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7/30/2019 CK:12 Algebra I Second Edition v1 s1
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7/30/2019 CK:12 Algebra I Second Edition v1 s1
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7/30/2019 CK:12 Algebra I Second Edition v1 s1
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7/30/2019 CK:12 Algebra I Second Edition v1 s1
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>%? Yfqjl~ fea Sylslyqjle~ % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % 616
>%8 Soynoeq Syli`ob~ % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % 61:
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1%? Gyfsm~ _~jeg ^`lso"Jeqoynosq Hlyb % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % 6:8
1%8 Ajyonq Xfyjfqjle Blao`~ % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % 931
1%7 @jeofy Huenqjle Gyfsm~ % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % 966
1%= Syli`ob"^l`xjeg ^qyfqogjo~ " Gyfsm~ % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % 967
? Wyjqjeg @jeofy Ovufqjle~ 991
?%6 Hlyb~ lh @jeofy Ovufqjle~ % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % 99?
?%9 Ovufqjle~ lh Sfyf `o` fea Soysoeajnu`fy @jeo~ % % % % % % % % % % % % % % % % % % % % % % % % % % % % % 9>:
?%> Hjqqjeg f @jeo ql Afqf % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % 91=
?%1 Syoajnqjeg wjqm @jeofy Blao`~ % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % 9?=
8 @jeofy Jeovuf`jqjo~ 987
8%6 ^l`xjeg Jeovuf`jqjo~ % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % 98=
8%9 _~jeg Jeovuf`jqjo~ % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % 978
8%> Nlbsluea Jeovuf`jqjo~ % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % 9=3
8%1 Fi~l`uqo Xf`uo Ovufqjle~ fea Jeovuf`jqjo~ % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % 9=:
8%? @jeofy Jeovuf`jqjo~ je Qwl Xfyjfi`o~ % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % >36
7 ^l`xjeg ^z~qob~ lh Ovufqjle~ fea Jeovuf`jqjo~ >63
7%6 @jeofy ^z~qob~ iz Gyfsmjeg % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % >66
7%9 ^l`xjeg @jeofy ^z~qob~ iz ^ui~qjquqjle % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % >96
7%> ^l`xjeg @jeofy ^z~qob~ iz O`jbjefqjle % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % >9:
7%1 ^sonjf Qzso~ lh @jeofy ^z~qob~ % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % >16
7%? ^z~qob~ lh @jeofy Jeovuf`jqjo~ % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % >?3
= O}sleoeqjf` Huenqjle~ >8?
=%6 O}sleoeq Sylsoyqjo~ Jexl`xjeg Sylaunq~ % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % >88
=%9 O}sleoeq Sylsoyqjo~ Jexl`xjeg Vulqjoeq~ % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % >79
=%> [oyl, Eogfqjxo, fea Hyfnqjlef` O}sleoeq~ % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % >77
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=%? Golboqyjn ^ovuoeno~ % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % >:9
=%8 O}sleoeqjf` Huenqjle~ % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % >:=
=%7 Fss`jnfqjle~ lh O}sleoeqjf` Huenqjle~ % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % 138
: Sl`zelbjf`~ 168
:%6 Faajqjle fea ^uiqyfnqjle lh Sl`zelbjf`~ % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % 167
:%9 Bu`qjs`jnfqjle lh Sl`zelbjf`~ % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % 198
:%> ^sonjf Sylaunq~ lh Sl`zelbjf`~ % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % 1>1
:%1 Sl`zelbjf` Ovufqjle~ je Hfnqlyoa Hlyb % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % 113
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:%? Hfnqlyjeg Vufayfqjn O}syo~~jle~ % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % 117
:%8 Hfnqlyjeg ^sonjf Sylaunq~ % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % 1??
:%7 Hfnqlyjeg Sl`zelbjf`~ Nlbs`oqo`z % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % 181
63 Vufayfqjn Ovufqjle~ fea Vufayfqjn Huenqjle~ 171
63%6 Gyfsm~ lh Vufayfqjn Huenqjle~ % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % 17?
63%9 Vufayfqjn Ovufqjle~ iz Gyfsmjeg % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % 1=:
63%> Vufayfqjn Ovufqjle~ iz ^vufyo Yllq~ % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % 1:=
63%1 ^l`xjeg Vufayfqjn Ovufqjle~ iz Nlbs`oqjeg qmo ^vufyo % % % % % % % % % % % % % % % % % % % % % % % % ?38
63%? ^l`xjeg Vufayfqjn Ovufqjle~ iz qmo Vufayfqjn Hlybu`f % % % % % % % % % % % % % % % % % % % % % % % % ?67
63%8 Qmo Aj~nyjbjefeq % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % ?9=
63%7 @jeofy, O}sleoeqjf` fea Vufayfqjn Blao`~ % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % ?>>
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66%6 Gyfsm~ lh ^vufyo Yllq Huenqjle~ % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % ??6
66%9 Yfajnf` O}syo~~jle~ % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % ?89
66%> Yfajnf` Ovufqjle~ % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % ?7>
66%1 Qmo Szqmfglyofe Qmolyob fea Jq~ Nlexoy~o % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % ?=3
66%? Aj~qfeno fea Bjasljeq Hlybu`f~ % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % ?:3
69 Yfqjlef` Ovufqjle~ fea Huenqjle~ ?:=
69%6 Jexoy~o Xfyjfqjle Blao`~ % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % ?::
69%9 Gyfsm~ lh Yfqjlef Huenqjle~ % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % 83?
69%> Ajxj~jle lh Sl`zelbjf ~ % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % 867
69%1 Yfqjlef` O}syo~~jle~ % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % 89>
69%? Bu`qjs`zjeg fea Ajxjajeg Yfqjlef` O}syo~~jle~ % % % % % % % % % % % % % % % % % % % % % % % % % % % % 897
69%8 Faajeg fea ^uiqyfnqjeg Yfqjlef` O}syo~~jle~ % % % % % % % % % % % % % % % % % % % % % % % % % % % % % 8>9
69%7 ^l`uqjle~ lh Yfqjlef` Ovufqjle~ % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % 813
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je eubioy~, ionfu~o wo nfe u~o xfyjfi`o~ `jdo ` fea w ql yosyo~oeq qmo uedelwe `oegqm fea wjaqm% Jh wo ~qfyq fq qmo
qls `ohq fea wlyd n`lndwj~o, fea jh wo u~o qmo `oqqoy S ql yosyo~oeq qmo soyjboqoy, qmoe wo nfe ~fz;
S 2 ` $ w $ ` $ w
Wo fyo faajeg 9 ` ~ fea 9 w ~, ~l wo nfe ~fz qmfq;
S 2 9 ` $ 9 w
Jq~ nu~qlbfyz je f`goiyf ql lbjq bu`qjs`jnfqjle ~zbil`~ wmoeoxoy sl~~ji`o% Hly o}fbs`o, 66} bofe~ qmo ~fbo qmjeg
f~ 66 } ly 66 } % Wo nfe qmoyohlyo f`~l wyjqo;
S 2 9` $ 9w
Fyof j~ `oegqm bu`qjs`joa iz wjaqm% Je f`goiyfjn qoyb~ wo goq;
F 2 ` w F 2 ` w F 2 `w
Elqo; 9` $ 9w iz jq~o`h j~ fe o}fbs`o lh f xfyjfi`o o}syo~~jle4 S 2 9` $ 9w j~ fe o}fbs`o lh fe ovufqjle% Qmo bfjeajhhoyoeno ioqwooe o}syo~~jle~ fea ovufqjle~ j~ qmo syo~oeno lh fe ovuf`~ ~jge -2*%
Je qmo filxo o}fbs`o, wo hluea qmo ~jbs`o~q sl~~ji`o wfz~ ql o}syo~~ qmo soyjboqoy fea fyof lh f yonqfeg`o wmoe wo
aleq zoq delw wmfq jq~ `oegqm fea wjaqm fnquf``z fyo% Elw, wmoe wo oenlueqoy f yonqfeg`o wml~o ajboe~jle~ wo al
delw, wo nfe ~jbs`z ~ui~qjquqo -ly s`ug je* qml~o xf`uo~ je qmo filxo ovufqjle~% Je qmj~ nmfsqoy, wo wj`` oenlueqoy
bfez o}syo~~jle~ qmfq wo nfe oxf`ufqo iz s`uggjeg je xf`uo~ hly qmo xfyjfi`o~ jexl`xoa%
Oxf`ufqo F`goiyfjn O}syo~~jle~
Wmoe wo fyo gjxoe fe f`goiyfjn o}syo~~jle, leo lh qmo bl~q nlbble qmjeg~ wo bjgmq mfxo ql al wjqm jq j~ oxf`ufqo
jq hly ~lbo gjxoe xf`uo lh qmo xfyjfi`o% Qmo hl``lwjeg o}fbs`o j``u~qyfqo~ qmj~ sylno~~%
O}fbs`o 9
@oq } 2 69 % Hjea qmo xf`uo lh9} 7 %Ql stea qmo ~l`uqjle, wo ~ui~qjquqo 69 hly } je qmo gjxoe o}syo~~jle% Oxoyz qjbo wo ~oo } , wo yos`fno jq wjqm 69%
9} 7 2 9-69* 72 91 72 67
Elqo; Fq qmj~ ~qfgo lh qmo syli`ob, wo s`fno qmo ~ui~qjquqoa xf`uo je sfyoeqmo~o~% Wo al qmj~ ql bfdo qmo wyjqqoe"luq
syli`ob of~joy ql hl``lw, fea ql fxlja bj~qfdo~% -Jh wo ajaeq u~o sfyoeqmo~o~ fea f`~l hlyglq ql faa f bu`qjs`jnfqjle
~jge, wo wlu`a oea us quyejeg 9} jeql 969 je~qofa lh 9 qjbo~ 69&*
NMFSQOY 6% OV_FQJLE^ FEA H_ENQJLE^
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O}fbs`o >
@oq z 2 9% Hjea qmo xf`uo lh 7z
66z $ 9 %^l`uqjle
7
-
9*
66-9* $ 9 2 > 69
$ 99 $ 9
2 91 > 69
2 936
9
Bfez o}syo~~jle~ mfxo blyo qmfe leo xfyjfi`o je qmob% Hly o}fbs`o, qmo hlybu`f hly qmo soyjboqoy lh f yonqfeg`o je
qmo jeqylaunqjle mf~ qwl xfyjfi`o~; `oegqm -`* fea wjaqm -w* % Je qmo~o nf~o~, io nfyohu` ql ~ui~qjquqo qmo fssylsyjfqoxf`uo je qmo fssylsyjfqo s`fno%
O}fbs`o ?
Qmo fyof lh f qyfso{lja j~ gjxoe iz qmo ovufqjle F 2 m9 -f $ i* % Hjea qmo fyof lh f qyfso{lja wjqm if~o~ f 2 63 nbfea i 2 6? nb fea mojgmq m 2 = nb %
Ql stea qmo ~l`uqjle ql qmj~ syli`ob, wo ~jbs`z qfdo qmo xf`uo~ gjxoe hly qmo xfyjfi`o~f
,i
, feam
, fea s`ug qmob jeql qmo o}syo~~jle hly F ;
F 2m
9-f $ i* ^ui~qjquqo 63 hly f, 6? hly i, fea = hly m%
F 2=
9-63 $ 6?* Oxf`ufqo sjono iz sjono% 63 $ 6? 2 9?4
=
92 1%
F 2 1-9?* 2 633
^l`uqjle; Qmo fyof lh qmo qyfso{lja j~ 633 ~vufyo noeqjboqoy~%
Oxf`ufqo F`goiyfjn O}syo~~jle~ wjqm O}sleoeq~
Bfez hlybu`f~ fea ovufqjle~ je bfqmobfqjn~ nleqfje o}sleoeq~% O}sleoeq~ fyo u~oa f~ f ~mlyq"mfea elqfqjle hly
yosofqoa bu`qjs`jnfqjle% Hly o}fbs`o;
9 9 2 999 9 9 2 9>
6%6% XFYJFI@O O]SYO^^JLE^
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Qmo o}sleoeq ~qfea~ hly mlw bfez qjbo~ qmo eubioy j~ u~oa f~ f hfnqly -bu`qjs`joa*% Wmoe wo aof` wjqm jeqogoy~, jq
j~ u~uf``z of~jo~q ql ~jbs`jhz qmo o}syo~~jle% Wo ~jbs`jhz;
99 2 1
9> 2 =
Mlwoxoy, wo eooa o}sleoeq~ wmoe wo wlyd wjqm xfyjfi`o~, ionfu~o jq j~ bunm of~joy ql wyjqo }= qmfe } } } } } } } } %Ql oxf`ufqo o}syo~~jle~ wjqm o}sleoeq~, ~ui~qjquqo qmo xf`uo~ zlu fyo gjxoe hly ofnm xfyjfi`o fea ~jbs`jhz% Jq j~
o~sonjf``z jbslyqfeq je qmj~ nf~o ql ~ui~qjquqo u~jeg sfyoeqmo~o~ je lyaoy ql bfdo ~uyo qmfq qmo ~jbs`jstnfqjle j~ aleo
nlyyonq`z%
Hly f blyo aoqfj`oa yoxjow lh o}sleoeq~ fea qmojy sylsoyqjo~, nmond luq qmo xjaol fq mqqs;www%bfqmxja~%nlb`o~~
lebfqmmo`s=8>"o}sleoeq~if~jn~%
O}fbs`o ?
Qmo fyof lh f njyn`o j~ gjxoe iz qmo hlybu`f F 2 y9 % Hjea qmo fyof lh f njyn`o wjqm yfaju~ y2 67 jenmo~ %
^ui~qjquqo xf`uo~ jeql qmo ovufqjle%
F 2 y9 ^ui~qjquqo 67 hly y%
F 2 -67*9 67 67 :37%:939 % % % Yluea ql 9 aonjbf` s`fno~%
Qmo fyof j~ fssyl}jbfqo`z :37%:9 ~vufyo jenmo~%
O}fbs`o 8
Hjea qmo xf`uo lh }9z>
}>$z9, hly } 2 9 fea z 2 1 %
^ui~qjquqo qmo xf`uo~ lh} fea z je qmo hl``lwjeg%
}9z>
}> $z92
-9*9-1*>-9*> $ -1*9 ^ui~qjquqo 9 hly } fea 1 hly z%
1-81*= $ 68
29?8
912
>9>
Oxf`ufqo o}syo~~jle~; -9*9 2 -9*-9* 2 1 fea
-9*> 2 -9*-9*-9* 2 =% -1*9 2 -1*-1* 2 68 fea-1*> 2 -1*-1*-1* 2 81%
O}fbs`o 7
NMFSQOY 6% OV_FQJLE^ FEA H_ENQJLE^
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Qmo mojgmq-m* lh f if`` je jgmq j~ gjxoe iz qmo hlybu`f m 2 >9q9 $ 83q$ 93 , wmoyo qmo mojgmq j~ gjxoe je hooq feaqmo qjbo -q* j~ gjxoe je ~onlea~% Hjea qmo mojgmq lh qmo if`` fq qjbo q 2 9 ~onlea~ %
^l`uqjle
m 2 >9q9 $ 83q$ 93
2 >9-9*9
$ 83-9* $ 93 ^ui~qjquqo 9 hly q%2 >9-1* $ 83-9* $ 932 69
Qmo mojgmq lh qmo if`` j~ 69 hooq%
Yoxjow Vuo~qjle~
6% Wyjqo qmo hl``lwjeg je f blyo nleaoe~oa hlyb iz `ofxjeg luq f bu`qjs`jnfqjle ~zbil`%
f% 9 66}i% 6%>? zn% > 6
1
a% 61{
9% Oxf`ufqo qmo hl``lwjeg o}syo~~jle~ hly f 2 >, i 2 9, n 2 ?, fea a2 1 %f% 9f $ >ii% 1n $ an% ?fn 9ia% 9f
nao% >i
ah% f1i>n$9a
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>% Oxf`ufqo qmo hl``lwjeg o}syo~~jle~ hly } 2 6, z 2 9, { 2 >, fea w 2 1 %f% =}>
i% ?}9
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1% Qmo wood`z nl~q Nlh bfeuhfnquyjeg } yoblqo nleqyl`~ j~ gjxoe iz qmo hlybu`f N2 9333 $ >} , wmoyo qmo nl~qj~ gjxoe je al``fy~%
f% Wmfq j~ qmo nl~q lh sylaunjeg 6333 yoblqo nleqyl ~ 66 $ 92 61 $ 92 69
i* Qmj~ o}syo~~jle mf~ sfyoeqmo~o~, ~l wo sty~q oxf`ufqo 7 66 2 1 % Yobobioy qmfq wmoe wo ~uiqyfnq f eogfqjxojq j~ ovujxf`oeq ql faajeg f sl~jqjxo;
NMFSQOY 6% OV_FQJLE^ FEA H_ENQJLE^
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1 -7 66* $ 9 2 1 -1* $ 92 = $ 9
2 63
n* Fe o}syo~~jle nfe nleqfje fez eubioy lh ~oq~ lh sfyoeqmo~o~% ^lboqjbo~ o}syo~~jle~ wj`` mfxo ~oq~ lh sfyoeqmo~o~
je~jao lqmoy ~oq~ lh sfyoeqmo~o~% Wmoe hfnoa wjqm eo~qoa sfyoeqmo~o~, ~qfyq fq qmo jeeoybl~q sfyoeqmo~o~ fea wlydluqwfya%
Iyfndoq~ bfz f`~l io u~oa ql gylus o}syo~~jle~ wmjnm f`yofaz nleqfje sfyoeqmo~o~% Qmj~ o}syo~~jle mf~ ilqm iyfnd"
oq~ fea sfyoeqmo~o~% Wo ~qfyq wjqm qmo jeeoybl~q gylus; 66 $ 9 2 6> % Qmoe wo nlbs`oqo qmo lsoyfqjle je qmoiyfndoq~%
1 T7 -66 $ 9*R 2 1 T7 -6>*R2 1 T8R2 63
O}fbs`o 9
Oxf`ufqo qmo hl``lwjeg;
f* > ? 7 9i* > -? 7* 9n* -> ?* -7 9*f* Qmoyo fyo el gylusjeg ~zbil`~% SOBAF^ ajnqfqo~ qmfq wo bu`qjs`z fea ajxjao sty~q, wlydjeg hylb `ohq ql yjgmq;
> ? 2 6? fea 7 9 2 >%? % -ELQO; Jq~ elq bu`qjs`jnfqjle qmoe ajxj~jle%* Eo}q wo ~uiqyfnq;
> ? 7 9 2 6? >%?2 66%?
i* Hjy~q, wo oxf`ufqo qmo o}syo~~jle je~jao qmo sfyoeqmo~o~; ? 7 2 9 % Qmoe wlyd hylb `ohq ql yjgmq;
> -? 7* 9 2 > -9* 92 -8* 92 >
n* Hjy~q, wo oxf`ufqo qmo o}syo~~jle~ je~jao sfyoeqmo~o~; > ? 2 6? fea 7 9 2 >%? % Qmoe wlyd hylb `ohq ql yjgmq;
-> ?* -7 9* 2 6? >%?2 66%?
Elqo qmfq faajeg sfyoeqmo~o~ ajaeq nmfego qmo o}syo~~jle je sfyq n, iuq aja bfdo jq of~joy ql yofa% Sfyoeqmo~o~ nfe
io u~oa ql nmfego qmo lyaoy lh lsoyfqjle~ je fe o}syo~~jle, iuq qmoz nfe f`~l io u~oa ~jbs`z ql bfdo jq of~joy ql
ueaoy~qfea%
6%9% LYAOY LH LSOYFQJLE^
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Wo nfe f`~l u~o qmo lyaoy lh lsoyfqjle~ ql ~jbs`jhz fe o}syo~~jle qmfq mf~ xfyjfi`o~ je jq, fhqoy wo ~ui~qjquqo ~sonjstn
xf`uo~ hly qml~o xfyjfi`o~%
O}fbs`o >
_~o qmo lyaoy lh lsoyfqjle~ ql oxf`ufqo qmo hl``lwjeg;
f* 9 ->} $ 9* wmoe } 2 9i* >z9 $ 9z $ 6 wmoe z 2
>
n* 9 -q 7*9 -u> x* wmoe q 2 6:, u 2 1, fea x 2 9f* Qmo sty~q ~qos j~ ql ~ui~qjquqo qmo xf`uo hly } jeql qmo o}syo~~jle% Wo nfe suq jq je sfyoeqmo~o~ ql n`fyjhz qmo yo~u`qjeg
o}syo~~jle%
9 ->-9* $ 9*
-Elqo; >-9* j~ qmo ~fbo f~ > 9 %*Hl``lw SOBAF^ " sty~q sfyoeqmo~o~% Je~jao sfyoeqmo~o~ hl``lw SOBAF^ fgfje%
9 -> 9 $ 9* 2 9 -8 $ 9* Je~jao qmo sfyoeqmo~o~, wo bu`qjs`z sty~q%9 = 2 8 Eo}q wo faa je~jao qmo sfyoeqmo~o~, fea stef` z wo ~uiqyfnq%
i* Qmo sty~q ~qos j~ ql ~ui~qjquqo qmo xf`uo hly z jeql qmo o}syo~~jle%
> ->*9 $ 9 ->* 6
Hl``lw SOBAF^; wo nfeelq ~jbs`jhz qmo o}syo~~jle~ je sfyoeqmo~o~, ~l o}sleoeq~ nlbo eo}q%
> ->*9 $ 9 ->* 6 Oxf`ufqo o}sleoeq~; ->*9 2 :2 > : $ 9 ->* 6 Oxf`ufqo bu`qjs`jnfqjle; > : 2 974 9 > 2 82 97 $ -8* 6 Faa fea ~uiqyfnq je lyaoy hylb `ohq ql yjgmq%2 97 8 62 93
n* Qmo sty~q ~qos j~ ql ~ui~qjquqo qmo xf`uo~ hly q, u, fea x jeql qmo o}syo~~jle%
9
-6:
7*9
-1>
9*
Hl``lw SOBAF^;
9 -6: 7*9 -1> 9* Oxf`ufqo sfyoeqmo~o~; -6: 7* 2 694 -1> 9* 2 -81 9* 2 892 9 699 89 Oxf`ufqo o}sleoeq~; 699 2 6112 9 611 89 Bu`qjs`z; 611 89 2 =:9=2 9 =:9= ^uiqyfnq%2 =:98
NMFSQOY 6% OV_FQJLE^ FEA H_ENQJLE^
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Je sfyq~ -i* fea -n* wo `ohq qmo sfyoeqmo~o~ fyluea qmo eogfqjxo eubioy~ ql n`fyjhz qmo syli`ob% Qmoz aja elq fhhonq
qmo lyaoy lh lsoyfqjle~, iuq qmoz aja mo`s fxlja nlehu~jle wmoe wo woyo bu`qjs`zjeg eogfqjxo eubioy~%
Sfyq -n* je qmo `f~q o}fbs`o ~mlw~ felqmoy jeqoyo~qjeg sljeq% Wmoe wo mfxo fe o}syo~~jle je~jao qmo sfyoeqmo~o~, wo
u~o SOBAF^ ql aoqoybjeo qmo lyaoy je wmjnm wo oxf`ufqo qmo nleqoeq~%
Oxf`ufqo F`goiyfjn O}syo~~jle~ wjqm Hyfnqjle Ify~
Hyfnqjle ify~ nlueq f~ gylusjeg ~zbil`~ hly SOBAF^, ~l wo oxf`ufqo qmob je qmo sty~q ~qos lh ~l`xjeg fe o}syo~~jle%
F`` euboyfqly~ fea f`` aoelbjefqly~ nfe io qyofqoa f~ jh qmoz mfxo jexj~ji`o sfyoeqmo~o~ fyluea qmob% Wmoe yof`
sfyoeqmo~o~ fyo f`~l syo~oeq, yobobioy qmfq qmo jeeoybl~q gylusjeg ~zbil`~ nlbo sty~q% Jh, hly o}fbs`o, sfyoeqmo~o~
fssofy le f euboyfqly, qmoz wlu`a qfdo syonoaoeno lxoy qmo hyfnqjle ify% Jh qmo sfyoeqmo~o~ fssofy luq~jao lh qmo
hyfnqjle, qmoe qmo hyfnqjle ify qfdo~ syonoaoeno%
O}fbs`o 1
_~o qmo lyaoy lh lsoyfqjle~ ql oxf`ufqo qmo hl``lwjeg o}syo~~jle~;
f* {$>1
6 wmoe { 2 9
i*
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n* 9
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9 $ >
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F`qmlugm qmj~ o}syo~~jle mf~ el sfyoeqmo~o~, qmo hyfnqjle ify j~ f`~l f gylusjeg ~zbil`jq mf~ qmo ~fbo ohhonq f~ f
~oq lh sfyoeqmo~o~% Wo nfe wyjqo je qmo jexj~ji`o sfyoeqmo~o~ hly n`fyjqz;
-9 $ >*
16
_~jeg SOBAF^, wo sty~q oxf`ufqo qmo euboyfqly;
?
1 6
Wo nfe nlexoyq?1 ql f bj}oa eubioy;
?
12 6
6
1
Qmoe oxf`ufqo qmo o}syo~~jle;
?
1 6 2 6 6
16 2 6
1
6%9% LYAOY LH LSOYFQJLE^
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i* Wo ~ui~qjquqo qmo xf`uo~ hly f fea i jeql qmo o}syo~~jle;
> $ 9
6 $ 1 6
$ 6
Qmj~ o}syo~~jle mf~ eo~qoa sfyoeqmo~o~ -yobobioy qmo ohhonq lh qmo hyfnqjle ify*% Qmo jeeoybl~q gylusjeg ~zbil` j~
sylxjaoa iz qmo hyfnqjle ify% Wo oxf`ufqo qmo euboyfqly -> $ 9* fea aoelbjefqly -6 $ 1* sty~q%
> $ 9
6 $ 16
$ 6 2
?
? 6
6 Eo}q wo oxf`ufqo qmo je~jao lh qmo sfyoeqmo~o~% Hjy~q wo ajxjao%
2 -6 6* 6 Eo}q wo ~uiqyfnq%2 3 6 2 6
n* Wo ~ui~qjquqo qmo xf`uo~ hly w,},z, fea { jeql qmo o}syo~~jle;
9
66$->9-9**-6$9*9
6
Qmj~ nlbs`jnfqoa o}syo~~jle mf~ ~oxoyf` `fzoy~ lh eo~qoa sfyoeqmo~o~% Leo boqmla hly oe~uyjeg qmfq wo ~qfyq wjqm
qmo jeeoybl~q sfyoeqmo~o~ j~ ql u~o blyo qmfe leo qzso lh sfyoeqmo~o~% Wlydjeg hylb qmo luq~jao, wo nfe `ofxo qmoluqoybl~q iyfndoq~ f~ sfyoeqmo~o~ -* % Eo}q wj`` io qmo jexj~ji`o iyfndoq~ hylb qmo hyfnqjle ify4 wo wj`` wyjqo qmo~of~ T R % Qmo qmjya `oxo` lh eo~qoa sfyoeqmo~o~ wj`` io qmo % Wo wj`` `ofxo eogfqjxo eubioy~ je yluea iyfndoq~%
9 T66 $ t> 9-9*rR
t6 $ 9r9 6
^qfyq wjqm qmo jeeoybl~q gylusjeg ~jge; tr %
t6 $ 9r 2 >4 t> 9-9*r 2 > $ 1 2 7
2 9
T66 $ 7R
T>9R6
Eo}q, oxf`ufqo qmo ~vufyo iyfndoq~%
2 96=
: 6
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2 9-9 6* Hjef``z, al qmo faajqjle fea ~uiqyfnqjle%2 9-6* 2 9
Oxf`ufqo F`goiyfjn O}syo~~jle~ wjqm f QJ"=>=1 Hfbj`z Gyfsmjeg Nf`nu`fqly
F gyfsmjeg nf`nu`fqly j~ f xoyz u~ohu` qll` je oxf`ufqjeg f`goiyfjn o}syo~~jle~% @jdo f ~njoeqjstn nf`nu`fqly, f gyfsmjeg
nf`nu`fqly hl``lw~ SOBAF^% Je qmj~ ~onqjle wo wj`` o}s`fje qwl wfz~ lh oxf`ufqjeg o}syo~~jle~ wjqm qmo gyfsmjegnf`nu`fqly%
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93 www%nd69%lyg
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Wyjqo f Huenqjle Yu`o
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Elqjno qmfq oxoe qmlugm qmo ~fbo soy~le nfeq mfxo blyo qmfe leo mojgmq, jq~ ldfz hly blyo qmfe leo soy~le ql mfxo
qmo ~fbo mojgmq% Je f huenqjle, blyo qmfe leo jesuq nfe mfxo qmo ~fbo luqsuq, f~ `leg f~ blyo qmfe leo luqsuq eoxoy
nlbo~ hylb qmo ~fbo jesuq%
O}fbs`o 66
Aoqoybjeo jh qmo yo`fqjle j~ f huenqjle%
f* -6, >*, -"6, "9*, ->, ?*, -9, ?*, ->, 1*
i* -">, 93*, -"?, 9?*, -"6, ?*, -7, 69*, -:, 9*
n*
} 9 6 3 6 9
z 69 63 = 8 1
^l`uqjle
Qmo of~jo~q wfz ql stguyo luq jh f yo`fqjle j~ f huenqjle j~ ql `lld fq f`` qmo } xf`uo~ je qmo `j~q ly qmo qfi`o% Jh f xf`uolh} fssofy~ blyo qmfe leno, fea jq~ sfjyoa us wjqm ajhhoyoeq z xf`uo~, qmoe qmo yo`fqjle j~ elq f huenqjle%f* Zlu nfe ~oo qmfq je qmj~ yo`fqjle qmoyo fyo qwl ajhhoyoeq z xf`uo~ sfjyoa wjqm qmo } xf`uo lh >% Qmj~ bofe~ qmfqqmj~ yo`fqjle j~ elq f huenqjle%
i* Ofnm xf`uo lh} mf~ o}fnq`z leo z xf`uo% Qmo yo`fqjle j~ f huenqjle%n* Je qmj~ yo`fqjle qmoyo fyo qwl ajhhoyoeq z xf`uo~ sfjyoa wjqm qmo } xf`uo lh 9 fea qwl z xf`uo~ sfjyoa wjqm qmo} xf`uo lh 6% Qmo yo`fqjle j~ elq f huenqjle%Wmoe f yo`fqjle j~ yosyo~oeqoa gyfsmjnf``z, wo nfe aoqoybjeo jh jq j~ f huenqjle iz u~jeg qmo xoyqjnf` `jeo qo~q% Jh zlu
nfe ayfw f xoyqjnf` `jeo qmfq nyl~~o~ qmo gyfsm je blyo qmfe leo s`fno, qmoe qmo yo`fqjle j~ elq f huenqjle% Moyo fyo
~lbo o}fbs`o~%
6%8% H_ENQJLE^ F^ GYFSM^
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Elq f huenqjle% Jq hfj`~ qmo xoyqjnf` `jeo qo~q%
F huenqjle% El xoyqjnf` `jeo wj`` nyl~~ blyo qmfe leo sljeq le qmo gyfsm%
F huenqjle% El xoyqjnf` `jeo wj`` nyl~~ blyo qmfe leo sljeq le qmo gyfsm%
NMFSQOY 6% OV_FQJLE^ FEA H_ENQJLE^
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Elq f huenqjle% Jq hfj`~ qmo xoyqjnf` `jeo qo~q%
Faajqjlef` Yo~luyno~
Leno zluxo mfa ~lbo syfnqjno gyfsmjeg huenqjle~ iz mfea, zlu bfz wfeq ql u~o f gyfsmjeg nf`nu`fqly ql bfdogyfsmjeg of~joy% Jh zlu aleq mfxo leo, zlu nfe f`~l u~o qmo fss`oq fq mqqs;yonmeoyle`jeo%aohuenqjle"gyfsm~% Ku~q
qzso f huenqjle je qmo i`fed fea syo~~ Oeqoy% Zlu nfe u~o qmo lsqjle~ ueaoy Aj~s`fz Sylsoyqjo~ ql {llb je ly sfe
fyluea ql ajhhoyoeq sfyq~ lh qmo gyfsm%
Yoxjow Vuo~qjle~
6% S`lq qmo nllyajefqo sljeq~ le qmo Nfyqo~jfe s`feo%
f% -1, "1*
i% -9, 7*n% -">, "?*
a% -8, >*
o% -"1, >*
9% Gjxo qmo nllyajefqo~ hly ofnm sljeq je qmj~ Nfyqo~jfe s`feo%
>% Gyfsm qmo huenqjle qmfq mf~ qmo hl``lwjeg qfi`o lh xf`uo~% -f*
} 63 ? 3 ? 63z > 3%? 9 1%? 7
6%8% H_ENQJLE^ F^ GYFSM^
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-i*
^jao lh nuio -je%* 3 6 9 >
Xl`ubo -je>* 3 6 = 97
-n*
Qjbo -mluy~* 9 6 3 6 9Aj~qfeno hylb qlwe noeqoy -bj`o~* ?3 9? 3 9? ?3
1% Gyfsm qmo hl` lwjeg huenqjle~%
f% Iyfeale j~ f bobioy lh f blxjo n`ui% Mo sfz~ f !?3 feeuf` bobioy~mjs fea != soy blxjo%
i% h-}* 2 -} 9*9n% h-}* 2 >%9}
?% Aoqoybjeo wmoqmoy ofnm yo`fqjle j~ f huenqjle; -f* -6, 7*, -9, 7*, ->, =*, -1, =*, -?, :* -i* -6, 6*, -6, "6*, -1, 9*,
-1, "9*, -:, >*, -:, ">* -n*
} 1 > 9 6 3z 68 : 1 6 3
-a*
Fgo 93 9? 9? >3 >?
Eubioy lh kli~ iz qmfq fgo > 1 7 1 9
8% Wyjqo qmo huenqjle yu`o hly ofnm gyfsm%
f%
i%
7% Qmo ~quaoeq~ fq f `lnf` mjgm ~nmll` qlld Qmo Zluqm Yj~d Iomfxjly ^uyxoz% Qmo gyfsm io`lw ~mlw~ qmo soy"
noeqfgo lh mjgm ~nmll` ~quaoeq~ wml yoslyqoa qmfq qmoz woyo nuyyoeq ~bldoy~% -F nuyyoeq ~bldoy j~ fezleo
wml mf~ ~bldoa leo ly blyo njgfyoqqo~ je qmo sf~q >3 afz~%* Wmfq soynoeqfgo lh mjgm"~nmll` ~quaoeq~ woyo
nuyyoeq ~bldoy~ je qmo hl``lwjeg zofy~;
Nfyyz luq qmo s`fe " ^l`xo
NMFSQOY 6% OV_FQJLE^ FEA H_ENQJLE^
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Qmj~ j~ wmoyo zlu ~l`xo qmo ovufqjle zlu aoxo`lsoa je ^qos 9%
^qos 1;
@lld " Nmond fea Jeqoysyoq
Nmond ql ~oo jh zlu u~oa f`` zluy jehlybfqjle% Qmoe `lld ql ~oo jh qmo fe~woy bfdo~ ~oe~o%
^l`xo Yof`"Wly`a Syli`ob~ _~jeg f S`fe
@oq~ elw fss`z qmj~ syli`ob ~l`xjeg s`fe ql f syli`ob%
O}fbs`o 6
F nlhhoo bfdoy j~ le ~f`o fq ?3/ lhh qmo yogu`fy qjndoq syjno% Le qmo ^ueafz ^usoy ^f`o qmo ~fbo nlhhoo bfdoy j~
le ~f`o fq fe faajqjlef` 13/ lhh% Jh qmo stef` syjno j~ !96, wmfq wf~ qmo lyjgjef` syjno lh qmo nlhhoo bfdoy?% Hjea qmo qlqf` nl~q jh qmo ~f`o~ qf} j~ 7%7?/%
9% Qmj~ zofy zlu glq f ?/ yfj~o% Jh zluy eow ~f`fyz j~ !1?,333, wmfq wf~ zluy ~f`fyz iohlyo qmo yfj~o% Bfyjfef aosl~jq~ !?33 je f ~fxjeg~ fnnlueq qmfq sfz~ >/ ~jbs`o jeqoyo~q soy zofy% Mlw bunm wj`` io je moy
fnnlueq fhqoy qmyoo zofy~ mf~ > if``~, ylw 1 mf~ 1 if``~, ylw ? mf~ ? if``~, ylw 8 mf~ 8 if``~, ylw 7
mf~ 7 if``~, ylw = mf~ = if``~%
Wmoe wo faa qmo~o wo goq; 6 $ 9 $ > $ 1 $ ? $ 8 $ 7 $ = 2 >8 if``~
Qmo fe~woy nmond~ luq%
Elqjno qmfq je qmj~ o}fbs`o wo bfao qfi`o~ fea ayow ajfgyfb~ ql mo`s u~ lygfej{o luy jehlybfqjle fea stea f sfqqoye%
_~jeg ~oxoyf` boqmla~ qlgoqmoy j~ f xoyz nlbble syfnqjno fea j~ xoyz u~ohu` je ~l`xjeg wlya syli`ob~%
S`fe fea Nlbsfyo F`qoyefqjxo Fssylfnmo~ ql ^l`xjeg Syli`ob~
Je qmj~ ~onqjle, wo wj`` nlbsfyo qmo boqmla~ lh Bfdjeg f Qfi`o fea @lldjeg hly f Sfqqoye iz u~jeg ofnm boqmla
je quye ql ~l`xo f syli`ob%
O}fbs`o 1
Feayow nf~mo~ f !6=3 nmond fea wfeq~ qmo bleoz je !63 fea !93 ij``~% Qmo ifed qo``oy gjxo~ mjb 69 ij``~% Mlw
bfez lh ofnm djea lh ij`` alo~ mo yonojxo363 9 !63-63* $ !93-9* 2 !613: > !63-:* $ !93->* 2 !6?3= 1 !63-=* $ !93-1* 2 !6837 ? !63-7* $ !93-?* 2 !6738 8 !63-8* $ !93-8* 2 !6=3? 7 !63-?* $ !93-7* 2 !6:31 = !63-1* $ !93-=* 2 !933> : !63->* $ !93-:* 2 !9639 63 !63-9* $ !93-63* 2 !9936 66 !63-6* $ !93-66* 2 !9>33 69 !63-3* $ !93-69* 2 !913
NMFSQOY 6% OV_FQJLE^ FEA H_ENQJLE^
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Je qmo qfi`o wo `j~qoa f`` qmo sl~~ji`o wfz~ zlu nfe goq qwo`xo !63 ij``~ fea !93 ij``~ fea qmo qlqf` fblueq lh bleoz
hly ofnm sl~~jij`jqz% Qmo nlyyonq fblueq j~ gjxoe wmoe Feayow mf~ ~j} !63 ij``~ fea ~j} !93 ij``~%
Fe~woy; Feayow goq~ ~j} !63 ij``~ fea ~j} !93 ij``~%
Nmond
^j} !63 ij``~ fea ~j} !93 ij``~ 8-!63* $ 8-!93* 2 !83 $ !693 2 !6=3Qmo fe~woy nmond~ luq%
@oq~ ~l`xo qmo ~fbo syli`ob u~jeg qmo boqmla @lld hly f Sfqqoye%
Boqmla 9; @lldjeg hly f Sfqqoye
_eaoy~qfea
Feayow gjxo~ qmo ifed qo``oy f !6=3 nmond%
Qmo ifed qo``oy gjxo~ Feayow 69 ij``~% Qmo~o ij``~ fyo f bj} lh !63 ij``~ fea !93 ij``~%
Wo wfeq ql delw mlw bfez lh ofnm djea lh ij`` Feayow yonojxo~%
^qyfqogz
@oq~ ~qfyq iz bfdjeg f qfi`o ku~q f~ wo aja filxo% Mlwoxoy, qmj~ qjbo wo wj`` `lld hly sfqqoye~ je qmo qfi`o qmfq nfe
io u~oa ql stea qmo ~l`uqjle%
Fss`z ~qyfqogz~l`xo
@oq~ st`` je qmo ylw~ lh qmo qfi`o ueqj` wo ~oo f sfqqoye%
QFI@O 6%6?;
!63 ij``~ !93 ij``~ Qlqf` fblueq
69 3 !63-69* $ !93-3* 2 !69366 6 !63-66* $ !93-6* 2 !6>363 9 !63-63* $ !93-9* 2 !613
Wo ~oo qmfq oxoyz qjbo wo yoauno qmo eubioy lh !63 ij``~ iz leo fea jenyof~o qmo eubioy lh !93 ij``~ iz leo, qmo
qlqf` fblueq jenyof~o~ iz !63% Qmo `f~q oeqyz je qmo qfi`o gjxo~ f qlqf` fblueq lh !613, ~l wo mfxo !13 ql gl ueqj`
wo yofnm luy glf`% Qmj~ bofe~ qmfq wo ~mlu`a yoauno qmo eubioy lh !63 ij``~ iz hluy fea jenyof~o qmo eubioy lh
!93 ij``~ iz hluy% Qmfq wlu`a gjxo u~ ~j} !63 ij``~ fea ~j} !93 ij``~%
8-!63* $ 8-!93* 2 !83 $ 693 2 !6=3
Fe~woy; Feayow goq~ ~j} !63 ij``~ fea ~j} !93 ij``~%
Nmond
^j} !63 ij``~ fea ~j} !93 ij``~ 8-!63* $ 8-!93* 2 !83 $ 693 2 !6=3Qmo fe~woy nmond~ luq%
Zlu nfe ~oo qmfq qmo ~onlea boqmla wo u~oa hly ~l`xjeg qmo syli`ob wf~ `o~~ qoajlu~% Je qmo sty~q boqmla, wo
`j~qoa f`` qmo sl~~ji`o lsqjle~ fea hluea qmo fe~woy wo woyo ~oodjeg% Je qmo ~onlea boqmla, wo ~qfyqoa iz `j~qjeg
qmo lsqjle~, iuq wo hluea f sfqqoye qmfq mo`soa u~ stea qmo ~l`uqjle hf~qoy% Qmo boqmla~ lh Bfdjeg f Qfi`o fea
@lldjeg hly f Sfqqoye fyo ilqm blyo slwoyhu` jh u~oa f`leg~jao lqmoy syli`ob"~l`xjeg boqmla~%
6%=% SYLI@OB"^L@XJEG ^QYFQOGJO^; BFDO F QFI@O FEA @LLD HLY F SFQQOYE
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^l`xo Yof`"Wly`a Syli`ob~ _~jeg ^o`onqoa ^qyfqogjo~ f~ Sfyq lh f S`fe
O}fbs`o ?
Feeo j~ bfdjeg f il} wjqmluq f `ja% ^mo ~qfyq~ wjqm f 93 je% ~vufyo sjono lh nfyailfya fea nuq~ luq hluy ovuf` ~vufyo~
hylb ofnm nlyeoy lh qmo nfyailfya f~ ~mlwe% ^mo qmoe hl`a~ qmo ~jao~ lh qmo il} fea g`uo~ qmo oago~ qlgoqmoy% Mlw
ijg alo~ ~mo eooa ql nuq qmo nlyeoy ~vufyo~ je lyaoy ql bfdo qmo il} wjqm qmo ijggo~q xl`ubo91 je>@oq~ bfdo f qfi`o qmfq ~mlw~ qmo xf`uo lh qmo il} hly ajhhoyoeq ~vufyo ~j{o~;
QFI@O 6%68;
^jao lh vufyo Il} Mojgmq Il} Wjaqm Il} @oegqm Xl`ubo
6 6 6= 6= 6= 6= 6 2 >919 9 68 68 68 68 9 2 ?69> > 61 61 61 61 > 2 ?==1 1 69 69 69 69 1 2 ?78? ? 63 63 63 63 ? 2 ?338 8 = = = = 8 2 >=17 7 8 8 8 8 7 2 9?9= = 1 1 1 1 = 2 69=: : 9 9 9 9 : 2 >863 63 3 3 3 3 63 2 3
Wo ~qls fq f ~vufyo lh 63 jenmo~ ionfu~o fq qmj~ sljeq wo mfxo nuq luq f`` lh qmo nfyailfya fea wo nfeq bfdo f il}
fez blyo% Hylb qmo qfi`o wo ~oo qmfq wo nfe bfdo qmo ijggo~q il} jh wo nuq luq ~vufyo~ wjqm f ~jao `oegqm lh qmyoo
jenmo~% Qmj~ gjxo~ u~ f xl`ubo lh ?== je> %
Fe~woy Qmo il} lh gyofqo~q xl`ubo j~ bfao jh wo nuq luq ~vufyo~ wjqm f ~jao `oegqm lh qmyoo jenmo~%
^qos 1;
Nmond
Wo ~oo qmfq ?== je
>
j~ qmo `fygo~q xl`ubo fssofyjeg je qmo qfi`o% Wo sjndoa jeqogoy xf`uo~ hly qmo ~jao~ lh qmo ~vufyo~qmfq wo fyo nuq luq% J~ jq sl~~ji`o ql goq f `fygoy xf`uo hly qmo xl`ubo jh wo sjnd ele"jeqogoy xf`uo~< ^jeno wo goq
qmo `fygo~q xl`ubo hly qmo ~jao `oegqm ovuf` ql qmyoo jenmo~, `oq~ bfdo felqmoy qfi`o wjqm xf`uo~ n`l~o ql qmyoo jenmo~
qmfq j~ ~s`jq