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^CI_JW

^citjwy bwc tajyc rsbftdtdcy {adia bwc ij`}lctcl octcw`dfco dn tacdw lcfktay !blyj ibllco `bkfdtsoc$ bfotacdw odwcitdjfy df y}bic bwc kd~cf& Njw cqb`}lc, ~cljidt, biiclcwbtdjf, njwic cti& bwc ~citjwy&

Odwcitco ldfc yck`cft

B ~citjw jw b odwcitco ldfc yck`cft dy ocfjtco g t{j

lcttcwy {dta bf bwwj{ `bweco j~cw tac`& _ac ndwyt lcttcw dytac ytbwtdfk }jdft !jw tac dfdtdbl }jdft jw tac jwdkdf$ bfo tac

ycijfo lcttcw dy tac tcw`dfbl }jdft jn b ~citjw& _asy, BG

dyb odwcitco ldfc yck`cft {ajyc dfdtdbl }jdft dy B bfo tactcw`dfbl }jdft dy G& GB dy b odwcitco ldfc yck`cft {ajycdfdtdbl }jdft dy G bfo tac tcw`dfbl }jdft B&

B

B

G

G

_ac lcfkta, BG, jn tac ldfc yck`cft dy efj{f by tac `bkfdtsoc jn ~citjw BG

bfo dy {wdttcf by BG jw

yd`}l g BG& ^citjwy BG

bfo GB

ab~c tac yb`c `bkfdtsoc gst tac odwcitdjfy bwc j}}jydtc& Acfic,

BG

bfo GB

wc}wcycft odnncwcft ~citjwy& [c {wdtc b

, g

cti& tj wc}wcycft ~citjwy bfo b , g cti& tj

wc}wcycft tacdw `bkfdtsocy&

Nwcc bfo ljibldxco ~citjwy

Dn {c bwc nwcc tj iajjyc tac jwdkdf !jw tac dfdtdbl }jdft$ jn b ~citjw bt bf }jdft, tacf tac ~citjw dy ybdo tj gcb nwcc ~citjw& B nwcc ~citjw ibf gc ysghcitco tj }bwbllcl ody}lbic`cft tj dtycln {dtajst iabfkdfk dty`bkfdtsoc !bfo odwcitdjf, jn ijswyc$& Dn tac dfdtdbl }jdft dy wcytwditco tj b y}cidndco }jdft, tacf tac ~citjw dyibllco b ljibldyco ~citjw&

Crsbl ~citjwy

_{j ~citjwy b

bfo g

bwc ybdo tj gc crsbl, dn tac ab~c tac

yb`c lcfkta !`bkfdtsoc$ bfo tac yb`c odwcitdjf, wckbwolcyy

jn tac }jydtdjf jn tacdw dfdtdbl }jdfty, bfo {c {wdtc b

0 g

&

_asy, crsbl ~citjwy ibf gc wc}wcycftco g }bwbllcl ldfcy jncrsbl lcfktay, df tac yb`c ycfyc jn odwcitdjf, dwwcy}citd~c jntac dfdtdbl }jdft&

B]

C

NR

Gb

 

g

 i

 

Sfdt ~citjw

B ~citjw dy ybdo tj gc b sfdt ~citjw dn dty `bkfdtsoc dy jn sfdt lcfkta& _ac sfdt ~citjw, ijwwcy}jfodfk tj b

~citjw b

jn lcfkta b bfo df tac odwcitdjf jn b

, dyb

b

& [c ocfjtc dt g bˎ & 

Xcwj ~citjw

B ~citjw b

dy ybdo tj gc xcwj jw b fsll ~citjw dn dty `bkfdtsoc dy xcwj, d,c& b 0 =& Dty odwcitdjf dy

dfoctcw`dfbtc& [c wc}wcycft xcwj ~citjw g J

& BB

, ]]

bwc xcwj ~citjwy& 

Odytdfitdjf `syt gc `boc gct{ccf yiblbw J bfo xcwj ~citjw J

& _ac yiblbw J dy b wcbl fs`gcw {acwcby

J

dy b ~citjw jn xcwj `bkfdtsoc bfo bwgdtwbw odwcitdjf&Ijlldfcbw ~citjwy

B fs`gcw jn kd~cf ~citjwy bwc ybdo tj gc ijlldfcbw dn tac bwc }bwbllcl tj !jw ijdfidocft {dta$ tac yb`c ldfcdwwcy}citd~c jn tacdw `bkfdtsoc& Ydfic xcwj ~citjw ibf ab~c bf odwcitdjf, dt dy ijlldfcbw {dta bf jtacw~citjw& Ijlldfcbw jw }bwbllcl ~citjwy bwc blyj ibllco ldec ~citjwy&

Fckbtd~c jn b ~citjw

B ~citjw {ajyc `bkfdtsoc dy tac yb`c by tabt jn b kd~cf ~citjw b

gst dy df tac j}}jydtc odwcitdjf dy ibllco

tac fckbtd~c jn b

bfo dy ocfjtco g b

& _ac fckbtd~c jn b ~citjw dy ijlldfcbw {dta tac ~citjw dtycln&Ij}lbfbw ~citjwy

B fs`gcw jn kd~cf ~citjwy bwc ybdo tj gc ij}lbfbw dn tac bwc }bwbllcl tj tac yb`c }lbfc& Jg~djsyl,~citjwy ldfk df tac yb`c }lbfc bwc ij}lbfbw&

Boodtdjf jn ~citjwy

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 7

Df tac ydoc {dyc ndkswc tac ys` jn tac ~citjwy b

 

bfo g

dy ocndfco byJG JB BG b g

&

Jg~djsyl, {c ibf iajjyc bf }jdft by jwdkdf&Acfic, tac ys` jn t{j ~citjwy dy dfoc}cfocft jntac iajdic jn dfdtdbl }jdft !jw jwdkdf$& Ydfic, JBGdy b twdbfklc, tady dy blyj ibllco tac twdbfklc lb{ jnboodtdjf&

J B

G

g 

Bb 

b g

 

@jwcj~cw, tac `bkfdtsoc jn JG dy fjt crsbl tj tac ys` jn tac `bkfdtsoc jn ~citjwy b

bfo g

& Dn

JG b g =

, d,c& J bfo G ijdfidoc, tacf g b

jw BG

dy fckbtd~c jn JB

&

  ^citjw boodtdjf dy ij``stbtd~c d,c& b g g b

&

  ^citjw boodtdjf dy byyjidbtd~c d,c& b g i b g i

&

  _ac }wjicyy jn boodtdjf `b gc cqtcfoco tj yc~cwbl ~citjwy& _asy , tj boo f ~citjwy 2 7 9 fb ,b ,b ,&&&,b

,

{c iajjyc J by tac jwdkdf bfo owb{

2 2 2 7 7 7 9 9 f 2 f fJB b ,B B b ,B B b ,&&&,B B b

 

yj tabt

2 7 f f 2 f 2 f fb b &&& b JB B B JB  

Acfic tac ys` dy wc}wcycftco g fJB

& _ady dy ibllco tac }jlkjf lb{ jn boodtdjf&  Dn tawcc ~citjwy 2 7 9b ,b ,b

bwc wc}wcycftco g tawcc ydocy jn b twdbfklc, tbecf df jwocw,

tacf 2 7 9b b b =

& Dn ~citjw 2 7 fb ,b ,&&&,b

, tbecf df jwocw, bwc wc}wcycftco g tacf ydocy jn b

}jlkjf, tacf 2 7 fb b &&& b =

&

  _ac odnncwcfic b g

jn t{j ~citjwy b

bfo g

 

ibf gc ocndfco by tac ys` jn tac ~citjwy b

bfo

g

d,c& b g b g

&

[c ab~cJB b

, BG g

, BG+ GB g

 

JG+ JB BG+ b g

& 

G

B

G— 

J

b g

 

g

 

g

 

b

 

b g

 

  _ac ocndfdtdjfy jn tac ys` bfo tac odnncwcfic jn t{j ~citjwy yaj{ tabt b = b bfob = b &

@jwcj~cw ,b = b = b

&Yiblbw `sltd}ldibtdjf jn ~citjwy

_ac `sltd}ldibtdjf jn b ~citjw b

g b yiblbw ` dy ocndfco by tac

~citjw`b

, {ajyc `bkfdtsoc !jw `joslcy$ dy ` td`cy tac

`bkfdtsoc jn b

& _ady ~citjw aby tac yb`c odwcitdjf by b

, dn ` dy

}jydtd~c bfo aby tac j}}jydtc odwcitdjf jn b

dn ` dy fckbtd~c&

Blyj, `b ` b

&

b̀

 

`b

 b

 

  `f b ` fb f `b

!`, f yiblbwy$&

  ` f b `b fb

   ` b g `b `g

 

  [c ab~c, bb

b

bfo gg

g

& Dn b

bfo g

bwc ldec ~citjwy, tacf ˎbˎ g , yj tabt

b g

b g

 b

b gg

jw,g

g bb

&

Acfic, jfc ~citjw ibf gc cq}wcyyco by b yiblbw `sltd}lc jn tac jtacw&]jydtdjf ~citjw jn b }jdft

Lct J gc tac jwdkdf jn b icwtbdf ij ’jwodfbtc yytc`& _acf c~cw }jdft df y}bic ibf gc wcncwcfico {dta

wcy}cit tj tady jwdkdf& Dn ] dy bf }jdft df y}bic, tacf J]

dy ybdo tj gc tac }jydtdjf ~citjw jn tac }jdft ]&

]jydtdjf ~citjw dy sfdrsc&]jydtdjf ~citjwy df wcitbfkslbw Ibwtcydbf yytc`8

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Df tac tawcc od`cfydjfbl ij ’jwodfbtc !wcitbfkslbw$ yytc`, sfdt~citjwy df tac odwcitdjf jn }jydtd~c q-bqdy,

-bqdy bfo x-bqdy bwc ocfjtco g ˎ ˎ ˎd, hbfoe wcy}citd~cl& Df tac

ydoc {dyc ndkswc _ac ˎ ˎ ˎJB qd, JG h, JI e

&

Fj{ 2 2 2 2w J] J] ] ] JB B] ]]

 

0 ˎ ˎ ˎJB JG JI qd h xe

&

^citjwy ˎ ˎ ˎqd,h,xe bwc ibllco tac ij`}jfcfty jn ~citjw w

df tac

odwcitdjfy jn tac ij ’jwodfbtc bqcy& !q, , x$ dy yj`ctd`cy ibllco tac

}jydtdjf ~citjw jn ]!q, , x$ bfo {c ocfjtc dt by ]!w$

& Blyj

!J]$7

0 7 7 7J] q x w

&

]2

G

]!q,,x$ 

I

B

J

q

x

ˎd  

 ˎh  

eˎ  

dn B!q2, 2, x2$ bfo G!q7, 7, x7$ gc bf t{j }jdfty df y}bic& _acf ~citjw BG

ibf gc {wdttcf by !sydfk !2$$,

2 7 9ˎ ˎ ˎBG JG JB b d b h b e {acwc b2 0 q7  ’ q2, b7 0 7  ’ 2, b9 0 x7  ’ x2&

[c ndfo tabt bf ~citjw ibf gc cq}wcyyco df tcw` jn sfdt ~citjwy ˎ ˎ ˎd, h, e & _acyc bwc efj{f by gbydy !jw

gbyc$ ~citjwy& Df kcfcwbl, bf tawcc `stsbll }cw}cfodislbw !jw jwtajkjfbl$ ~citjwy, yb b,g,i

ibf gc

iajycf by gbyc ~citjwy&

  _ac }jdfty B, G, I {ajyc }jydtdjf ~citjwy bwc b, g, i

, bwc ijlldfcbw dn BG % GI 0 BI

jw dn BG GI BI

  B G I

d&c& dn g b i g i b

&

Odwcitjw Ijydfcy jn b ^citjw8 

Lct , , gc tac bfklcy {adia tac ~citjw w J]

`becy {dta tac }jydtd~c odwcitdjfy jn tac

q-bqdy, tac -bqdy bfo x-bqdy wcy}citd~cl& _ac ijydfc jn tacyc bfklcy d&c& ijy , ijy bfo ijy bwc ibllco

tac odwcitdjf ijydfcy jn tac ~citjw w

& _ac odwcitdjf ijydfcy bwc sysbll ocfjtco g

l, `, f wcy}citd~cl& Nwj` tac wdkat bfklco twdbfklcy JB], JG] bfo JI], {c ndfo tabt ijy 0 qw

,

ijy 0t

w

, ijy 0x

w

 

ijy7

% ijy7

% ijy7

07 7 7

7

q x2

w &

_ac odwcitdjf ijydfcy !l, `, f$ df tady jwocw, tasy ijfytdtstc b sfdt ~citjw bljfk tac ~citjw w

& Njw bf

fjf-xcwj ijfytbft e, el, e`, ef bwc ibllco tac odwcitdjf wbtdjy jn w

&Od~dodfk b ldfc yck`cft df b kd~cf wbtdj !Ycitdjf njw`slb$

Df tac ydoc {dyc ndkswc tac }jydtdjf ~citjw jn ] dyb g

 

B

]

G

g

 

J b

 

  Dn ] dy tac `do ’}jdft jn BG, tacf 0 , bfo acfic tac }jydtdjf ~citjw jn ] dyb g

7

&

  _ac }jydtdjf ~citjw jn tac }jdft ] {adia od~docy BG !cqtcwfbll$ df tac wbtdj 8 dyg b

&

Ldfcbw Ij`gdfbtdjf jn ~citjwy8

  _{j ~citjwy bwc ijlldfcbw !jw }bwbllcl$ dn tacdw odwcitdjfy bwc tac yb`c jw j}}jydtc, {abtc~cw tacdw`bkfdtsoc&

  Lct sy ijfydocw tawcc ~citjw b, g,

  i

ldfk df b }lbfc& Dn tac dfdtdbl }jdfty jn b, g

bfo i

bwc odnncwcft,

{c yadnt tac ~citjwy !g }bwbllcl yldodfk$ yj tabt bll tac tawcc ab~c tac yb`c dfdtdbl }jdft J& Bf ~citjw

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df tac }lbfc jn t{j fjf-ijlldfcbw ~citjwy b

bfo g

ibf gc wc}wcycftco by b ldfcbw ij`gdfbtdjf jn b

 

bfo g

&Dn i j

bfo b

bfo g

bwc fjf-ijlldfcbw, tacf ` 0 =, f 0 =&

  Dn b, g, i

bwc fjf-ij}lbfbw ~citjwy tacf bf ~citjw w

ibf gc wc}wcycftco by b ldfcbw ij`gdfbtdjf

jn b, g, i,

&

]wjosit jn t{j ~citjwy8 

_ac }wjosit jn t{j fs`gcwy dy b fs`gcw& Gst tac }wjosit jn t{j ~citjwy dy ocndfco df t{j {by, fb`cl,

yiblbw }wjosit {acwc tac wcyslt dy b yiblbw bfo ~citjw }wjosit {acwc tac wcyslt dy b ~citjw rsbftdt&

Yiblbw }wjosit jn t{j ~citjwy !ojt }wjosit$8

_ac yiblbw }wjosit jn t{j ~citjwy b bfo g

dy kd~cf g |b| |g| ijy , {acwc != $ dy tac bfklc

gct{ccf tac ~citjwyb bfo g

& Dt dy ocfjtco g b&g g&b

, bfo njw 0 =, b g | b | | g |

&

 7 7b&b b | b |

, by 0 =&

  _{j ~citjwy b bfo g

`bec bf bistc bfklc dn b g =

,

bf jgtsyc bfklc dn b&g =

bfo bwc bt wdkat bfklc dn

b&g =&

 

b

ijyg

 

  b& g i b&g b&i

&

 7 7 7b g !b g$ !b g$ b g 7b&g

,

 7 7b g & b g b g

&

  Dn d, h bfo e bwc tawcc sfdt ~citjwy bljfk tawcc `stsbll }cw}cfodislbw ldfcy, tacfˎ ˎ ˎ ˎ ˎ ˎd&d h&h e&e 0 2 bfo ˎ ˎ ˎ ˎ ˎ ˎd&h h&e e&d = &

  Dn 2 7 9 2 7 9ˎ ˎ ˎ ˎ ˎ ˎb b d b h b e bfo g0g d g h g e

, tacf 2 2 7 7 9 9b&g b g b g b g ,

 

7 7 72 7 9b b b b

bfo 7 7 7

2 7 9g g g g

, ijy 0 2 2 7 7 9 9

7 7 7 7 7 72 7 9 2 7 9

b g b g b g

b b b g g g0

b g

| b | | g |

&

  Dn b g b i

, tacf dt ojcy fjt bl{by d`}l tabtg i

& Ydfic b g b i

 

b !g i$ =

, dt dy }jyydglc tabt b

dy }cw}cfodislbw tj ~citjw g i

&

  Njw b yiblbw , ! b$ g !b g$ b ! g$

 

Ij`}jfcfty jn b ~citjw bljfk tac ijjwodfbtc bqcy8 

Dn 2 7 9ˎ ˎ ˎb b d b h b e

dy b ~citjw {adia `becy bfklcy , , {dta tac ijjwodfbtc bqcy, tacf

2 7

7 7 7 7 7 72 7 9 2 7 9

ˎˎ b bb hb d

ijy , ijy| b | | b |b b b b b b

 

bfo ijy 0 9

7 7 72 7 9

ˎ bb e

| b | b b b

bwc tac ijwwcy}jfodfk odwcitdjf ijydfcy jn tac ~citjw&

^citjw }wjosit jn t{j ~citjwy !iwjyy }wjosit$8 

_ac ~citjw }wjosit jn t{j ~citjwy b bfo g

, {wdttcf by b g

, dy tac ~citjw i b g

ydf fˎ , {acwc dy tac

bfklc gct{ccf b bfo g

, != $, bfo fˎ dy b sfdt ~citjw bljfk tac ldfc }cw}cfodislbw tj gjta b bfo g

&

_ac odwcitdjf jn i

dy ysia tabt b, g bfo i

njw` b wdkat - abfoco yytc`& Fjtc tabt

b g g b

, b b =

,

  b g i b g b i

&

ˎ ˎ ˎ ˎ ˎ ˎ ˎ ˎ ˎ ˎ ˎ ˎ ˎ ˎ ˎd d h h e e = bfo d h0e,h e0d,e d0h &

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_{j fjf - xcwj ~citjwy b bfo g

bwc ijlldfcbw dn bfo jfl dn b g =

&

2 7 9 2 7 9ˎ ˎ ˎ ˎ ˎ ˎDn b0b d b h b e bfo g0g d g h g e, tacf

 

2 7 9 7 9 9 7 9 2 2 9 2 7 7 2

2 7 9

ˎ ˎ ˎd h e

ˎ ˎ ˎb g b b b b g b g d b g b g h b g b g e

g g g

&

Blyj, ˎb g | b | | g | ydf f  

b g | b | | g | ydf

0 72

| b | | g | ydf7

 

0 7 !Bwcb jn twdbfklc BJI$ 0 Bwcb jn }bwbllcljkwb` JBGI&

_ac bwcb jn tac }bwbllcljkwb`, {ajyc bohbicft ydocy bwc wc}wcycftco g ~citjwy JB b

bfo

JG g, dy b g ,

bfo tac bwcb jn tac twdbfklc JBG dy2

b g7

& Acwc b g

dy ybdo tj gc tac ~citjw

bwcb jn tac }bwbllcljkwb` {dta bohbicft ydocy JB bfo JG&

_ac sfdt ~citjw }cw}cfodislbw tj tac }lbfc jnb g

b bfo g dy

b g

, bfo b ~citjw jn `bkfdtsoc

}cw}cfodislbw tj tac }lbfc jnb g

b bfo g dyb g

&

7 77 7b g b g ydf

077 77 7 7 b b b g

b g b g ijy b b g g b gb g g g

&

Yiblbw twd}lc }wjosit8 

_ac yiblbw twd}lc }wjosit jn tawcc ~citjwy b,g bfo i

dy ocndfco by b g i&

[c ocfjtc dt

g Ub g iP&

  !b g$ i& b&!g i$ g&!i b$ i&!b g$

d&c& Ub g iP0 Ug i bP 0 Ui b gP 0 -Ug b iP 0 -Ui g bP&

  Dn 2 7 9 7ˎ ˎ ˎb b d b h b e ,g

0 2 7 9 2 7 9

ˎ ˎ ˎ ˎ ˎ ˎg d g h g e bfo i0i d i h i e

 

tacf b g i

0 b g i

0

2 7 9

2 7 9

2 7 9

b b b

g g g

i i i

&

  b g i

wc}wcycfty !bfo dy crsbl tj$ tac ~jls`c jn tac }bwbllclj}d}co {ajyc bohbicft ydocy bwc

wc}wcycftco g tac ~citjwy b, g bfo i

&

  _ac ~jls`c jn tac tctwbacowjf BGIO dy crsbl tj2

BG BI &BO> &

  _awcc ~citjwy b,g bfo i

bwc ij}lbfbw dn Ub g iP 0 =&

@jwcj~cw, Ub % g, i, oP 0 Ub i oP % Ug i oP&

 b&i g&i

b g & i ob&o g&o

,

  Ub g iP Us ~ {P 0

b&s g&s i&s

b&~ g&~ i&~

b&{ g&{ i&{

&

  Njsw }jdfty {dta }jydtdjf ~citjwy b,g,i bfo o

bwc ij}lbfbw dn

Uo g iP % Uo i bP % Uo b gP 0 Ub g iP&

  b b g g b b g !b b$ g = =&

 

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^citjw twd}lc }wjosit8 

_ac ~citjw twd}lc }wjosit jn tawcc ~citjwy b, g bfo i

dy tac ~citjw8

b g i b&i g b&g i&

 

Fjtc8

  !b g$ & ! i o$

0 b g i o

0 b& U ! g & o$i- ! g& i$o P

 

0 !b & i$ ! g & o$ -!b&o$ !g &i$

0b & i b & o

g & i g & o

&

_ady dy ibllco Lbkwbfkc—y docftdt& 

  !b g$ !i o$ U!b g$ oP i U!b g$ iP o Ub g o Pi Ub g iP o

&

Lct b,g bfo i

gc b yytc` jn, tawcc fjf - ij}lbfbw ~citjwy& _acf tac yytc` jn ~citjwy b ,g bfo i

{adia

ybtdyndcy b&b g&g i&i 2

bfo b&g b&i g&b g&i i&o i&g =,

dy ibllco tac wcid}wjibl yytc` tj

tac ~citjwy b, g, i

& Df tcw` jn b, g, i

tac ~citjwy b &g &i

bwc kd~cf g

g i i b b g

b ,g , i 0b g i b g i b g i

&

Kcj`ctwdibl b}}ldibtdjfy8

Lct ˎbˎ bfo g gc sfdt ~citjwy bljfk t{j ldfcy dfildfco bt bf bfklc & _acf ˎ ˎˎ ˎb g bfo b-g bwc tac ~citjwy

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2 7w b bfo w0 g

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