor quarta; si au;tem res itafl: habenprima eod-enâinodo continebit [toundam , vel
(and: co’nüncbitur , que ter-çia contîilcbit quitta!!! vel àquattzçontincbiwr. Igizur’qua-mgr-Â quantitates dicqntur pro-P°m°nilcm cum prima eqdcmm°dP C9nÈinçt («milan f 7c!
"-1. -:-- A «A;
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libriquimm. - âof tontinant à (’cçnnda , que tafiagomine: quartant vcl cantinera:a quarta. ’. Nord banc dcfinizianem «3n-ucnirc mm quantilmjbus ruina.nalibus . nia: irrationalibus. Suspercfl: tamtam expliçandus i116modus continentia’c kl conten-tionils qui diciturlidcm. Il]: au.tcm modus dicitur idem duplici-ter . primo cum prima quahtitascontinu 2.". au: tontinant à fe-
I cunda tories lcxaâè, quotics un.I ü: cantine: quantum. au: Con.
tinemrà quartacxaftè 5 iman: nur-v’ la par: fuperfit vagJinea duorunivpedum tories comme: lincam v-
nias pedis,quotics lima. 6. pcgiuniil. comme: lincam ;.pcdum. SlmFlitcrguc fine: Vains pedis torii:continent: in [inca duorum pe-
3 dumquoties [inca 3. pqdum con-’ ducturinlinea’ë. pedumÆt-proà
* inde 4. illæline: diminua: pta-
pottionafcs. . . æSecundo, ille modus çanuncnfi
’
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106 3km. Euclidi:lia: vel côtentionis dieitur idem leûm prima feeundam , a: tenuquantum "que cantiner; la præ-teçcà eandcm pattern, vel cardent
armure! cum prima , cum tali tui pute auttalibus partibus cô- A
tincal: in (ceux-Ida. quoties tatincum cadem, au: talibus partibus tcantinera: inqüartaNth’nea la. 1pedum contipct tories linnm 5 lepedum 8C talem infuper dus par. dtem quoties lineam 6. pedum ’
ualemue du: pattern tontine:hac: la. pedum. Nam [inca 10.continu tcrvliueam trium pedum ,dkinfuper trientcm ipfius terna- -1rii,ficntlinea 2.0. pedum conti- Inette: 6. &infuper tricotent ip- Ifins fenarii. Snmüiter fine: 1 1.pe-dam tories comme: Iineam g. pe-dum a: tales eius partes , queueslineain Io. pedum qualefve du: 1pattes continetlinea 14. Rurfu: dme: 3: pedum cum un fui.par-
te contlnctur in luxez 10. pedumficutlinea 6. pedumcum tahfui Â
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I Liber quintUl z 01’Îpartic continent in [inca 1.0. pt.dura. Similitcnlinca 5. pedum
i cum talibus fui partibus contine-tur in [inca n. pedum, fieu: linea.x0. pedum cum talibus fui par-tibus c9ntinctu; in [inca 2.4. pe-
dum. t7. 54min» d’un» haha;
un) rationna quantitatcswoug«mur proportiomluc
NArn qu: babcnt candelarationcm. barbent rationum
fimilitudincm feu proportionem. V039:1 fi proportio non intermin-pitur,dicitur continua proportio,qualis cf! in hi: numcris 4. 8. 16.32.. qui proptereâ dicuntur conti-
:., nué proportionalcc : (au: autel;n dicunlur tantdm proportionalcc
d p 4.. 2.. 6.3.
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t un chiant-:25:"8; tu»; àand; aflcmultiPIiÂ
fiuk,multiplexprimz, exci-.firit mùltiplicmjèmndæ: 4Emultiple"): "m’a, hon cxceflë-
fit multiplicemïquaîu: nous
prima 4d flandrin: , maie-vnm rationna bah-r: dirent;qui"): territ, adquartm.
’ 1i6. 13:34. à):
4,. i3." 6. - j.A B C En
I Vta li propônantur (influai -. quantitatcs A B CD. quiaquad’ruplum primzt fupcijat quin-
Ïupium fceundæ ; quadruplantautcm tc’rtiæ; mon fuperat quin-tupiur’n quartz -, diccmus main-i-cm en: rationem primæ id fe- Àcundam, quàrn terri: ad qua:-nm.
9- Pré
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liât! quintidi sa,
Profartio «un if: tri-bu: minimum tcrmim’: au»:
fiflir.
CVm prbpoflio fit rationnafimiluudo z ratio nutem lit
duatum magnitudinum eiufdemencris comparatio, quarum vu:icitmf anteccdens,’ allia confe-
’qucns: in proportione , ad mini- i.muni duo tequîruntur.ancccc-, denti:,& duo confequcntia: qui:11men medius tetminus’ cfl’:eiTc confcquens przmæ ante-ccdens feeundç rationîs,propter- ven prçpprtin pntefl elfe lin tribu:, terminis, mmlrum qu: continu:et! "16.8. 4.. qua: VCJO non en:
- continua,pofl:ulat quatuor termi:nos "16. 4.12.. 3.
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Env enflamma. .. a tu; Càm 4mm M3914];3m!teivpxopgrtionalnfucrinè:prima 44 2min» daignât.rhum?» [aubert ratinent, zUn»: «me»: baht: ad fiCÜIà v
dam. Amant quatuor 9mm1m": continué. proportiànde
hsfucrim; prima 4d quarta!. dicitur triplicatambcbm ro-ciogmn, en»; que»: bah: 4d
’fimndam : âfimperidgiàccp:
2mn mplins, 11m., infimetf0, enflait.
Ï Dlfi’crunuatiq «pas; tarin ip duplicata 1 pitcmquc ratio
p çrlpia, gracie triplicata , ytühpflcndunt exemplap ’ t -
54- 1.6- 4- 1-A. a." c. D.
mil-"æ 5.55 quatuor. amuïs
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liber quintm. au(ne! AIR. C. D. continué pro-portionales, nulla cx ipfis cricratio dupla vel tripla, 8c cri: m-hilominul in ipfis vna ratio du.Plicata a: vna triplicata: quia ra-tio’prïmz ad fçcnrrdam critinà
ce: primam a: tcrtiamgtriplicaàta. En: porté illa ratio prima adfeelindam quadrupla. même adreniam quadra la hplicata, idun quater qua tupi: [En l’enle-eupla. Prima: ad quatrain quaddrupla triplicata , id cit quaterêuater quadru la . id en: quatercxdccupla. i en, fixagcquag
drupla.Secundum. Sint quantitath r
1. 1. . 3’ .quatuor B..F. . continuéroportionalesl, cri: prima rub-upla recundx. Secunda renie.
Terri: quarte: Eric tamen ratioprimac ad retriam dupla rationîsquam habet prima ad fceundam.Exit item ratio primae ad quar-cam , tripla rationis quant barbe!
. . . s li
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2.12. El:m.lrulidi:prima ad feeuudam , nec, and
’ critprima dupla tettiç, [cd du:bbquadrupla: ne: prima et]: tri-pla quartae, (et! eius fuboâupla.
Vno verbe difcrimen aperio.Inter duas quantitates non dici-tu: elfe ratio dupla nifi ma prao Ilciré bis altcram continent: dici-tur autcm en: ratio duplicata,pquamcumqp habeanc incquali.ratent , modo bis ca .repetaturcomparatio quac en: inter primtîa: 2m. termines: a: triplicata,fitertiô eadem initituatur.
11. Hamolagæ quadrum-diauntur a]? autel-clame:quidam antecedemibu: , tanr-fiqucntn flan) confiqgtcnri-
6m. v ’A r. q. t. gr:I proportionales funt,A BCD.a: vr rima ad feeundam, in
renia a quartam: homolo çdiccnturprimaô: renia inter c,
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vz
t Liberguinmrï n :15Canada item a: quarta inter fa,quia eafdcrn vices germa: prima8c tertia , 8c fimilitcr faunin
a. quarta. ySeqmlurmli argumtnüin propertimibm , fui infinie;[nichât dehonfiràbuamr. A
1 . 12.. Alterna ratio, ejlfian;l pria amenderai: ad durera-I
daman , d’confèqucnti: M
; configuraient. -.i Via Gcomcttç quinque «liftt mais conclufiencs com; I. p gant ex gnafiuatuor quantitatum
pro ortronc , proptcrea quinque,me os.quinquc illarum conclu-iionum nunc dcfinit, Euclides.
. Prima en alterna,hoc cit pentanei tata ratio,fcu permutando quan-
titates a: comparando i fa: ante;cedenres inter il: , et ipFas carafe:
queutas inter Ce: *
l ’ j a sur
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a .p 1 ElmÆucliÆ: a lia; g. a. a.A. 3. C. D.
’ l ne: en quodiprçportionales intpABC’D. e que u Lad:
4B. rira-Cg au D. [infctam ergo apermutando v: A. ad C, ita B.
au); A . s ..l I3. 1mm and 2 efl fluxé r,50 eaùfcqmti: en imme-l dans, 4d «unification velu:
coufiquenrcm. 7 . lS Ecunda fpecies feu modus arÂI gumcntandi dicitur mucrfa 9quia , quando confequens inilatanteccdcntis fumitur , inucrtcc-do (ci-lice: a terminas proportio-nisv, et ad anteccdcnsivclut ad .canfequcns comparatur. .Nm z
. v * 6’ aquia en v: Â. ad à. ira c. adD- aîrgo inuertcn do. infcrani Il
a 9 I z i . c »la"! 4-, 59195219..
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a; Mn ruinai VairI a4; * Comofiria anodinsa! 13mm. Mauritanie-unçqn :qlfiçntc , - me unités, mi
à? mèonfeqmm. ». - .r
fpceiesa dicitur com;pofitio rationis. Clin! Inter.
calen; Êmul cum confequcntcirritai vinas lbmitur, a: ad confis.
’quens’comparatur. SigŒgcfh
, , ,. . .. 3 . - I *l n A. ad B. ira C. ad D. ergo;. . * H v ; l I3 ’ r!componendo crit. vt AB.. adB.
p r 4 z 1 - i, w .ira CD. ad D. i
1;. Diuifiomtianiceflfirnt;pria. mafia, que trafique»;V tu» frayent: «recèlent; «àa: t’pfirm tonfiqueutm.*i rj HOe cit comparatio ’diEee.1’ renriçrcrminarum cumul:
j centroipforunta .. ,r
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a2 ’ MmÆmlîdir t i
. . IVt"quia et! vt Â. ad si in c. ad D. 4
exit diuidendo vt 6. ad a. ita 4nd:-’. i -ve1 vt 6. cd Lita 4. ad t.
T16. i Cutterfio rationù, a]? ifilmptio anteccdenti: 4d ex-
. «film ,’ en finance 4mm;du»: ipfiam coufiqucm.
.Oe en: cit. comparatiov-nius tcrmini-cum diEcren-
tia tetminorum.
’ .’ - 9 3 g a 1v: quiaelt vt A. un. in c. au.Erit conucrtendo rationcm
vr 9. ad a. ira 6. ad 4.-vel vt3.ad 6.ita1.. ad4. 2
Vndclvides quad conucrfio et!.diuifionia inucrfio.
. -* 17., Ex candira" ratioefi,ji plan: duabnsflut par"hui? é hi: «Un multitudi-"f 19m! o que En; filmant"!Ü in «de»: ratine : tu»: rit l
a inprimit,1
x i i
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V liber quintidi auin primitmnghimdinilm: prièm4 dd VItimar’n , fichât in fe-
pundi: l Mngnitudinjbu: , pri-ma ad whimijê habebit. V e].
vaèig extrem oruin,pcr rab,duâion’em mediorum; V!
En: pantes magnitudincs; .
Il 4 A B C 3 E: aljæ totidcm.
I V i a zE. D E 35’ Sinaïbinæln «des: rationefioc en v:
n l 5, Lad B. quidpiam. in D. id E.- quidpiam,3c (r B. ad C. in E. andl P. exit et àcquo v: in prioribuà
0;."5 A. au! vltimam in in page;i”fioribus ad Nullum au:r, incrum opbrte: opponerc ipfis B;8c E. quiazhîc nonIagitur si: xpfoàd! kamicqucmibus. mnème: mg?j . V. - . , .1
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2.18 item. Euclldù àtut! acqualitas razionis duos mo- gdes argumentandi ex proportio-nc plurium, quam quatuor quan-titatum z bos du: fequcntcs deli-niriones explicant.
18. Ordinampropanio cf!” tu»; fum’t qucmadmodnn;
macadam ad canfeqnemm,in: anteceden: ad confiüuenè
tem ; fanoit criant-w confi-quem ddalifldquidpiam , incoufiquem 4d aimai quid-
pia-m, . xDIcimr ordinat: propomo,qui: duç partes proportionis
eundcm feulant fuamm ratio.num ordinem. -*
n. 6 4.A ,13 c6. ,4 tuD El F.
Excmplum 5 cita vuiufqucqarl
,1»...
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Lié» gamma. a,tîs prima ratio dt dupla,fècun-da ratio cil fefquialrcra. Conclu-
àitur qudd un en; ad incfl ad È* 19. Parmrlmm un!»proportia efl,cum tribuxpofizi:magnitudmibm , dab): quafinthi: multitudine paru; w Iinprimi: quidam magnitudi-o ,miam fi baba: amende»: ad «configuennm: in; infimndi;magnigudinibm amendoisad canfiqmntem : en 4mmin primù mngîzimdinibm.confiqutn: 4d «lind- quid- vpian: : fic infpundé: magni-mdinibm quidpiam ad ame-
cedcntem. a * l«H03: en, nîm vt in primïsl
Puma f: baba ad (aux-dam , in in fccundis [hamada ad
Ï T Ü
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" *«-’ ;....-. -
.. unv-..r
»x DEF
121 o En». Euclidü ,tertiamgàvl: in primisfccunda à!perdant, in in Œcundis; primàf’:babel: ad fccnndam, chenu: hacproportio peumbaza, qui: vu: üprçportionis par: non renia: et. Adincm rationna: alterins partis.Exemplum Efto." ’ ’ "
il. 6 4.A’B C 6 4 2.,
tic dupla præccdizfchqiaketama.In feeundà patté feqmtuf.
I Concluditur amen peuplez;-qüc in proæqttionc oxdmata. I;(E341 7::
Ï n prima propofitionîs par: , râ- g
A
l
1
1
l
1n .A a: c . ,;Sicefl: 6 a. -r 1*D ad , - P
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Lib" pâmas. auPROPOSITIO I.
3.- i. ;. si fin: fqabtcungu:A.E.C.F. magnitudinu gnomon-
6. 2., au; mngm’ugdinum laG.H. qualium "me"; . fin-
gullfingulamm. quemuhiplim;gnan malgiphx q]! uuius vnnmagnitude, Mm multiplia: "un:à. amnuomnium.ID en quia I squçmultiçüces fun!".A. adE..& C. un. 31A. &C. lun-
.gantu: in G. fimilitezque E. au. in.H, quam multiplex en! A. iPfius E.&Cdpfius F. un; mulüplcpetiz G.igfius H.
1’64.
a 44h.1°.
Prob. Main: tu: minora . Tant.tout, un) En: omnes Putes pro-v,
, priè du ç. Ergo non potefi tomasaggregamm pluies vel pandore
humera comme": .mtum aggrega-tum H. quam A. 8:0. panes omncstarins H. Et veto quarks E. numcnç
.A. &F. nument C. tories H. nume-I la: G.hnc eu: ter. 1d veto intelligen- dam non tanmm de multiplia in-crefcentc, fedeciam (le decrcfcemgq
à: mixte.. 1. n,
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11.!
aux . EhflEuch’di:
PROPOSITIO I I. ;6 3 4 z Sipinu utlêcudcp moqua www»
Â. B.C. D- «pauma C. quartat ’D.7m: un»: à aima E.
9 6 15 m [amide B. qu’à multi-. . plana a exul’. un-
! F H a ’D. fibré: ("gadinprima un: zain: E.nempc G. [2mm "3.1114:an ipltx , aga: 1mn C. au[un F. ncmpc H. guru D-
Rob. ex hypozhçfifecunda B. a:quarta D. pari numero conti-
ncmu: in fins multiplicibus A. 8c C,campe bis. .Similiterque eadcm fe- lcundaaB. ô: quarta D. par: numexocommenta: in fuis aliis multiplici-bus E.&F. nempe tu. Ergo pet pri-cedentem. connnebuntu: etiam æsi numero in multiplicibus ce le-ais,hocc&fi componantur A. a: E.u fiat G.fimilltcrque F. ô: G. vt fiatH. quemldmodum G. u. continua. a. quipquics; la H. le. continebxlD. a. quanuies.
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Liôn gainais; u;
PROPÔ’SITIO III.
.4 3 6 3 Sifitprinm A. 7’471 LA 3 c pli-cumins B. 47:43g n multiplex,atqueE P renia C. quarta:
D. finrmntur 4:4-tem æquemnltiplices E . é F;prima A. étertia C: erit exque finnptdmm , enraya:’vtriufèue agile multiplex .agitera guident E. ficundc B.
. , alun un»; F. grume D. m
Rob. Ponuntu; 3.8: D. ac;qualiter contîheri in fingulis "5’
A.B C. ergo zqualitcnconti-mm: miam in iifdcm pari nu.mers multiplicatis in B. a P. p
.T mi
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a;
il". EkMJucliël. 4p EL’EMENTVM IV.’
4, 1’ 6 3, Si prîmddfiqa:A .B Ç D tandem, eqndenga a n 9. [94.614011 ratinala 1: G Hâteniaadqmg.’ sa,» : criant, agité
k multiplia; prima câ- terril,aiguë multipliez: flagada,(6* qimrtæ , aux gammamflltiplimfiançmamndem lm.-hbum ragiolner’nfi prout inter,
[e refiandem, atafimpm fuc-
nm. v v ofita a: explicats fuguât" à nantbis dcfînitiène 6. han; pfopofip
(minem (a broum: pexflxingo. - ASi prima,A.artfccundaiu Embu-
tir eam ratibn’em , quàm babel tu.ria C. ad quartant Duf’umantuxque.prima: A. 8c zani: squamuhîpliq.
’ ces E. &G Item (and: B. &quar-’1; D. xi r dçm vel aJîîs æquçmulxipli-
abus F. a: H cri: E. multiplexipfiusA a; E.xquhipljççm ipfiug 1?. fient;
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Lüçzquiatug. C a;a- multiplex tetüzC, ad H. multiiRhum quitta D. idque iuxta nonv mm cancan! ont àhenm multiplî-C rçationçm, fed iuxta quamcurnque v:àbi diximns , a: multipliais rime:terri: non folum ma de eient àmultiplîçibus koumis a: qu- «au:«ü na «un: animant vnâ excedent;(cd puma candela (ploque haha;hune fauchon. C nRatio ça qui: ex dahir. 6. idem.çà guano: magnimdinee in nous:çl’e ration! a: 63mm æqqemultanÂJÇà val vnà defieere, vel vnï excedeg’
1e, vel "à z nana une. Idemque cilval confene mghlas B. G: D. ad fin- ’galas A. à: C. atqùe B. arnaquai.ter multiplïeuas au. a: C. parfin; ,tu f: numçto multipliant.
- Corollmium.Bine etiam putt veina; ratinât
commît, Nam fi A. et in mains ipJTo B. ficus: C. ipfo D. en euidemB.in minus fore ipfo A. fient D. ipfqGrains en. Nee minus foret, cui-dens fi A. a: C. fun! a cirent min;-lia. au: minoraipfisg. a; D. "
..-.
.41", î.
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15.1
ut 2mm.PRO posmo v: f
E 4 Î 1 Si magnitude A:c 8 D 4 magnitndinù Erin:A tu. B 5 multiplex fuerit: v:
1614:4 C. 6514M D. "in:relique E. relique F. in mul- pafin: erit, «mm A. tatin: B.
Met. si! enîm A.dnp!um ip« (in: 8.5: par: ablnta. C. do-
pln fimiliter partis oblat: D. er-o fi refidua E. non en: duplex le;du: F. canes partesrrotius B.
non eontinentur m omnibus par-:ibu: rotins MEN: tomm in to-to. HIE ergo xefidua refiduæ inmultiplex. v: contenu;
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r
î
plias.
Lilaquiinm. , 22.7 à
PROPO Sl-TIO V1.gaz? (Èst n. 574114417".
to 1 4. F 6 ’ . ’Ali. 3.153 A :1518 lC D C D ’a. 3 3 863. d’un-mm magnimdinum C. 55 D-fin: quemultiplicn: à derm-flw qudam EF. fiât enrun- .de»; CD. æquemultiplicçr.
ReliqueGH. iaflem CD.-au; «quais: fin! aquemultfi
æ
. - l Ol Rob. C. se D. in taris A. a: Bra: in eorum aliquibus parti-
bus alfumptis B a: Il: militer vconrinentur ex hypothe mergo a m;:qualirer etiam continebuntllrin reliquis G. a: H. Erfgo reliquæeifdem,an: aequales, un: au: «1 ,quemultipliees.
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i
tu
a 6.ea-
u! ,ÉImÆmb’Jù ’
. movosmo’ vu.
2.4 2.4. 3 cÆqernAB- dA C and"): C. candeurIl u 4 1:er r4:ionem:é-cddemÇ. 44147134ch AB. Ë p
ne: ex terminir. Geomerriçâverb v; demonllrerur, concipe
mpgnirudinem clapi: fumi,qutfi di-ceremr, vrfehgb r A. ad C. in B. .-nd’C. hoc parmélie dico ".5: u. 2-. pqucmulriplieia primo un itudinisA. a: terriç B, a funt zqua iaiam fu-
. man quodcunque multiplex ipfiusG. par: 8. Ergo cum quemulnpli-ciuipforum A. à: B. qupeun ne mo-do mlelpllcenmr, fin: æqua la l’un. .puma vna dallaient imam fiel C. l
b (par. val vnâ æqualia grime, val m exce-
ri dent, "in dompta exernplo. b. Ex-l gain eadem fun: anone. Eodcm
modo dieam multiplient: lpfius C.pute à. vel’mlnorem elfe 12. 8c 13.:-quemultâplicibus A. 6:. B. 76.1vaau au" . :1..an Initiateur. V
k
à
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ille; pima" a;l PRQPOSITIÔ VIH. 4.
un 1 6 3 I 4 1714711414514»): ml-! A B ’cgnimdinumAÆma-l 6 in A. 44:01:10?! C.
maure»: rationna bain, quiminorB: fluaient Cadmi-uarm B: micromlbalæt me
,1 tianqm,gu4m 4d migre») A.Rob. 1l ars.Si A.efl’ctèqnâ.5
lis B, ve fi A, 8c B,aequalitercontinuent C,èandern rational:haberenta id. C. a: C, candeur a 5. , Iad A.& B,çer przcedentem : (cd nef? 3maie: poultur A. hoc cit gloirescantiner: G. ergo pet de nitrognom 8.11. maigrem habet’ratio-nem ad C. Prob,2.. Et quia C, lu-ries eonrinerur ab A, quam B,-minorem .habebir ad A, ratio:
’ nern quarn ad B, per a. clef.
ni.
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,19.
13.!.
a 8.!
go y mais. EW
Pnoposmo 1x.A B C 2m: AB. 4d 24n-’f 15 4 de": C. andantin-lmxt rationna) agitait: filminterfi,0 ad qua AB. "de"!C. and")! babel rationna, b4gangue AB. aqualerfint iri-
terI . - ’v à.Ienim «lices A. elfe mains
quem B. ilergor’naioreznna-rio naioris A. ad tandem C.
p quàm minoris B. ad candem C.Item maie; ratio ipfins C. ad B.quamîad A, quad dt contra hy-
perhefim. o
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Liber gnian" :31PROPOSITIO X. *
I5 8 4 Imam magnitudiq unA 3 (3mm: AB. gymkhan-de»; C. balzan: ratinent: gusA. ration"): maint»; baht,hac main e]! : ad que») au-tan B. «du» Camion»; r4-n’anèm hdbtt, hac B. mineroff.
si enîm B, effet ne ualis au:maie! quart: Anima crent A, * 7.5
a: B. tandem rationna: ad C. vcl b 3.;B, b baba-ct maïorat: , and dlcomté hypothclîmJtcm C. ha-be: maiorcm arioncm ad A.quam ad B. minot cl»! A, quamB,vel vtrumquc , quad dixi , (c.quem: abfutdum, H31: connu.tir 8.
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. a; wwwa? "PROPOSITI’O. xi.
L a?! ’4 H fifi mimi
I . .A 9 È 21C muon", l86 F 4D: inttrfifimt:
’ 7-4. m 31- «dm.K;6;M.q4.l..48
Il 8 16A.Jar rident: Nid B. a: C. ad
D. eædcm, rationi E, ad F:«jam A, ad B, fic (Lad D.czdcminter [à erunt.Prob.pet 6.dcf. hu-ius. Si çnim fumantux ad 0mm
. antccede’nm: A. C. B. aqumul.. iipliccs GHI, a: ad configuemès
DDF,çqucmul:ipli ces KLM.fem-pet Ve! "à dcficicnt, yel vuà ae-gualcs nuant, n! fin: enculent,.1: (me: in fatum.
P60:
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I Lihr guigna; V unPROPOSIÎIO x11.
- 4 z ,6 3 si mt Imam neA B f q q un.1° I mlguimdim: pro-A c B D portionnles ABÇD
qxemadmadvmkabuki: vu anhadenfimA. ad au»! coufiqunn’fim
3.. in 0mm autmdmmA C. ad "me: (endiguant:BD.
V06 flop. t. de proyortîoncmultipllci dcmôflratur, hîc .
de. ennui fopouione ctiam in;-fionnlièlîcnditur pet candë 4m-math a: dcfin. 6. fi fumantur au-.tcccdcmium fic confcqutntium
v aquemultipliccs. Ratiq autangaz: crans cfl,quia cum ton nihilfiat aliud quam cames (une par-tes,quæ cric ratio A.ad 3,8: Cm!fi, cadcm cri: a: AC,ad3D.
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1’64;
,31
a; hm". un» PROPOSITIO .XHL6 43 a. 43 Siprinm AndA B C D- M: ficundam B. ei-de"! habitent ratinent, quantmm C. adqudrtam D. ter-ri»: ver?» ad quartant , main.un: bahnm’tmtianam qui!»quina! E. adfixum F. primagangue A.4djècuuddm B.m4- me»; ration»; 1:46:61: au»: I
3:13:14 E . qui]?me F. Îfllob. Ramones A. ad 3,, a: C,
ad D, fum- fimilcs ex hypotlnv: qui refquialccxz. Ratio C. adD! maint cfl quàm E, ad F, (cc.quircrtia. Ergo :atio A, ad B,ma-ior cfl: quam E,ad F, pçr u. 8: 92-.(et à figno cum denominatot. A.cd 3,, la î a, fitmioxguam E, ad
I .z
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la" quartai. 2,;’ PROPOSITIO XIY.
1" 3 8 11v Si prima A. 4d un:à ,8 â 9fèumd4m B: can-
A B c D du» habitent r4-tianem, qua»: trin)
C . a! quartant D. prima ve-r?» A. qua»: tanin C. "nierfuerit , critzrjèmnda B. m4-iar 1mm quarta D. Quodjiprima A. fueritcàualj; untu C, cri: à! jèmnda B. 4-9144113 quarte D. Si 0m) mi-
nanominorcrit.PRob. si: A. maïor, C. minon . g. , ’
- crgo ratio And B.maior en;quam C. ad B, Ruyrfus cil: C, adD,ficut A, ad B. ratio aurcm A.cd B, maie: dt. quam C, ad B,nmaior ergo en: ratio C. primi bu. çcd D, fecundum, vquam C, quinti
va;
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çmJ.
d»;-
en
in;gray
:36 Blum. 21431345:3 8 n. ad B,fcxtum. Minot9 9 9 cergo ca D.qunml.
z 8 a 4 Sir A. çqualisC,e-A B C D rit; urgoA, ad B, Y:
C, ad D.&quia C, adD, à: C, ad B. ratines. «audcm funtrnioni A, ad B, étant 1
I flaque C, ad D, a: C, ad 35e:- jemmtcr (e. ISi: A, quant C. miner, ’ mais:
exit ratio C, ad B, qua And I:litent-minorât ratio C, grizzlyad D, fccundun, quina C, quint! lad B, fatum , minus cri: B, g
guzla D. V Ill
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1.550! Quint"; h 7.17
PROPOSITIO :xv. »il ’3’ B 7 lædrm’ABmumC ’4’ D 35’ paner multipli-
cibm CDJ’n endemfint m-’tâçnfifi prout [Mi 1mm refi
pondont,imfim4ntur.. S l: A, parsipfius C.& B, ipfins
D, cantine: C, unies A, quia-tics D, coatincrigl’am B. 0353 a-
o un: anteccdentium A, advnàm confeæncntium un l om- -
mes C, ad macs! mices .anteccConfequcates D. Ego v: (1,64 D,
’ il; And B: 4 »
r in
à. 1;;
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* D
fifi
1.58 Un». nidifiaa ’PROPOSITIÔ xvx.
, AT B ï «un»:c D - V "inti-n; I .5 ne: ABC ,D. pro- d
fouinait: funin: à ricifiin’ proportions!" on Mn
Oc en , fifitA, ad G, finir 1A334 D. cri: permunndo v:A, ad B, in C, ad D. , a’ Prob. Sup namus enfin A:continue C, is , fieu: continuD. (i diuidamus A, in B. bifa-u’àm a: g. in F, cri: E, æqnalis C,
a F, æqualis D, [cd v: E, ad F, ;fic dupla A, ad B, per u. Ergovt
v dupla A. ad duplam B, fic G, z-Paalis ipfif, ad D, æqualemilafi
t
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Lib" quintal; 2;;pnevosmo xvn. ’ *
magnat me: gl a: m proportionalc:
à. . ’ fuerintîi haA If gangue im’fic
- 8 proportion!"chant.
Oc efiA.com,ofltumex en.a: B. ex Il. dentu: : ô: fit n A;
. 16. ad fixipaxtemD.4. in B. 8.ad1?.la cm a: v:C, n. «19.4495. 6.adF. a,
1d ptobant Theon 8: alii yer a-que multiplias. Dibualdus quad l-m: raquent!" gamma cite qui:lemmn. Nos fic brame: A. à; B. a 4;pomma: pxoPoxùonales: a çrgo fi- nef.go 6min ration: continent panesD. &F. [nua quater ’ cxgofi adamëfuis fingulç rotis aufenmur, 5mm-tex in refiduis AC. DE. coniinebune
. tu: exit ergo v: ac. ad (2mm BÉ-ad En
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:4 or " mon. Euclidix.
PROposmo xvm.ID d Si du]; m.
I 4 3033411.)!!! finTua. C12! pnporfionalea ,
hg gangue -cô’«
"le: "tout.
I: v: DG; MICA. in 121-1,:EB. Exit a: AD, ad DG, x
DE. ad EF. A’ Prob. Ex hypothcfi par: en!r DE, fimili ration: continent yar-
’m DONS. ergo fi b8, un: ad-,danmr, tout AD, BF, adhuè fi-
’ mili ration: condncbun: filas’ partes DG. Il.
â
f
PRO-
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13h? quËntiùI à, 4:
Pkoipogx’no xù’cy Je
Si jucmzdm’a- fila
I au)» tond» ÀmdV ’.F2 hmm B. un a.en E6 Un"); CD. (à
t Infini: . a?! a., v Hua?» Et. à. ra-fle; 8 quuum ("A ail
l v üüqqum .Bhvid rotait: ADdeotumBF: [chuta
L in). -’ Paul). .AD. sa CD. ÈF poanuüthr proportionalecss tri!
auge v: F8. ad EF. ira AD, ad îCD. Ergo b exit vï FE ad E8. in
’ DC.,ad CA.!Ergo v: FE. ad DC.v in BE.’ ad AC. hoc tf1! Vt-tbta
AD. ad miam BE- cum pofita (in1113.14 DE à: ad BF. I
V Breuius quia aliter 0mm: par-a tu d’un mannes minibus gag;
tibus, gnan: togum au;
4’
râk;
x74g
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170.10
18.;
un. du». Enduit
PROPO SITIO XX.u. 9 5 Si finttrermagnitu.â 2 C dine: ABC. (9’ dia: ÏD E ÊDEF. if]?! 1151416
ramera , que [aime (7in «de»: narine finnanmr(hoc CR Vt A. ad B. na D.
ad 15.8: vtB. ad C. ira E.adF. ) Ex aequo duremprima A.qua»: renia C. maiorfuerit,"iræ quant D. qui": fixa ’P. main. godfiprima terri:aqmlnfiænr , ni: (9- quartaaquali; fixa 3 fin i114 miner,
’ hm 9140un minorait.
PRob. si: maioè A. quam C..luge maior critratio ipfiu!
2d B. quant). ad 9m amm-
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I a: aqfiîltfl. a."v: A. ad B. in D. ad E. &’v: B.ad C. ira E. ad F. Etgo canner.rendo en: n C. ad B. ita F. ad E.-Ergop. ad E maiorê la, habctra- Vus:lion-nm quam F. ad E. quarc ma- d ".5in: c d! D. quam F. Haud (un:concludam fi A1ipfi C. :qualîsPonant au: minon? Intcrpme:Idem probant de quqccunqucmagnitudinibus . non de tiibus
xanmm. a
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n. u.
144; Un». Ëmh’dït
PROPOSITIO XXI.
18 I 4 .Sifinlmr rugi-Î7: Staline: ABC (’9’-D E P Ëfiquualunumerv
* EF. que binag-in «d’un ration: jümntxr,
fuefirque perturbant un»:propania ( hoc div: A. adB.fic E. adiF.ôc v: B. ad C.fic D. ad E.) Ex æquo autanprima A’. quant renia C. m4-
iorfuerit: cri: (g- qutru D.’ 1114m fixas F. putier. agoniprima tertiæfueritæqudix, cri:(9* quark: 44144113 fixtæ, finil]; miner, ba quoqugminorcm.
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LÀ" gainait, 2.4.5
P-Rob. si: A. maie; qunm C. zergo A468. maitncl’na ha- 38.;
be! razioncm quam C. ad B; E6:autem v: A. ad B. ira E. ad F. .Ergbbmaiôr cfl: ratio E. ad F. ["35 Iquam (La! B. Et qui: n B. saCita D.ad E. et o conucrtcng
.dovtC.adB.ita .ad D. Ergomaie: ci! raçio E. ad F, quam E.ad’D. .Ergo maie: dt D. quam n°6F. [démo endçtg: 6,4. minot
. (igné :311: 15.3
X iîi
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a 4 6 En». EmlidltPROPOSITIO xxu. Ï
n. 9 6 8 6 4. Sifum’n: guet.A B C D E E maque magnant
"’- "’ 1.4. 18 n. 16 u. 8 dine: ARC. du un
G H I L M N [il ipfi: «palu.v plumera DEFqun
En bi "la: un)»: fummtur(hoc cil; v: A. ad Bit: D. ad 5.86v: B. ad Cita E. ad F.) à» a
. gallium in «de»: mime mît; çfloc en: cri: A. ad AC. fieu: D. adF.
Pkob. Summum ipfuum ARC.. æquerpultiplicia 6H1. &ipfarumBEY. squemaltiphciaŒMN. cum
us. s. fimplicia fin: in «du: ration: AMI
r
5
î
l
B.vtD. ad E. 8:8. ad C. VIE. 111E.a «un: connu multiplicia G. u! H.8: H. ad. l.vtL.ad M. &M. adN.
b 2°, ç Ergofiquotms magnitudines GHI.c 6, auna rotidem LMN.binzfumanmrDgf. in eadcm. (mon: quarumb prima
vlnmam m "roque enfin: fimulcxccdunt,æquamur, tu! dufîciunr, earum fim luesA. ad C. . n! *D. ad p mu un
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Lihr gainait. 247.rEOPOSlTI Q xxm.
18 un 4 Sifuerinbpes m4-A B cgnimdine: ABC. 4- TELL3.7 9 6 . .D E 1.- lzœque zpfi: agada: -i manne D EF. qué:
binai): «du» ratione fiançan-d tûrfuerit 4mm peflurbdtd c4...
deni raie (hoc cfi fit A. adB.vt 5.34 F. &.vtB.-ad C. *a. D. ad E.) au»: ex æqud: . .[farcin and?!» ration: mon ’ ,hoc en: vc A. ad C. in D.
ad F.) ’ -Rob. . Si Lundi: C.æqu"a4 a 1Mtu: vel dcficit; D. exccdctf. d
æquabirurucl dcficict. b Idem.que fic: in :qucmultiplicibus. c ,7.
’ Ergo ex: æqualitate in d cadeau meration: en: v: A. ad’C. in D. d a. ,.
ad-F. d A D4-X iiijk
hm; ’
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1094.
113J
148 a Elsmœmlidis,
PROBOSI’IIO 30(let4 1 5. Sipn’nn A44];
. A B C mutin,» B. tandem Ï3 If; 1è habqerü; radium,
u u que"): nm! 44G H guru»: D. bafiu- *
xi: un»; (9 quintq E, «fa.andain B. caudal: ratinent,quant [2x14 171M guru» D.5mm G. compofim prima (üquina, «véranda»: unde»; lmhbit "nouent . quant,H. 2m11 au»: fixa, 447140-
tam Q. ’PRob. Ex hirpoghefi n. «alcali;. pars fingularum A. 8: 2.1103-
lis cil D. fingulamm (La: F.Ergqun; quoquc B. un: pars capoti-tarum A. a: E in Ggualigcflip,(étym coxnpèfiçaxgpi in H.
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Iîhrguimw. . 14,04 Il("toron-no xxv, n
, Si qudtaarma-gnitudin’e; ABC.1 D. proportianlç:P 4 fla-finn- maxima,
A. éminima D.
( reliquat «imbu:a ’ Ï BC- mqiomr c-
A DE], 73111.1249-7 RobÆxh oth.v,9; V? P444 1.33 C. :5-’ a nm A. maior,abe
au fer-tut A. 9.:qualis ipfiC a: à 8’:tallant B. 3.2qualis mmiszÆxi’igitu: vnonlisA. la. ad parçialenA. mali: 3.4,. ad panifiant B. 5. a:
’ a reliquap. u.fcillcet;.ad reliquam . ,g. 4. tancer n. vt A. matin. 4. la: l "4P.mac maint «in. quamx. Ex . ab-lhmdamr 9. me: cl 1. finalisa. 4.hoc efi LErgo A5. Lhoceft met-Mine!magnitudipes C. 9. a: 5. 4. hot en x.Ergo A4. a; D. hoc eût). æqualeq
. (un: magnitudinibus C3. 8c 3.41.5go fi addatur [.112 hoc et! a. magni-çùdo A.n.. 8: D. x;.hoç c1! u.maiooLes (un gnan B. 4.8; C. 9.ho c en la.
77:. aï
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.130. ElenÆmh’dis
.PROPÇ’SITIO xxvx.
fl-”5’ 8 4 ç 3a sipn’nu A.dficul-A B C D, dm B. babilan) and»
nm rationna), qui»: ."m’a C. ,54 quartant D. 5550H:conmncndp, finaud. B. si pri-mat» A. minant» rational», au)!»
quartant Dmdnm’am C.
HÆc a: reliquæ 0&0 ropo- yfidones , cûm non n: Eu-
clidis, cas non aliter demonflraobimus gnan: indicando propofi-tioncs
continentur. 4Han: veto, propofitiona 4. bu-. in: elcmcnli confinai, pater ma.
lifeflê.
uclidis in quibus virait: I .
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. L556: aux»... V2.7!2109931110 xxvu.
8 4.19 siprima A. 4d]?-A ne DICllnddm B. habitait "417.radium» ratinent, 7144m œr-ti4 C.adqu4rt4m D. babebitquoque vicifiim prima A. ad(tentant C. "mon": rations-m,quam [humain B. 4d qui»;
un D. aContincturdèrop. 16.
..PROPÇSITIO xxvnu8 4. 5 ; siprima Anadfmm; LA B C D du» B. habucri: tufE n. F 8 in»)! niionem,qmm
un!) C. ad quart"):D. 5562H: 11mg" compofiu pri-ma du)! finauds E. ad [21.103lel- maint»; ruioncm , 5mm com-pofim tartis un» "un F. al
peut») D. rContinuum: prog. Il.
.10,
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, à.»
’ * mo-
zp. film. EuclililPROPOSITIO mina8 4 r 3 siæwfim il";A BC D. ma turîfuuù , ilE u. P 8 fmmùmB. union»
blâmât "dans ,qu)»: mnpojim F. unis sur:aux": Ml guru»; D. bûchâtgangue dinidcnda,prims A . 41 fa-
çunùu B. miam! ruina-guàm tanin C44 quand»: D. .
Continues: pmpofitionè x7.
PRO? OSITIO. X XX.g ù SitnnpofiuEpnbnl.A D, fcmdzndfiaudanlsc.Bi Fsbmüuuùmuçnùpr.
z pangolin 1:1thgmc,dçumnp 54W?" 4’”adieux: "timing": :30.me E.41mm minimum". yuan:mùmguflaldwmc. -
Càniinçmrprog. la.
j:
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librquinius. iyàPROPOSIT! O XXXI.
16 8 4. 9 5 à Si [un tu:A B C- D El: m4 limdihe:
*AB C. a 4th: api: agada:hantera DEFfitqu’: maiorm’a
rio primé priant»: A. calfe-cundam B. que"); prime po;
fiaient": D. 4d [écundam E;lUn» ficuhdæ 12mm»: B. 4dn tan-Mm C.m4iarqu4mjècun-Tdæ pafleriorun’l E. dd tefliafri
faF. cri: page ex æquditat:d mxiorratiaprzmæp’ridrum A.44 œrtùm C. qùmprimæpdcfleriamm D. 4d tænia»; F.
Continent grog. 1.0. 8c ai.-
le. si;
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76.1;
a Elena; inclût?PROPOSITIO XXXIÎ;16 8 4 fifi»! tu: installai?A B C ne: ABC à dia ipfi:9’ 6 4. qui" humera DEF.’D E F fitglu "nier utip pri-
. ’ un priant!» A. giflai. adu» Bqunm faraud: Pofifl’ùfllm aE. ad anima F. Ittmfi’nïdc pria-un» B. Ml mais» C. qui!» pli.æu paflm’ornm b. au! [cumulant -
E. tri: quoqu: ex aqualiran,main "rio prima priant») A. a ntanin; c. 9113)» prima pnflcn’o-un» D. qui tanin» F.
Continent: prop. 21.8: 1;.
l
1
PROPOSITIO xxxm. dIl 6 Sifimù Mnramm’îüol. îA B dans: I. que» du. (.113
ablatmDJriI ànliqm’E. cd aî reliqu- F. and" "de, M
mixa A. Minimal.
î .F . dl
l
Haï»;
LCominetur propofitione 18.
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v
Lihrquintm. 1;;’PROPOSITIO xxxw.
la. I 4. 6 y; Sifint quot-A B a .D E cangue m4-gnitudinuABC. édicipfi: *
Y æqlule: mantra DERfitquî maior nui» 1mm: prima» A.-. adprimà’ pajlm’arü D. que)»
ç ficumlæ B. adfitundam E. àLa B. ad E. maior, qui» ter-piz C. 4d terni F. àfic dain-ap: : [mâchant 0mm priori:jimul AB C. 4d 01mn! pafle-
’ rions flaira! DE F. maiorê’m-Ï
3150125, gai omnupriore: BC.b relifiaprima A. 440mm: pp. vv fierions EF. "lifta quogueï prima D. miner? 410?, qua»;
prim4priorum A. adprimampofleriarü F. marbré" daigne ’mi qui abîma priarum’. C.
Ï ad Vitimamptajfeziorum f.
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53;: I h 4 l Ï&ÆÆÆÆÆÆEVCLIDIS,ELEMENTVM v1. 1DEPINITÎONES. d
r. Similej’ p figura . "au-
D au 124m, quad
a a: r gagée: fin-, gala: fingüliy qui" baba»),. figurefiamlazefa, que «me.arguas maki Propre
’. üpfiafino
i
D’as conditioth requisit.A, k in. "anguli Enrgçqualcsfin-gulî finguligvthic À. 8: D. B. 8C
. C. &P. 2°. vautra du: a;«au Mo! a r" émion-
fiïlhbc «in: Fa 19:13:: 311,36.AC, v: BD, ad D1" quad fi ha-
’ D and!
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C
Libüfmmn. am,’ 1mn airera dcfn, mm dicemu: fi-
milcs. si; quadrarum En a’t’c’va
parte Imagina non fun: fimilcsfigura
n ’c fi" 1. me: sehâter» " I m,
. .. par, Çfim’înë-
,F traqhè fignht,I . , . aquatinte: d
a confinent: animantlamina. fmrbn. a
HOc parc: maxime in paral- .klogrammis 8:.triaagulis:
mm fi qua ration: AB cit ad BD.in eadcm fi: BE. ad BC. crun: te-tiærocæ figuræ. mm in vtrcqüee antccedcns a confcqncns dl-ucrfamm rationaux. ’ ’
’ x
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Ë.
.95! au... ficelai:. 3. épaulant "d’unà» ondin» actinium , î:Ai. En A5. [c514 a c dia-ù",
un» au un; A. ad malin:[magnum AC. in qui»: AÇAj
’ gnian; fihhablvuriîo
. 0h. miam. fui viliwcm s hicprôqutio , digina çommünikct.
rggçllztlplr. I ’d I A L 4.. Altitude çuiufi
" * guïfigura, a1! limaftrpapdjçubari: AI).à vomie: «a; w»
(dudit, ï ’in c B ’ ’ A
cm." Ai: Ptol.lib.dç nahua. ï(au cüipfqhe toi debeàt efl’e Rata,
D merito Eudidesoà peçpendiculari», iuldincm pe’gîÏ cuiufius figurzzfq-
la efiim pçrpcndîcularisa dt fiat: a:banlon itudin’xs :I banc Vero un:indium ib. a. vouait çfiçin au?Pwvmflelia * v a a *
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13.1.55» final. ’ in
y. Ratio, ea- nm’anüu: «0me .
dicimr. rima ration)» quantita-t tu, inter]? multipliant; alignant
afeurim rationnant.
me»; Euclide. voeu quamitatearationnant. folent Geomçtrz vantaDenominarorcrn. Numerus enfin et311x20 peintuç- nomen ptqponiorrîl;fi: a». CR de minator ramonât qua.drupla g. t fla, tarir) lima: en nerionibus [agoni dicitur. quandobarrant d nomïnatores feu quanti-tatesnti and! inter fa multiplientaîrquam . aliaîaationcm îecetim.si: ex En: u h 1 trip a con. ’gonflés. xtuphâuzxïfi ratio et ta-Ërfiribus mm (sa ce ponitur etmon" tore duplz 1.. a: tripla s.
intcrùemrn multiplie tifaciunt 6.dcnomînatorcm ra t ’s («tapin
«moflas. -
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un EhmÆmh’dir
ÏPROPQSKTIO I.
erv AtGADu. T.Wî V la A 3 C.DER à t. ’ par!!!». 1 a: ce r-- r. hmm
9&4 ÎCG. DE. «au», * calenaltitude GH. 8P. fait Intermi-ntfi, ratafia BC. El.V De&,eam inter fehabent ra- ’I floué narn bafëà.Pro’b. Trii-
illf. 4 gnian dam altirrrdinisa ana3* inter parallelas confinai: mua .
imam qu: :qualcîrr habcbuntbafim, crunt æquaîia,guz laio.En: maïorat, qua, miner mi...nora. Idcmqucceft dexquemulr
° W- tiplicibuè. r Ergo abfolutè trian-guia f: habent vt barca. fimüiter.
ne parallclogramma; cum fiat ’d au. 11918 d triangnlorum.
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Ï.Lihrfixml .v a6;
PROPQWSJTIO n.A * 55-adtrinngxliÂBC.
lamantin» CB pa- 11,4.fiât-111d.» duastur ED. ’
, "(in proportionnât"c B feula": ipfilu trirngulilaura AC. AB.Etfi tringlai].-rcià,piofiàrliwr4üurfc&4finr.a.au DE. pçrfiâionet 45534, Erikpanada a ad reliquat») igfiutrianguli 14m: CE. . IRob.Du&is duabus mais 23.!) 187.12
(La cranta triangula EDC. son.» foyer caduc Bailli). rumina. b h 5
dom patalklu’EDÆLqulaül. un.go v! AfiD.ngCD. in AIE. «se. à. Ç funtenim in’eadem alt’rtugiinc)& c fi.-ü: noua on. m A». ad ou et. 7.5go v: AE.ad EC. ici ADJdDIJ’o- -nanan: veto latera AC. A3. propor-tionfliterkfla hm). un: 45D. Id VBEC. candcn’habere rationna. quiad EDB. Ç mm en ngE. ad fic, fic ,At). ad Dit cum niangon tînt eîuf- Adam alûtudïnis’) cura! DUC. BOB. l R 9 .
ualia . a: qui. tu... in calera un. f sur;
fi tarant napalm? r
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un IMÆMËJÏ: V’rgopcsi’rgrd un,
siniduzrli A80; aandin, A. bift-n’àmfiëusfi r];-
. en»; un»! angu-’n lamas AD-fefa: à hl!» BC. bali: [agneau ABD. DC. and"): Inèrbum m?» rtungar"); "ligua trianguli lan- A
je BA.AC. fi lût-[ù [Emma dBD. DC. tandem habens: nuio- jnm, quant "ligua "l’ampli 14- 4un 8A. AC. radia AI). par Averrier Addfiëfionaq D. produ-titur, bifilriàm [un trianguli if
. fi»: "galion A. : i
CE
7M
t t f Rob. Ad pundumlflagamrBEJ DA. parallela, curCA.
- 1.9.1. produ a boçcu’rrat in E, tuneI 9 19.-: cri: mA. . aeqùalia alterna BAR.
- - a: E. externe BAC. ergo «unN°291? www .
v
I
Il
a
I
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-- æ-rr- -v
n Lîbctîfcztm. u;gageur , errant angnli 85A. 8c E.æqualesjc reflue BLAE. a æcjua-1:3. Ergo cumin triangulo BEC.refis DAÆE. yarallelæ tînt . r:15A. hoc ça BA. ad AC.e ita BD.ad DC’.Sit mrfus vt 5A. ad AC. eufic BD.ad DO. y; auteur BD. adDG. itaFcü EA. ad AC.: Ergo f üà 8A. ad AC. ita 8A ad AC)! z- [Hquales et 63A. HA. 8U angulr . a. s4ARE. a; . Cüm ergo. ARE. al- * N-tetno BAI). arquant fit 8:13. ex; ’terne DAC. cran: angul’r BAD.
d La
LPAG ëjùikîc ”
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l54 l’un. guettai:PROPOSITIO 1v.
me r Æ!"WJ"Ï*. ü un "in: abriC B E ACE: DE . pn-
. v V . remoulut [mulatin (hoc efi vt AC. ad CE. à:DE. ad DE.) que du; quiet!ongulé; C. (9- B. à 501501034 [un
laura gAÆD. yangs-aidant»!gulirC. à. B. fabtlndfllfltf. 1
Rob. Sic in direétnm Rumen-lêtas C8. DE. w angnlus entrera.
. 13.! DBE.interno CÆtzgnahsnuncDL8e AC. I cran: yarallelzzfim’mrer cl
- ED. BA. cura anguli E. a: ARC. tu.zquales. Et quia angul’r ACB. ARC;
19.194. hoc b en DEB. minores fur-At e duo-Ac r7. r bus reâis. fi producantur ED.CA. Id 4x. connement d puta in F. e liritqut:îu. DA. parallxclogrammum. Cam igr- .e 34.!. tur in triangulol’C E. refis DE. tu;f au; fintparallelæ. ferixvt ED.ad nanan
cit BA. in E3. ad BC. Cumque tuIl fin: item parallèle, en! Cu. a!DE. vt CA. ad Ali. hoc cit BD. du!A3. ad Bain FD. hoc si! A8. ad
PRO-I
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lita) mais: a;151m posmo V.
I SI du (rii- .A gaz. "A B c, "a? 1X E F DER; la":
’ BC. pif-,4c a - pbrtigndù.
B ( ipfis D E.21.13 babuàiht, cri-lmllguùnguà14, ufdanpqüc qbgulu, DA.EB.
CE, bahbahuant; gain: in: l-În’ologa litc’ufuitèndumu’r;
RasIaLVSuiSerteïâ: Flac! immun) Rayonnant in un: HG. àn- à g, ê
I119 B. æquàIis 8c; , P. mais 1951C. .- confequente: reliquat G; aligna b V t
A. bzqüalië, ficque fiant iriangulç 3’”
ARC. EFG. æquiangula. 5 Tan; (andV Lî’kquales anguloà A. a: 6.: «un jard;
à pardonna Iatel’lÂÈAâ AC.thE.’ c" 4- àLad GF. a: A]. and 8C. v; GE, ad BEL * ’
a: AC. id on. vt sa guinchai. A, gal: plat-fluât: ingngenpymmne a 9.;ï En ponuntur, :41 and. grima 2-; 3.319v. maux): ip G. a: finalisme! au. EDEF. «musulman ipfi AZBCx
f * xh lr . . t
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.266 1 film. Emb’di:
PROPOSITIÔ -» v.1.-
Si du tringla.ne? .. ’èé°, la ABC. DES.
4 5 - 1mm» hxbuntB C G quai")! angu-
3 la"! A. D- (9’ Imam cirez au!»’ propaflionalia ( v: 13A. adACJta
BD. ad DE) "un; gquianguln, .angulofqm babelaù’: qui" RE.CF. quibus hom’alogn laura En. . ED. AC. DEJubnndumur.
Rob. .Ad métaux EP. angon):FEG.EFG. fac zquales ipfis 8C.
un: a: G. munis A. qui: ergo squi-’ angula fun: ARC. GEF. I Hum: vt
Muni ACM GE. ad GF. pxoçor-b "’ tionalin: fed fun: miam Proportio-’" 9* malin au. AC. 6:05".- DEfifimter-c 8*! go huera DE.DF-.iplis CE. GE.æ-
34.6.
a A15 qualia. Cumqu: bafis EF. fit comgnu- ,nais. triangula DEF. EEG. c zqunn-gal: (nm: d ergo «la!!! zqnianguh
ARC. DER Ia .-
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Liber fana, 161PROPIO’SITIO vu, ’
« Si du:l trisngldien: ABCDEF n-7o Î, 14’111!" un.B CE F gnian» A.
and mygale D. l’aile»), circulaauna) , dans angulos C.F. It-nn proportionnlia habla»; ( v:AC. ad CB.ixa DE. ad FE.) "hlquanti» un) B. E. fini»! 1491m); »
A 9m. au! minore": au: nm même.rem. refis: aquinngula arum triai. V
gain,àqrulnhnlnhmunguln ’AC B.DF E tircum que: [un pro-ptm’oulia un", 8c angulos .a: E. zqmlcs.PRob. Si: cnim 8.8: E. minot
mélo, tune fi anguli ACB. à.P. non En: æqugîes, fit ACB.’ma-
in: quam F flanque ipfi F. arqua.lis ACG. cum igitur angulus A.angulo D. papaux: æqualis 1 «in. ,34.a: reliquus AGC. relique E. z. I
. qualis, idcoquc triaznggla AGC.
I , q
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1 un. Èutlilîâ . ,,un n D E F. il;man
b 4j ’ Euh. hg;-. ’ ’ o vi AC.B CE F à ce. inexit Dr, a! in, :31szde
c :st 17E. in punira: AC. ad C3,":. figitut AC,adCG.icaAc,adCB,
. N à: propzercaa aqualgs CGacnia: e an’guli CBG, CGBiaequalcs.Cuir: igimf angulus B, lit Mao
ï in minot, cri: 8c CGB,minonp&o,&ci deinCeps AGC. fumier re-flo. En: aucun oftcnfus àngulusAGC. angulo Eiacqualis. Maior
V îgimr CH: rcâo angulus E, qlli« . minot pouchatur. , .
à t 3.: 15 fit au ùlus 3,8: E,rc&o non’ ginkgo abitur v: plus man
CB,CG, tif: aequales,& n confe-5 quentcr angulos CBG,CGB, cire
4 h un .’5 «31315.45: non minores-dupbus1’, 1’: 15,h quod CR abfurdum. Non
ergo iniqualcs sût ànguli ACE,la Plu! acquits, a: coàfcquenpterrdiqui ’anguli B, 8c E. ’çqu.
7:5,quod cm probandnm. ’
9»4--g-7lé.--n«’ Mr M -»- -
Q î. au
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l
Liber fuiras. 26, ’
PROPOSITIÇ) VIH.’ ’ Siin triuguh
84»;qu BAC. ab 1-5.;tagBIoBéeflo Afin. ’
un. . en À.æ .7 D c min? Aydsflqfit .- que si pqpmiiculnm "fluait’ADCADB. par: zoritriangula ARC. ’
çlfmiffa ADC. ABD inurfi
Il. .JP Rob. In triangulis ARC. BADJanguli nAC, ’ADB. xeâifnntêc
ingulus B. cqmmuniszcrgo dreliquiACB.BAD.Iz malcszçrgptriangula 3313ABC.ADB.b rm’xlia. Non aliter o- *mandera: ADCJinfiIe ABC.&ADC. b ’-
txiangulo Ann. ’ ,4:(mil. 1. Pqpmliculari: ü "(dene. in bah, gfi mât Wfimfilil!" 414004: fagnes". , . .cNam vt BD. adDA. in DA. ad .ç 414DG. quad cit :eôtamDA: elfe me: A *(liant propoççipmÏem inter bali:partes BD. DÇ, v’
Coral’. z. H3: ctîam garez vum-libcthtcmm angulum rectum am-bientium , medium progonîonajeimgnozam bafim a illu remuen-çun; bçfis quod c1 land agace;
A z. u;Â
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5.x
I :70 1km. Euclidù
A trin.
v. PRax. Ex A, &uèarur reâa AC,
v PROPOSITIO 1X.
Ta a! data "a!En A8. im-pfrnî par-
’ r2 puta tu?tiam AG. aufcrrc.
T
vtcunque facicns angulnm . a:v - exAC,fumatur quæxlis rars,pnu
. AD,,ac du: aliz addanmr çqua-l les DE, EF.iungatnr, FB, cuit:D? patafiola fiat DG, crique a-hlm AG. pars tettia ipfius AH.
Prob. in triangule AFB. lazzi.y 5,5. BF.parchla efl: [inca GD. 3ergob 18.5. cri: v: FD, ad DA, in BG, ad
6A, &b’componcndo vt m, adDA, in BA,adG . m autanAD par: renia il ms Aï. Ego
’ AG,crit parstemaipfius A3.
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Lîbzrfumr. z 52,7";
a .PROPOSITIQ x.
Dard») rafla»; Mit
V infifiam A8,];-D Xx-LÀH militer ficaire, wx...) data alter-4 "(in
A? û HA A C.ftfl"n funitin D. 8c E.PRax, maganant datælincæ in
A. conncaamur méta BC, La;exD, 8: agnelin DE , EG. ipfiCB.wrallclà,& faâum en: quad
petituç. I a I, v7 Piôb.1nrriafigulo ABC,du&æ ù., (un: DF,EF,paralltlæ latcri BC. a L5
I . ergo "AD. ad DE, ira AF,ad. FGzl’roRortionalcs ergo sûtpar-
tes AI, FG, partibus AD, DE.hm fi ducaton DH,parchla’ipfiAB.eritÏ v: DE, ad EC, in Dl, adlH,bhoc en: FG. ad GB, quarc 5 34m;
J; proportionales fun: panes FG. aa en, partibus DEJËC.
A z iiij
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in: 1;ka 22mm;pRoposmo x1;
Pat”. E Dam, 4144614; r:-fiir. A3. ACM.-tiqm prqportinflç
’A B D CEJnuenire.. RI]... E’x dada AB,AÇ, fac
anglican CAEüqnge urany-guc geÇta CB, pmaqclatera A8.AC, fumeipfi AC, zqüalexp BD,duc DE, ipç BÇ, finallclam. Re-* 33 CE; agit ténia piofiqrtianalig
uæfiia. , "I ’ . "Proh. Rcâz BC,DE, fitnt’pa-
à 15:5: gallelæ: aCIgO vè’fé’habetABqd
P M. .BD, in AC, ad ÇE. En: alitent!’ a BD,ip(1AÇ, æqualis ; 1’ergo y:
(a habctABJ ad AC, ira 3D. hod,cfl: AÇ, ad ÇE, quod dl CE, ça:flapi cire priopbvgtionakxg; "
a
ï
4
1
l
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&Ïhf [531’442 2,73,
PROPOSITIO x11.
E Tribus dais rqf 1 A (1’13 A13. BC. AD.
- 9144m4»: proportio - "95-. 1
A ne 341?")k (tin.Pan. Ex datis,duas AC,BC,’ 4
l in dire’âfum ;côlloca , ex au;
na AD, a: wtali ACJac angu’. ,nm BAC, iungç mêla BD, a: fac
7" i911 parallclam, CE, qûaçtatopordbnal i; eût.
a Prob- CE. BD. fun: parallclæ;’ ergov: fe habc: A3. ad BC,i;a i zig46D: ad DE Ergo DE, quarta dté’ës’rcësionâlâïe I . * a ’ .
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:74. ElenEudi dis
PROPOSITIO XI".
rhô, ç Dam dauba Irefit) A3. B-C.media!» propor-
rA E P Ç and"): BD.Menin.PRax. Colloca in direQurn
A3, BC, fuper AC, duc fènii- .Icirculum ADC. In B,excira per-dpcndicullarcmdBD, ad fefiionem
d femicircnli , illa exit quzfita." Prob. Quais mais AD,CD. î3 erir angulus ADC, in femicir-
* 3!” eulo retiras: avertie: D.ad ba-ïfim AC, ana: perpendicularis ’
b 8.5308. faci: b ergo duo qiangula:qaiangula: c ergo ptoponiona-
c 4.6 lia: ergo vrAB, ad BD, ira BD,ad BC. efi: ergo BD. media pro-yortionalis inter AB.BC.
------..-..w. .
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h. ...,Un.
1 Iïûerfixtm. i175. 4PROPOSIIIO x1v.
A D c g Æqtmlimn 48, 1, DE, é- ’0an A 712.9A - B BC,m’EBG, a-
gaulan- habrntiü’
EI angulum , panl-lllagmmmorum, reriproufum I4-"!!! A3, BG,EB,BC,1u4 aima»aplati: algide: : é- quarrir") pn-rallalagmmmomm, 1mm» angu-lum mai angula , qui"): habeas-V.sium , nerprun fabulateur, "un Üchum qui" onzain. 5114 Il»:
«malin. d *Kobjunganrur parallelogram- wma ad angulum squalem B. ira ’ , 4
vr AB &BG.iaccanrin direâunh ia- a ’4-cebunt a; reliquz EB.BC. perficiarur (515-1yuallelogrammum 3H : ergo yr’ la. 7- S4d EH. irai: cri: BD. a’d 13H. fed v: C 1 dFB. ira c en EB. ad BC. 8c v! DE. adEH. in AB. ad BG. igirur vr E3. ad3cm: efl au. ad BG. d m; 1
Prob. 1.. pars. Ex hypolh. En. ad 1BC.eû vr A3. ad BG : ergo c ÏBB. ad e 1.5
A Bu.eay:DB. ad sa. f up par. f ,4, *lelog! aminaæqualia fiant.
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.1 .. L .... w .,
.. , Î Î. : ... : . w... .0. a. a .
.
.. çïszv. 1 . fir g Ê? ï... â.
.
v,.4.-
Uildvad r
4o a ..2 a .3 .î
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m. *0 XVI.yuan"? fait” z B, pro)...du funin: ’1’ [nô urubu;
r BG. rompra.r’ A C, 4,114.
.71 151:, F6;6213qu EG- ,ËBC, son:
m 4C, 4.la!» "me;rafiafigulo’
propanid-
li rem É;V: fi: habetSergqla.;ulos B; a:parallelo- in]qualia. l -îigula A,
rquales;go b larera’ B 14.:
.Cclvhroca;
Tiré g
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a7; d 51m. Hormis
211012051110 xv.N Malin» A
A Il! ne. osa. à.n. a. B ’X un 8. mi’ A landamm-bnm’m. -
C . .5 M,m:;57.4ru, mipmafuu («en vr An.ad sa.ra DE. ad BG. würmqualu a.
galet B. é- querra): triangulation» au»!
aussi" and, qui": htbtfiflm , mi-jnulut lanugo; 5m agada u-n» «au *
Rob. sic iunge triangulfi ad an-gulum a ualcm a." A8. au...
l 7, g, nant in dire um.dn&a CE. "tu v:A I ABGad BCE. ira DBE. ad ICE. fedb L g; vr ARC. ad BCE. in A3. ad 315.6erA ’ D315. ad BCE. in BD. ad 3C. Pari-
. torque dèmonfirarur ABCDBE. Jez nana. fi fitvr Alad taira DB.adn . Nana carra ponamr vr au. ad DE.in DE. ad ne. a: "An. ad BE. iratriangulun’r ABC. ad 86E. a: vr D3.ad ne. ira DBE.ad BCE. un" ABC.
, ad BCE.ira DBE. ad BCE.ergo trian-t 9: ’r gala AIE. Un. c [ont gomina. "
z
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H tihrj’cxrui. i a???
,rRoPosxTIo xvr.. I . Siquaruo? MM.,E’A 73. A 1: z B, pop».
Iï 5E r tincal" fanimâ’u fil l la guadfubtxrniniab 4 vu I AB.BC;compr’e.L d ditûrkrlfiiàngulufiiACMquà-7e. (fi ci, quodfuô vinifia E17, F6;
mi ;
egçmpnhenditùr, réfrangqu BG. .ait-fi [ab extremis AB,BC, uni-) :hcnfitm "flagada": AC, 4-
1’ mule falun bi guéri fui: "IldiüG. EF, éliminant? "éfaufilé
G, i114 quatuor nm prapërriô-tu!" [un
. admît çqualcs,& vu: (ë habetA3, ad [G5 ira E1. ad BC.crg’o la-
. sût reciprocaga ergo parallclo-I", gramma AC,EC,funt æqualian" * Prob LÆqualia sût reââgula A,A; C,EG,& habër angulos zquales;w" trempe ratios 3,8: I. ergo b lacera
rires ho: ango’los crû: rcciproca;
Relax; parsAhgnli refli É; y
1er: circa æqualcs angulosvË; saaux;
b 14.6
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273 .I ElamÆmlidia.PROPOSITIO XVH. AA? EBA E Si tu: "a.
ra. u (12:64 3’. fi"D E F propnrrmu-’ (1T la: quodfuô
B ’ H Guarani: A-B,BC, com-
d prehendirur;rtfiangulum dC.l-guzla a]! ci; quad à medi4,F.de -cribitur quadra!" HG. Et fi abextremis AB .AC, tornpnhenfumnûangulum A C, aqualzfit,ei Jquad à media r, defcribirur qua-.dnto EG,illL tu: "a. proportin- , 5
mule: 3mm. . iRob. ra. pars. Sume reâamJîF. .qualem iyfi FG. erunt quatuor
"en AFEB. proportionales. critque aquadramm EG. comprehenfuih fub Vmediis F6 EF. aergo rcâangulum l Î
a 15.6 AC.æquale erit quadraro. ’ nProb.1. Œadratum EG’.mediz EF.
( voccmus patafiologrammum) re-&angulo AC. fub externis AB.BC. lsquale ponitur , a: habenr angulo:avoualeszergo larera vr proximc dixi,me: ho: angulos cran: zeugma. , a
f.r
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,Liâtrfcxms. 1 279(P ROPOSITIO XVIII.
1 Super dataF .* "fia AB. put;Hadg. data rafli-AA B C D lima CDE
. FG. fimile,:militerqm ’ pafitum refîm-
Laura ABHIK. defivibere.Arum reailineum refolue in -.triangula.du5tis mais pura CF.
1A3. rouans ipfi FCD. &ipfi FDC. b sa!arquahs lBA.-& b eonfequcnre: re- .liqnus reliquo : A uîangula ergocrunuriangula PCL). A3 8: fimrhag amer. ad ALita c0. ad An. Ad F u-reâam A]. fac fimilirer ariangulum .IKA. :quiangulum triangule EGO.8: quia anguli BAI. IAK. zqualcslfun! angulis DCF. FCG. totalesKAB. GCD. zqualeaerunt, 6: larera .
I proportionalia. Idemque rcpcren-dum , donc: 0mm: rriangula coderamame que iacenr abfquanrur , fic- ,quantum reâxlineurd roti remli- d r.neodfimile exir,&fupcx dama An. Paf.fimilnerdcfcrigtum. L I . v -. a
ï DE. Adpunâum A. a fiat angulus 3 321..
.-
u
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550v Élu»;PROPOSITIÔ 5cm.
[ I Simili”)
f tringla
"a Dfin.d a FEFJnnrfine . . .I: l . -. fin! tupliant ranima banian; bofmolngorum; ’
Ï Vando trîàn (la, En: a;k . -quàlia,hocc quapdo BC;
EF, ne: non renia prbpouionaliàBG,funt tailladas; tes en: maniîe.
ftà tænia me làiuàJC,Efi
En: inçqualiggdcmonfiratur,hocm0116. Si: 3C," latuà, laper: PIF;’ïnaiu’s.& Ex BC;abfcihdàtur a te.
Çtis BC,.EF. tertià .rdpohiohaliid n. 6 BG,ducaturquetc’ a AG. Qui:
. igituràn uluè B,cfl: æquâliè 5,8L
5’01)th mititudinem trian -11!th A3, ad 8C, DE; [à
x
K
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1130]":th ausa perInmando v: AB ad DE,ir:,B C, ad EF, hoc CR EF, ad BG,cula: cire: angulos æquales B E,tarera reciprocè procortionalia.(hue pet 14.. uiangula ARC,par. exun: æqualia; ac pet 7.quimi v: triangulnm ARC , adABG, in cri: idem (tian ulumABC,ad DEF. v: autem ARC,ad ABG,îta en par 1. huius BC,.a BG. Ergo ARC, ad D517. cri!
v: 3C, ad BG. l .Coralhp’um. si tu: lima ful-, vint proportionalu, wpn’mn 43
reniant, in trianplùmfupcr ri-ma»: adjïmilc "ng14111"! Il)"[mandant
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.....
37244:.
»
l
Ç; a?
’55: monnayai; . I[A monos-1:10 *x , w, sémiliç pas
M in mi!!![Ïninngnlç dît"- »
C. "416mm, é- l”!que" 49144114,
gui: hgmqloga: à. poljgnm dupli-cata») halent mm ipnrfi ram-uçm , quant igue: homologua) 14,bandera?! 14mn,81m polygona fimilia A un K.
COEFG. habemia angulos zqurles K.G.Itqmque LE. &lficdçinceps.à: 13;:va progonionàlj: gîta angu-lpstqu 9,91113 vç An. si 3,11m
CD. ad . Bic. i qI Dico "J11. diuiçi in triqngnl: fi-miüa’ a; numero æquaüa. En!» ah».
àngulis La: F. duc tafias ad angelot.gnomes An. CD. diuifa mm: 111:poygona in griiguh hamac çqul-lia.Quod criant in fimilia.
n05. Anguli.K.&G.flnt squales,a: Cîlçlipfos laterq (un! reportio-nalip. I ergo çquiangula un: man-gulla lKA. FGC f ergo finilialndem"flanc. emmi 6min: triàngulq un.FIE-P.- Ê? mû se Y! "z "1. "’- "â «
y
l
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Eibtrfaxnu. ’ 2.8 !tu. aù El. vt auteur H8. ad 3A. inIl). partita; ad DC. e exitexsquo v: c n .m. ad sa . un and une: quoniam 4-anguhas 83A. npfi EDC. et! squaws;"ôe ablatus HILablato EDF. cran:(quia: IRA. FDCJquales. d E: o d 5 aalangui: 15A. EDC. zquiangu a . ’Clnnt a: Emilia, cadença: ratio de9mnibus,
Dico z. quad fient vnnm triangu--lum ad "inguinal fibi tefpondensale: nus polygoni -. in elfe pina-a
rota inter C. ’ .Prob. 04g: mania triangula fun:fimil-ia,fmgula fingulis: et ofunt in e 1 aduplicaza ruionelaterum omolo- f ":5
hmmscumque fingula fingulis pro. *’ iata (me proportionalia , fic vt ihtriangulavnius fin: omnia autoce-dentia,in alio confequentia tapon.immun , f vt vnum amen ans en:aù hmm confequens in omnia adomnia. En ergo polygonaux ad P°” Ï
1-Ygomlm vt triangulum ad trian u- a . 1um:ergo ca triangula [hm tofu o-
mologa ,e &quia tïiangula fun! Induglicataratione latemm homolô-gomm , nunc 8: polygona in eademxatione duplicata laterum homolo-xuæ par: A81. Cg).
A! i)
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au lit-JUÆÆJ
PROPOSITIO XXI.
a a 21de»: "[1111; .
1 cg: r’mçH!’
t , fis: [induHGDEF. aimerfifimi; fimiluv.
Rob. Angulîl. &D.ponun-tu: æquales mîG: ergo a: ino a
(et f: . cedemque modo fingnlila l "n8- fingulis: 3 latera etiam circaeo:
pomma]: proportionalia,quia [aueeribus emmena tenii (un: pro-
l poreionalia: ergo (un babeurre ’I angulos zquales a: lama me!Ë g 3 fou Proportionalia, b fun: fixai-g
I * la.. fi - e
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Ww
....aæ
amputa; 83’ drnoro-smo xxu.
P .. M LN o squame. -- 54e un.a 9.- «quïmmujm
, FV Wien-d i" A: Ü le: funinb ’ étai (à n-A BC D3 s asti-«fini.[üMterneùfiI-i’u un. cnx. aceMI. NH. proflonùulu «me. tuf 3
À "Je: lmei.fimlù.fimlüarque filin)" I"and... Mania-du fanny, tu? n-84 enfonùulu une: rPkob..8umatut ipûmm AI.& . "j
CD. tara oroyorziomlis P. 8: 55.4.. ipfanun a: FA: GH.tertIa .’b cri: vt
Al. ad t. na triangulum un adtriagulum KCD id et! in ration: du-
lieaza,ôc v: EFad un Mikael NH.à: vr A8. ad CD. ne EF. ad GH. a:v1 CD. ad lita GH.ad geins ’ex c ,34;que vt Alu! P in EF. ad .4 et a tu.go v: ABLadCDKJn MF. m NH. ela veto 653m: ptoportionales 8c fi-miles fimiliterque (in (me , a: re-&çfuper quai peut: funtmropor-
I flocules en’mnam "de vniqs figuraad akeram c en «a: ad «et: dupli, a m6,
’ cala: urge ratio leur: cade-m exit. 2.0.5nèpe v: ÀB,adCD.îta et. ad cg. et f7 ,5goûlaxülateu rxoplxonapjafinfe .
a n
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au th.EWEÆJPROPOSIT10 X X111.
D H aligna)»-11.17. n c G gultC.,æ-
1-1- ufielo 2-. va. I F m4 A . C
F. inter jerainura 546e»: en», qu exdiatribe "0!!me BC. dCG. (9,- EC. ad CD. ï
habentia angulos ad (2.qu- ’îSIm parallelogtîma AC. Cf. î
. P, 165,5: ixadifpofieavt DCipfi CE. l- a: BG. ipfi CG. I iaceant in dire-
z. ,1, ’ Chu-n , compleamrque pataude. f1- grammum CH. b Cumergo En: .tu ne ad cama nonce. a: v;in CH. ad cr. ira ne. ad en ratio
enim AC.ad CES componimr etintermediis AC. ad CH. & CH.ad CF :Vcompeànemr quoque cadi,ratio .AC, ad CF, ex ratiœibusI3c, ad CG, a: oc, ad CE, qu;
flamand?»wv A me
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Liée: fana» 218,7.PROPOSITIO x x 1V.
, n la omnipl-fillebpmflpflDE. ne arachangea»! Thrü
[naupa-7. O en.
B au Cg. EH.à! tari DE. à! inçer fifuutfinilu. ’
., Axellelogrimum 6E. habet an-vf. s . gulum A. communem eum toto:; angulus alternas AEI.:qualis efi in-uierno ADC.fimilitqu;, angulus AQJ. anglflolABCÆc angulus 151G. an-
d gale EFB. 8c "Plus lFB. anguloV CH.exgo paralle ogxammaGEÆH..8: tari a: me: fc fun; aquiangula.(Laod autan bien, cire: zquale:angulos fin: emm propoxtianaliafic probo. . Triangula AC; ARC. d u’à.fun! zquiangula, fimihxerqpe trian-
I gala Mil. ADC. «je b ergo v: A8., adBC.ita AG. ad CI. a: vtBCL ad bçg, (3A. ira G1. ad 1A. item v: C4. ad c î; i
. CD.ita 1A.,adlE. t largo exzquo vt l. ’a 8C. ad DC. in en QI. ad na. ergo la-
yera cite: squales angulos BCD.d GlE.funt (marihuana, Idemque.
demonfixaî’xtul de lateribus eixc,alios angùlos,&de parallelogtagn:
u
moiti. expliqua,
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a: Ehm.8uelidis .PROPOHTIO mon?
Data refiilx’e
M7. DE neoAfimilqfi-c . militerçm pa-
’ At g [hum éebm’F
fiEH! K dan B. agnela
L. un nuera.)Rax. Ad dat’x reàiline’x A. Ian!
CD. a fiat teâangulum CEJqIIPle îpfi.A. Producatut CD. verfusfi
a 45.1. au»: DE.in luzule [BG.fiatteâlbgulum pH. baquale iyfi 3:: fiai;
b ter CD. DG media proportionah44"! 1K. (apex quam En! xeâllineum L
fimile ipfi A. fimlhterqne pofima. c" 6 eritque reâilineam L. aquale du)d B. &fimilei fiA.g a mob. Re en. un D635!!!".fi proportionales: f ergo exit vt prix" *f l, ’6’ cauchemar! DG. in mail: en!w k fuyez pnmam, id en A. ad xeâillntâ
I’ à Taper fccpndamdd en L. (cd ne».il; î’ Id DG. au: parallelogrammuma-à ’. hoc eflA.ad DH. hoc en B. h ergo’94. cm y; Lad 3.51a A. ad Lildeoqpe ï
1:3de 8.6: L. au: confiai"); IJ
1
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l
L56" [8951111. et); ’
PROPOSITIOXXVI.i B c Sià anl- 77m.. x Ielogrcïrgm mg *
1E BD.p4r41-d lelograïmü
A m. 1256.4514;’ tumfir, Üfimile roli, Üfimi-
3 liter pofimm, commune": tu":’ to [7456m 4ngulumEA 6,7115à Circæedndem cum toto (liante-U
sa "un: AG.;onfijI-et.
SI neges: fit alia AHC. Agam:’ ex H.re&a HLpat’allela FG.
une paralldogramma B D-EI.circa eandcm diamctmm ARC..erumfimiliazb une cricvrfiA. 414.6.
1 lad au. itaEA.a AI. Sed y: BA. inde!"-. ’ adAD. in CR EA. ad *AG. cûm B ’
- 4 D. BG. ponantur fimilia.c Igitur us.g. eritv: EA. ad AI. ira EA.ad AG. 4 a. in4 Ac proprerea zqualcs AI. AG.
f parsec (arum.Bb
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no A Euclidi:novosrno xxvn: j
on". ’Ômnium 4141.,8- : l D E lelogmmnfomm v
jèumdum cam-dem raflant 4174 1
F J. G Iplicatomm defi- 3. cientiamque fi-j
’CA G K JB suri: pamllelongrainmi: fimili-bu: , fimiliter-
E que Pofitir,’ aï
quad à dzmidiæ
defiribitnnmd-AK C deimum efi, id.quad 4d dimididm applicbhlun Paullelolgmmmum fimilcflexiflen: défi-fiai.
SVPER AC. femiffem (orinsAB. applicatum fit parallelœ .
grammum AD. ha v; à toge A15. .l
4
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(i
l
"î
Liber fixtm. ’ 29:Ecficiat parallelogrammo CPEJ dl
110d fc et cf! æ uale a: fi;(dans ipfiËg’D. DeindËad quoduis
aliud fegmentum A K, fit appli-catum aliud parallelogrammumAG. îta deficnens, vt defeâus fi:parallelpgrammum KIfimileip-fi CE.hoc dl circa Communemdiametrum BGD. Dico AG. mi-
. nus efl’e paralklogrammo AD.Probatur.
LCŒndo punâum K. cf! inter. C 8c 13.:ücpazauelogrammüLI-I;
quad eft a æquale ipfi LE. mains a;CR quam GC. quia LE. mains en: bà
. quamGE. 6c GE,GC.funtb æ.qualiaAddim ergoLA. cri: AD.
d mains quem AG.
y.
Œysdo verà punaum K.efl in-ter A 84 C.xûc DE. DI.(unt æqua-lia, quia sût fuper æquales bath;&D[.DK. complemcnta , fun:æqualia: cage a: DE. DK. (En: ç-qnalia,& GH.min’ns 0K: adie-floque commuui KI-l.totum AG.
minustoto AD. " dB b ü
a .
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Pubs.
on EfitlidifPROPOSITIO XXVIH.
P 6" Addawn
y dam redi-M N linga (Le?p E on 9144!! [P4-nllelogmmmum AI. 41219 in
nadcficiem ligua p4mllelo-gamma OqufimiiiJfital-mi paralldogrnmmo data D.Opomt 41mm daim?! reŒIizeù’ .
C. mi agada applicandum efi’ AIan maiureflê caquai 4d
d 518.6.
dimidiam AE «pp’icatur, a:fimile: funin: defeüu: , (7 e-iu: quad 4d dimidmm appli-eamr, a" du: mi fimile deefï
[a nichet. .Rua... A3." priusbifTeca in E.
Tu pet mediâ EB.fac a parallelo-grammum EG.fimi1 e ipfi D.fimàlitere
u
1
l
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Hà" [man 2.9;flue pofitum:&comyle parallelogrâ.
.- mum 3H. SEH. ipfi C. efl: zqualefa- étain dt quad petituxmam et]: ampli-
U
.èv
.-.--Vw4k
catum ad AB.&dcficit parallclogrâ-me BG. fimili ipfi D. si 514.8: ipfi g-. male b EG.fit minus qui C.( nâ mi- 1, in.nus cire non debeî,cum EH.fit c ma- i 17.5.ximü cotir qu: apphcan gaffant adAB.)fiinquâ fit mains,d tapera qui. d M J.(une çucfus, e fac parallelogrnm. au: 4r-mum PIquuale exceîïui,& Gaule fin n qu-militetque pofitum ipfi D. à: Paul. mm.lclogrammo P Rabat! zqunlc fi- I 7-5 -5-militer yofimm KL; quad cric circa f44. l.diamcuumficque remanebît gnomôLBK. tquale rcâilinco C. Ian: pro-duflfxs 11.10311! parallclognmmumA]. ad 1:61am A3. Iyplicatum 8c de-ficîcns parallelogrammo ON.gfim5li 824.6.
v ipfi EG.hoc cl! ipfi v. Œod autan -.ALGt :quale ipfi C.fic probo.C0m
- gleannLNKO.hfuntzqualia,cr h 45-1:go addito communmo. exit 063.911d: ipfi EN. b hoc ca A K. Ergo1 æqualibus AK.OG.addas commu-
ne X0.erit AI. æqualc gnomoniLBK.ho: cit gamma C. v! probaui.
Bbfiü
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lit-clidisPROPPSLTI o aux.
L Al dan?F379: 1151A f . "a; AI K (Efl M B. data3:11:50 rem];-
h? PR ma (La:galle pdraflelagnmmum
appâtera. meulai; rcéîà’
datant AB.figar4 P074]?lelagfamma PQ.,quæ
-’ fimzlz: data alter: [2,41741];-
’Iagr4mmo D.
Vpcr rcânm EB. mcdîam da-
2235. ne ABHfiat parallclogram- mum EC. fimilc ipfi D. finzilirër- g
que pofitum: mm teâilinco C. V3.5.5, ,8; parallclogrammo EC.fiat b :-
" qua]: aliud parallelogrammurg vNMfimüc i136 D.habcuquc q;-
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É.
Liberfixtus. 19;gulum BEC. communem para":-logrammo EC.Completis paral-
’lçlogrammis QE.NB. P0. cumNM. fi: pofitumæqualc ipfis EC. à! D ablato communi E C.
- gnomon ERC.ipfi C. etit saqua.’ ]is.thuia æqualia C fun: p 3;, ;;
B. sa æquagiaa NB. BM. fi loch d 4M,ipfius En. fubfiituamr zqualc kE. cri: parallelogrammum A R.æqualc gnomoni BRC. idcoqucetiam tcâilinco CŒgrc ad re-flarri AH. applicatum en: paral-lclogrammum AN arquai: datarcâilinco C. cxccdens rcaam AB. figura paYallclogramma P0.qu: fimilis dl dam parallclo.’
ramrào D. cum fitcirca candcmgiamcnum cum. ipfo E C. quad.gofitum cil fimilc ipfi D. -
il» iiiî
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2.96 Emlidî:
PROPOSITIO XXX.
me. B Propofitm’°’ Ë’Tu p rafla»: m-
D - mimtzï AA B.extrmu
a: media ration: [Eure il:
H a Ûc u. 1.. Jfinuvn A8. ’în H. in v:
rcâangulum C H.fub (onAB. a: Tcgmento B H. fitzqualc-quadrato ARaltcrius fegmenu’AH. tune cnim trcs mât pro.
6 17.5. portionalec berunt; 8: triano-ta BA. ad HA. in AH. ad HB.
. 51914 Ergo A3. (26h en; in H.° fulm-dpm extrcmam, à: mediam ta:
. nonem.
M-L 3-0-- .4
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Libzrfixtm. ".9 2.97
rROPOSlTIO xxxt. -In triangule Tino,
a H n triangule) A 7-”B C- figura
FB ( g quauisBDJc-I l , firipm à ne.E D fflhëdfllil no
6mn ungulum BAC. quanti: efifiguri: F A. A I. qua priori IYIifi-milu à fimilim pafiu à 14m5.lm: BA.CA. "En"! ungulum un:
7. tinenIibns.dcfcribuntur.
’ Poumons): figüræFA.AI BD:
5.
l
à
?
ponuntur fimilcs , ergo fun: 410.3in ca Incrum homologorum du-plicata ration: , in qua «en; co-rumdcm latex-nm quadram. Ergocum quadrata BA.AC. b habcant l, un"rationcm çqualitacis cum gertioB C. habcbunt 8c polygonn FA.AI.:ationcm squalitatiscum ter-BD. c ergo cidcm mm: mina- c 9., gla,
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111.0.
a; .
ç. 2.9.1.
2.98 Euclidi:PROPOSITI o xxxn.
A Si duCL . D .tn’an la,(à AB .D:B C E CE. que
duo hmm A3. AC. duolzru(flamba DC. DE. propor-tiqngliq hâtant, ficnndumimmanguhmt ACDJam-pqfim fuerint,it4 w homolo-gd com»; lutera A B. D C,A C. D E. fin: au»: pard-Itla ,’ un» "ligna ilion»:trinngularum laura B C. CE. in rafla»: [imam B E. cob1004M repcricnmr,
4 PRon. Latex: homologaA B. I. D C. A C. D E. Panama: pa-
ranch,a ergo anguh ahemi A.&40D. (un: agnalcs a. D. aidez!
î
4
I
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n Lièerfixmà. p.95ACD ergo A. 8c D.zqulles. Hossquales angulos circunflant le.-tera proportionalia ex hypoth.b ergo triangula fun: æquiangu- 5- fi 6Kla . habcntqlie æquales angulosB. a DCE. additië ergo. æqudli- .bus A. 84 A CD. erunt B. 8c A.duobfisangulisDCE. ACD.hoc .dl angulo ACE. æquales. ErgoCaddiro communi AC B. eruntires apguli A B C. duobus ACE.A C B; æqualcs,’c illi autem tres c321 1. ’
üalenr dues reâos, ergo 8c hiduo;Ergo 4 BÇ.CE.vnam reâam 414.!.
Conflimunr: C ’ * ,
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Tino.
n.
m4.
:3. .î 50- C1. yonu’ntur zoualcsfico .
300 A Euclidis
PROPOSITIO XXXIIL
A In qualifias,n’y-cuti: DE. HF.
I Nnnguli A. E. D.B M a H. «miam I24-
L ben: ratiner» yK un: ipfi: periphe-
’ a me BG. FG. quiaF bu! infijhmt : fin:ad centra D. H. flua ad pari- »fieri." A. E. conflitmi infi-flnnt : infilper ocra à [effa-ru BDC. FHG. gain): qui îad centra, infifluntz. ,. o .
. l"Ron. Dué’cis BC. FG. ad.
Cu. applica G l rqualem ip- ,fi Boa: 3116.8: K. GK KL.’:quales fingulasipfi FG. dut": n1D. KH LH. fic dico. Reflz l.
l
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l
l arcus 3C1. ipfius 15C. rem multi-’ plex exit angulns BD]. ipfius
Liber fixa". 30xgo 8: arcusBC.CI. cergo a: au. c 17. 1guli BDC. CDI. squales. Idem- 3. .que cil de aucubas PG. 6K. KL. ia: augulia ad H. qui ipfis infi-flunt. Ergo quam multiplex en
ï B D C. a: quam multiplex anus.PGKL. ipfius FG. un». multiplex lexit angulus FHL. ipfius F H G.a ergo G anus B CI. FGKL. fin: d 17.1: læquales . erunt 8c anguli B D I. .4FHL. aulnaies. Si coran; arcuumvous fi! maie: , maior tri: a: an-
’ gulus , fi minot , minor.° Ergo .514;gcum æquemultiplicia vel vna ex- s.cedant, vel vna defician: ,quæ - lexit ratio nous BG. ad FG. ca,- 1
il; dem cri: anguliBDC.ad FHG.E:i qui: anguliad D. 8c H.- funt rdu. fzo.;.
yli angulorum ad A. 8c La ea- SIS. f-i dem cri: ratio angulorum A. a:
.. .I vil:
Il
E. que and H. a. fie eadcm am- l1guli A. ad angulum E. quæarcusBC.ad arcum F G. l1Rurfus , in çqxualibçs Segmeof
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301 334.1111:A lis B Ch C I fi fiant
’ anguli BMC. CNI.517-3. ’ x l h: uales etunr,cum ’
y N mâtant zqnahbusr. ’ i’ aucubas B A C. C
in" à 7 L A I. ergo i .fimilia»* flint regina: BMC.CNl’ôc aquahafium
’ F G fintfuper squales BC.CI.additis ergo alanguis BD .C.CDl.K quœ Lequalià faut, auna ofiâmes BDC. CDI. gequalesÆr-go mm multiplex dl fiat): BDLg(côlons BDC. qui multiplex ar- -eus BCI arcus BMC..Iclem alleu-dcrur de Rame FHL. Ergo lire-gqualis fit arcus BCl. arcuiFGL.fifeâor quoque BD]. æqualis crié.fedori FHL. fi dcficiat, deficiet,fi cxcedar, merder. Ergo quœ efl’.ratio are-us BC. a! arcum FG.ca-.’-l
flammes. [mais BDC. ad rc. fI :1, -, vëëmerG-rquod en: piot»: g
x.k: À,....---.;. v in ,. (au. 44,449", figuré»;"Lil-Jla’rnæiai ,Il iv .n ..« n
- .v