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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
, != $, bfo fˎ dy b sfdt ~citjw bljfk tac ldfc }cw}cfodislbw tj gjta b bfo g
&
_ac odwcitdjf jn i
dy ysia tabt b, g bfo i
njw` b wdkat - abfoco yytc`& Fjtc tabt
b g g b
, b b =
,
b g i b g b i
&
ˎ ˎ ˎ ˎ ˎ ˎ ˎ ˎ ˎ ˎ ˎ ˎ ˎ ˎ ˎd d h h e e = bfo d h0e,h e0d,e d0h &
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3
_{j fjf - xcwj ~citjwy b bfo g
bwc ijlldfcbw dn bfo jfl dn b g =
&
2 7 9 2 7 9ˎ ˎ ˎ ˎ ˎ ˎDn b0b d b h b e bfo g0g d g h g e, tacf
2 7 9 7 9 9 7 9 2 2 9 2 7 7 2
2 7 9
ˎ ˎ ˎd h e
ˎ ˎ ˎb g b b b b g b g d b g b g h b g b g e
g g g
&
Blyj, ˎb g | b | | g | ydf f
b g | b | | g | ydf
0 72
| b | | g | ydf7
0 7 !Bwcb jn twdbfklc BJI$ 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
bljfk tac dftcwfbl bfo cqtcwfbl gdycitjwy jn , wcy}citd~cl& _ac gdycitjwy jn tac bfklcy gct{ccf tac ldfcy
2 7w b bfo w0 g
bwc kd~cf gb g
w| b | | g |
! wcbl$&