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8/9/2019 Proof Methods | jiblm.org
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@GX\BNI GC OB^XO\_+LNQHD IHN\BOBM OB KNTFHKNTOAQ
Bg 4) &Qhzt"
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8/9/2019 Proof Methods | jiblm.org
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Agbthbtq
Tg tfh Obqt|xatg| " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " oo
Tg tfh Qtxdhbt " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " ooo
> Qyklgioa Igmoa Tfh tfobm tfnt |hniiy qhzn|nthq xq c|gk tfh nzhq" >
>"> Qtnthkhbtq " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " >
>"< Agkzgxbd qtnthkhbtq nbd igmoani agbbhatoshq " " " " " " " " " " " " " " " " "1 Okzioantogbq " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " 8
>"4 ^xnbtoh|q " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " =
< Z |ggc khtfgdq N|mxobm oqbt xqt cg| kn||ohd zhgzih ?
1 Kntfhkntoani obdxatogb Tfh dgkobg hcchat" >3
4"> Bgtntogb nbd dhbotogbq " " " " " " " " " " " " " " " " " " " " " " " " " " " " >34"< Shbb donm|nkq " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " >6
4"1 Qht gzh|ntogbq " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " >?
4"4 Qht z|gdxatq nbd zg}h| qhtq " " " " " " " " " " " " " " " " " " " " " " " " " "
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Tg tfh Obqt|xatg|
Tfhqh bgthq fnsh lhhb }|otthb cg| xqh ob nb obt|gdxatogb tg z|ggc ainqq }otf n Aniaxixq
O z|h|h~xoqoth" Tfh agx|qh oq dhqombnthd nq }|otobm obthbqosh nbd qntoqhq gbh gc tfh t}g
}|otobm |h~xo|hkhbtq cg| tfh kntfhkntoaq kn`g|" Kgqt gc tfh qtxdhbtq tfnt fnsh tnehb tfoq
ainqq nt Lh||y Agiihmh n|h kntfhkntoaq kn`g|q nbd kobg|q) lxt gaanqogbniiy gtfh| qaohbahkn`g|q }oii tneh tfh agx|qh" Nt tfh lhmobbobm gc tfh qhkhqth| qtxdhbtq gcthb }g|e ob qknii
m|gxzq gbh g| t}g dnyq zh| }hhe xbtoi tfhy lhmob tg dhshigz kg|h cnkoion|oty }otf tfh
thafbo~xhq gc z|ggc" Ob tfhqh qknii m|gxzq) tfhy qgkhtokhq }g|e gb agbqt|xatobm z|ggcq
tfnt tfhy komft inth| z|hqhbt tg tfh ainqq" Gtfh| tokhq) tfhy }g|e agiinlg|ntoshiy gb sn|ogxq
eobdq gc }g|eqfhhtq tfnt n|h dhqombhd tg fhiz tfhk qhh tfh xboty gc kntfhkntoaq nbd z|hzn|h
tfhk tg t|nbqzg|t tfh tfobmq tfhy ihn|b ob tfh z|ggc ainqq tg gtfh| agx|qhq" Nq tfhy lhagkh
kg|h z|gaohbt nt }|otobm z|ggcq) tfhy qzhbd ihqq tokh }g|eobm ob m|gxzq nbd kg|h tokh
dgobm z|hqhbtntogbq nt tfh lgn|d" Ly tfh hbd gc tfh qhkhqth|) hnaf dny gc ainqq oq qzhbt gb
qtxdhbt z|hqhbtntogbq"
Ob tfh bgthq tfnt cgiig}) tfh|h n|h ^xhqtogbq) Hvh|aoqhq nbd Z|glihkq tfnt n|h khnbt cg|
tfh qtxdhbtq" Tfh ^xhqtogbq n|h tfh|h tg mht tfh qtxdhbt qtn|thd tfobeobm nlgxt dhbotogbq
g| nvogkq lhcg|h tfhy qtn|t t|yobm tg z|gsh nbytfobm" Tfh qgixtogbq tg tfh Hvh|aoqhq n|h
mhbh|niiy kg|h |gxtobh nbd nq qxaf n|h obthbdhd tg lh xqhd tg qtokxinth ainqq) g| qknii
m|gxz) doqaxqqogb) }otfgxt tfh qtxdhbt fnsobm tg }g||y nlgxt agbqt|xatobm n cg|kni z|ggc"
Tfh Z|glihkq n|h tfh|h cg| qtxdhbtq tg }g|e gb nbd a|hnth z|ggcq" Kgqt gc tfhqh qtnthkhbtq
n|h t|xh) tfgxmf bgt nii" Tfh mhbh|ni obqt|xatogb oq khnbt tg lh Z|gsh) g| doqz|gsh nbd
qnisnmh) oc zgqqolih" Tfnt oq) oc tfh qtnthkhbt oq t|xh) z|gsodh n z|ggc" Oc tfh qtnthkhbt oq
cniqh) z|gsodh n agxbth|hvnkzih nbd tfhb bd n |hinthd qtnthkhbt }foaf oq t|xh nbd z|gsh
ot"
oo
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Tg tfh Qtxdhbt
Tfhqh bgthq n|h }|otthb tg obt|gdxah ygx tg tfh lnqoa thafbo~xhq gc kntfhkntoani z|ggc"
Tfh|h oq bg zn|toaxin| xbocyobm agbthbt n|hn) tfgxmf ygx kny inth| |hagmboph qgkh gc tfh
hvh|aoqhq nq agkobm c|gk bxklh| tfhg|y) nlqt|nat nimhl|n) |hni nbniyqoq g| tgzgigmy" Tfh
z|okn|y mgni gc tfh agx|qh oq tg nod ygx| dhshigzkhbt nq n kntfhkntoaniiy kntx|h qtxdhbtly thnafobm ygx tg }|oth agbsobaobm z|ggcq" Ob tfh z|gahqq ygx }oii bhhd tg ihn|b tg xqh
kntfhkntoani inbmxnmh ag||hatiy nbd z|haoqhiy" Tfh agx|qh oq niqg dhqombhd tg mosh ygx n
miokzqh gc }fnt ot oq tfnt kntfhkntoaonbq dg) nbd fgzhcxiiy tfh }ny tfnt kntfhkntoaonbq
mg nlgxt dgobm ot" Knby zhgzih tfobe tfnt kntfhkntoaq oq `xqt nlgxt qgisobm h~xntogbq
nbd ddiobm nlgxt }otf bxklh|q" Fg}hsh|) h~xntogbq n|h tg kntfhkntoaq nq tyzobm oq tg
}|otobm" Qgisobm h~xntogbq anb z|gsodh n khnbq tg nb hbd) lxt tfh nat gc qgisobm nb h~xntogb
oq bgt ni}nyq tfh hbd ob otqhic"
Ob ygx| |qt aniaxixq agx|qh) ygx ihn|bhd nlgxt iokotq) agbtobxoty) docch|hbtontogb nbd
obthm|ntogb nt nb obt|gdxatg|y ihshi" Kgqt ioehiy tfh ainqq }nq cgaxqhd z|okn|oiy gb tfh
dhshigzkhbt gc aniaxixq nbd fg} tg nzziy aniaxixq tg qgish z|glihkq" _gx kny fnsh
qhhb qgkh z|ggcq) lxt tfhy z|glnliy }h|h bgt qt|hqqhd tgg kxaf tg naagkkgdnth tfh bgb+
kntfhkntoaq kn`g|q ob tfh nxdohbah" Ob kg|h ndsnbahd kntfhkntoaq agx|qhq fg}hsh|) tfh
knob tf|xqt gc tfh agx|qh oq tg xbdh|qtnbd tfh tfhg|htoani xbdh|zobbobmq gc tfh tgzoa nt fnbd"
&Tfoq oq tfh qtxcc tfnt knehq knby kntfhkntoaonbq |hniiy dom kntfhkntoaq"/ Ob ainqqhq ioeh
|hni nbniyqoq) nlqt|nat nimhl|n nbd tgzgigmy ygx }oii qzhbd tfh kn`g|oty gc tfh qhkhqth|
ihn|bobm nlgxt tfh agbahztq tfnt mosh kntfhkntoaq otq |glxqt qt|xatx|h" _gx }oii qhh z|ggcq
gc tfhg|hkq nbd z|gsh qgkh gb ygx| g}b" Ob tfoq ainqq ygx }oii ihn|b }fnt agbqtotxthq n
|omg|gxq kntfhkntoani z|ggc nbd fg} tg }|oth gbh"
Tf|gxmfgxt tfh znmhq tfnt cgiig} ygx }oii bd sn|ogxq qtnthkhbtq inlhihd nq Nvogk)
Dhbotogb) Hvh|aoqh nbd tfh gaanqogbni ^xhqtogb" Nbytfobm inlhihd nq nb Nvogk oq n agb+
ahzt }h }oii naahzt nq nb n z|og|o t|xtf" Tfnt oq) }h }oii naahzt ot tnaotiy }otfgxt z|ggc" Lxt
tfoq oq bgt tg qny tfnt ygx qfgxid liobdiy naahzt ot nq mgqzhi" \ntfh|) ygx qfgxid mosh hnaf
nvogk an|hcxi agbqodh|ntogb nbd tfobe nlgxt }fy ot komft lh |hnqgbnlih tg naahzt ot nq t|xh"
_gx }oii ioehiy doqaxqq tfhqh nvogkq ob ainqq nbd fgzhcxiiy qhh }fy }h afggqh tg obaixdh
tfhqh nqqxkztogbq ob gx| qyqthk) lxt ygx }oii z|glnliy bgt dhlnth tfho| t|xtf" Tfhy n|h zn|tgc tfh agkkgbiy naahzthd zn|inbah gc kntfhkntoaq nbd }h }oii xqh tfhk naag|dobmiy"
]otf |hmn|d tg tfh Dhbotogbq) }h }oii dhbh agbahztq |omg|gxqiy }fhbhsh| zgqqolih)
lxt ob kntfhkntoaq bgt nii agbahztq anb lh dhbhd) g}obm tg tfh iokotntogbq gc inbmxnmh"
Qgkhtokhq }h }oii fnsh tg dhni }otf xbdhbnlih th|kq) lxt ob tfgqh anqhq }h anb g|dobn|oiy
nm|hh gb }fnt }h khnb }otfgxt }|otobm dg}b n dhbotogb) lhanxqh tfh t|xtf gc tfh nvogkq
moshq tfhk khnbobm" ]fhb tfh|h oq n dhbotogb gc n agbahzt ygx bhhd tg tfobe nlgxt }fnt ot
|hniiy khnbq" Tg tfh zh|qgb gb tfh qt|hht) n dhbotogb oq n zf|nqh tfnt fhizq mosh nb obtxotosh
ooo
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Tg tfh Qtxdhbt os
xbdh|qtnbdobm gc n }g|d g| odhn" U>=[ Fg}hsh|) tg n kntfhkntoaonb dhbotogbq n|h tfh
mixh tfnt lobdq n z|ggc tgmhtfh|" Tfh |hni docch|hbah fh|h oq tfnt }fhb }h xqh dhbotogbq nq
kntfhkntoaonbq) }h kxqt xqh tfhk z|haoqhiy nbd }otfgxt nby qg|t gc zghtoa ioahbqh" Tfxq)ebg}obm nbd xbdh|qtnbdobm tfh dhbotogbq n|h gcthb tfh |qt qthzq ob z|hzn|obm tg }|oth
agbsobaobm z|ggcq" Ehhz ob kobd tfh }g|dq gc tfh Dnino Inkn0
Dg bgt `xqt zny ntthbtogb tg tfh }g|dq5 Obqthnd zny ntthbtogb tg khnbobmq
lhfobd tfh }g|dq" Lxt) dg bgt `xqt zny ntthbtogb tg khnbobmq lhfobd tfh }g|dq5
Obqthnd zny ntthbtogb tg ygx| dhhz hvzh|ohbah gc tfgqh khnbobmq"
Thbpob Myntqg) Tfh Cgx|thhbtf Dnino Inkn
Tfh Hvh|aoqhq n|h tfh|h cg| ygx tg z|natoah xqobm tfh dhbotogbq nbd nzziyobm tfh nvogkq
}otfgxt fnsobm tg }|oth agkzihth z|ggcq" Tfhy n|h cg| z|natoah) lxt ygx qfgxid mosh tfhk
tfh ntthbtogb tfhy dhqh|sh" Gcthb tfhy }oii z|gsodh obqomft obtg fg} nb nvogk komft lh xqhd
ob n z|ggc g| fg} n dhbotogb anb lh nzziohd tg z|gdxah nb obthm|ni zohah gc nb n|mxkhbt"
Tfh ^xhqtogbq n|h kxaf ioeh tfh Hvh|aoqhq) lxt kny |h~xo|h ygx tg dhaodh ob ndsnbah
}fhtfh| ygx tfobe tfh qtnthkhbtq n|h t|xh g| bgt"
Lhqodhq tfh nvogkq) dhbotogbq nbd hvh|aoqhq ygx }oii qhh knby qtnthkhbtq inlhihd
Z|glihk" Tfhqh n|h tfh hqqhbah gc tfh agx|qh" Tfhqh n|h tfh qtnthkhbtq tfnt ygx }oii lh
z|gsobm gb ygx| g}b nbd tx|bobm ob cg| n m|ndh" Tfhqh n|h tfh bxmmhtq gc t|xtf tfnt ygx }oii
|hshni tg ygx|qhic ly a|hntobm tfho| z|ggcq"
Tfh|h n|h qhsh|ni docch|hbt khtfgdq gc z|ggc tfnt }h }oii hvnkobh" Qgkh n|h do|hat
nbd qgkh n|h obdo|hat" Qgkh }oii agxbt knby tfobmq nbd qgkh }oii ntthkzt tg qfg} tfh
hvoqthbah gc gbh tfobm" ]fhb nii hiqh cnoiq) t|y tg cnii lnae gb }fnt ygx ebg}" Zihnqh dgbt
cnii z|hy tg tfh thkztntogb tg kneh xz n z|ggc khtfgd tfnt qhhkq tg t tfh qotxntogb" Ob tfh
igbm |xb) tfoq }oii gbiy fhiz ygxlh agbcxqhd nlgxt}fnt ygx|h t|yobm tg dg" Nbd qobah ygx|
knob mgni oq tg dhshigz nb xbdh|qtnbdobm gc fg} kntfhkntoaq |hniiy }g|eq) ygx }oii gbiylh fobdh|obm ygx| z|gm|hqq" &Zixq ygxii ioehiy fobdh| ygx| m|ndh ob tfh z|gahqq"/ N }g|d
nlgxt z|ggc qtyih0 ygx| |qt mgni qfgxid lh tg ihn|b fg} tg agbqt|xat ag||hat kntfhkntoani
z|ggcq" ]foih tfh thkztntogb }oii nt |qt lh tg }|oth qfg|t z|ggcq }otf igtq gc bxkh|oani)
m|nzfoani g| obtxotosh n|mxkhbtq) ygx |hniiy qfgxid t|y tg obaixdh n igt gc dhtnoi nbd qgkh
doqaxqqogb nlgxt tfh agbthvt gc ygx| |hnqgbobm" Dgbt }g||y tgg kxaf nlgxt fg} mggd
ygx| z|ggc qgxbdq xbtoi ygx n|h ah|tnob tfnt ot |hniiy oq n z|ggc" Tfhb) gbah ygx fnsh lhmxb
tg knqth| tfh thafbo~xhq gc z|ggc) ygx anb tfobe nlgxt fg} tg kneh ygx| z|ggcq kg|h
hcaohbt g| kg|h zgioqfhd" ]otf |hmn|d tg zoatx|hq) n zoatx|h oq bgt n z|ggc" Fg}hsh|) n
mggd zoatx|h anb lh n snixnlih nod ob fhizobm ygx doqagsh| n z|ggc nbd fhizobm tfh |hndh|
xbdh|qtnbd ygx| z|ggc" Qg) oc ygx tfobe n zoatx|h }gxid lh fhizcxi obaixdh gbh" Oc ygx|h
bgt qx|h }fhtfh| n zoatx|h }gxid lh fhizcxi) mg nfhnd nbd obaixdh gbh nby}ny"
Fh|h oq nb obth|hqtobm) qhko+anxtogbn|y bgth0 tfh|h n|h qgkh zh|chatiy qhbqolih kntf+hkntoani qtnthkhbtq tfnt anbbgt lh sh|ohd g| z|gshb cniqh" Ob >?1> t}hbty+sh yhn| gid
Mh|knb kntfhkntoaonb Ex|t M gdhi z|gshd tfh cgiig}obm tfhg|hk tfnt qht tfh kntfhkntoani
}g|id gb otq hn|0
Mgdhiq Obagkzihthbhqq Tfhg|hk Nby qxcaohbtiy agkzihv igmoani qyqthk }oii agbtnob
xbsh|onlih nbd xbthqtnlih qtnthkhbtq"
Tfoq dghqbt qny tfnt z|ggcq n|h fn|d tg bd) g| tfnt }h n|h `xqt bgt a|hntosh hbgxmf tg bd
tfhk) lxt |ntfh| tfnt z|ggcq n|h bgt tfh|h tg lh cgxbd" Lxt tfh|hq bg bhhd tg }g||y" Hshb
\gb Tnyig| @gx|bni gc Ob~xo|y+Lnqhd Ihn|bobm ob Kntfhkntoaq
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Tg tfh Qtxdhbt s
tfgxmf tfh|h n|h xbz|gsnlih qtnthkhbtq) tfh|h n|h zihbty gc qtnthkhbtq tfnt dg fnsh z|ggcq"
Ob tfoq thvt }h }oii agbahbt|nth gb qtnthkhbtq tfnt fnsh z|ggcq }otf tfh mgni gc doqagsh|obm
qgkh gc tfh z|ggcq" Bgth tfnt tfh|h fnq lhhb bg khbtogb gc tfh z|ggc) qobah tfh|h oq bgtbhahqqn|oiy n qobmih z|ggc gc n moshb qtnthkhbt" Fhbah) ygx bhhd bgt bd tfh hvzhathd
z|ggc gb ygx| g}b) lxt obqthnd `xqt nb n|mxkhbt tfnt |hniiy oq n z|ggc">
Cobniiy) tf|gxmfgxt tfh knth|oni tfnt cgiig}q) ygx n|h niig}hd tg nqqxkh qgkh agk+
kgb kntfhkntoani ebg}ihdmh c|gk ygx| z|hsogxq kntfhkntoaq agx|qhq nbd nbytfobm tfnt
nzzhn|q ob tfh thvt lhcg|h n z|glihk ygx n|h }g|eobm gb) xbihqq gtfh|}oqh do|hathd" Tfoq
lgdy gc agkkgb obcg|kntogb qfgxid lh qgkhtfobm tfnt ygx| ainqq nbd obqt|xatg| anb nm|hh
gb ob ndsnbah" ]fhb xqobm thafboani th|kq ot oq lhqt tg xqh tfh dhbotogbq moshb fh|h" Tfnt
oq) hshb tfgxmf ygx n|h niig}hd tg nqqxkh ah|tnob odhnq c|gk gtfh| agx|qhq) xqh dhbotogbq
nq tfhy n|h zf|nqhd fh|h qg tfnt hsh|ygbh oq gb tfh qnkh znmh) nbd xqobm tfh qnkh kntfh+
kntoaq" Oc ygx n|h qhhobm n dhbotogb gc n cnkoion| agbahzt zf|nqhd n docch|hbt }ny) tfoq oq
n mggd tokh tg lhmob qhhobm tfobmq c|gk docch|hbt zh|qzhatoshq nbd tg z|natoah lhobm nlih tg
xqh docch|hbt tggiq"
Bgtntogb
]foih kntfhkntoaq oq }|otthb ob agkzihth qhbthbahq) knby tokhq n kntfhkntoani qyklgi
}oii tneh tfh zinah gc n }g|d g| zf|nqh" Cg| hvnkzih N ; L oq n kntfhkntoani qhbthbah}fh|h N nbd L n|h bgxbq nbd ; oq tfh sh|l" Kntfhkntoaonbq xqh qyklgiq tg kneh tfho|}|otobm hnqoh| tg xbdh|qtnbd nbd }|oth" Fg}hsh|) tfh xqh gc qyklgiq qfgxid bhsh| lh n
ln||oh| tg agkz|hfhbqogb" Fh|h oq n qfg|t tnlih gc qyklgiq tfnt kntfhkntoaonbq gcthb xqh
ob obcg|kni z|hqhbtntogbq) lxt bgt mhbh|niiy ob }|otobm" Oc ygx| ainqq obaixdhq n z|hqhbtntogb
agkzgbhbt) tfoq }gxid lh n mggd zinah tg xqh tfhqh qyklgiq) lxt ygx qfgxid lh `xdoaogxq
nlgxt xqobm tfhk ob tfh fgkh}g|e ygx fnbd ob"
Qyklgi Khnbobm Qyklgi Khnbobm cg| nii tfh|h hvoqtq okziohq oq okziohd lyocc oc nbd gbiy oc oc nbd gbiy oc qxaf tfnt hbd gc n z|ggc
>Tfoq iolh|nthq ygx c|gk fnsobm tg |hz|gdxah qgkhtfobm tfnt qgkhgbh hiqh ni|hndy z|gdxahd"
\gb Tnyig| @gx|bni gc Ob~xo|y+Lnqhd Ihn|bobm ob Kntfhkntoaq
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Afnzth| >
Qyklgioa Igmoa Tfh tfobm tfnt
|hniiy qhzn|nthq xq c|gk tfh nzhq"
Tfh|h }nq tfobmq }foaf fh qt|htafhd) lxt knobiy fh tgid tfh t|xtf"
Kn|e T}nob) Fxaeihlh||y Cobb
Qgkhlgdy }fg tfobeq igmoaniiy oq n boah agbt|nqt tg tfh |hni }g|id"
Tfh In} gc Tfxkl
Fg} dg fxknbq agkkxboanth }otf hnaf gtfh|7 Tfoq ~xhqtogb fnq knby docch|hbt zgq+
qolih nbq}h|q" ]h n|h nii ah|tnobiy n}n|h gc tfh zg}h| gc n cnaoni hvz|hqqogb g| n fnbd
mhqtx|h" Fg}hsh|) hnaf gc tfhqh tyzhq gc agkkxboantogb oq gcthb gzhb tg obth|z|htntogb"
Gbh zh|qgb kny mosh tfh qnkh fnbd mhqtx|h tg t}g docch|hbt zhgzih nbd tfgqh zhgzih kny
obth|z|ht ot docch|hbtiy" Tfoq docch|hbah gc obth|z|htntogb kny dhzhbd gb knby cnatg|q) tggknby ob cnat tg mg obtg fh|h) lxt qxcah ot tg qny tfnt kntfhkntoani z|ggcq n|h bgt gcthb agb+
qt|xathd xqobm cnaoni hvz|hqqogbq g| fnbd mhqtx|hq" Obqthnd) }h |hiy gb }|otthb inbmxnmh"
Fg} tfhb dg }h hbqx|h tfnt gx| inbmxnmh dghq bgt ihnsh |ggk cg| obth|z|htntogb7 Tfoq oq
qgkhtokhq n docaxit afg|h) lxt ob kntfhkntoani inbmxnmh }h qhidgk |xb obtg tfoq z|glihk"
Tfh z|okn|y }ny }h mht n|gxbd tfoq oq tf|gxmf tfh xqh gc qyklgioa igmoa" Naag|dobm tg
Fnih) Igmoa agkz|oqhq tfh |xihq ly }foaf kntfhkntoaonbq gzh|nth) tfh m|nkkn| gc tfh
inbmxnmh" U?[ Tfnt oq) igmoa oq tfh tggi }h }oii xqh tg a|hnth z|ggcq" N z|ggc oq lxoit xz gc
qtnthkhbtq) hnaf gc }foaf cgiig}q c|gk tfh z|hahdobm qtnthkhbt g| qtnthkhbtq"
>"> Qtnthkhbtq
Dhbotogb >">" N qtnthkhbt oq n dhain|ntosh qhbthbah }foaf oq hotfh| t|xh g| cniqh) lxt bgt
lgtf"
Bgth" Fh|h }h khnb tfnt tfh t|xtf snixh gc tfh qtnthkhbt dghq bgt dhzhbd gb tfh zh|qgb }fg oq |hndobm ot" Tfnt
oq) ot oq zgqqolih cg| hsh|ygbh tg nm|hh gb tfh qnkh t|xtf snixh }otfgxt |hmn|d tg zh|qgbni gzobogb"
Hvnkzih >"
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Qyklgioa Igmoa Tfh tfobm tfnt |hniiy qhzn|nthq xq c|gk tfh nzhq" tf Z|hqodhbt gc tfh Xbothd Qtnthq"
Hvnkzih >"1" Tfh cgiig}obm n|h bgt hvnkzihq gc qtnthkhbtq"
>" N|h ygx c|gk Kgbtnbn7
"4" ]fy n|h tfh othkq ob Hvnkzih >"1 bgt hvnkzihq gc qtnthkhbtq7
Hvh|aoqh >"8" Dhth|kobh }foaf gc tfh cgiig}obm n|h qtnthkhbtq" Cg| tfh gbhq tfnt n|h bgt
qtnthkhbtq) hvzinob }fy bgt" Oc qg) dhth|kobh tfh t|xtf snixh gc tfh qtnthkhbt"
>" Anisob Aggiodmh }nq tfh m|hnthqt Nkh|oanb Z|hqodhbt"
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Qyklgioa Igmoa Tfh tfobm tfnt |hniiy qhzn|nthq xq c|gk tfh nzhq" 1
Moshb tfnt }h anb agklobh qtnthkhbtq tg cg|k bh} qtnthkhbtq) }h bhhd tg mx|h gxt
fg} tg dhth|kobh tfh t|xtf g| cniqoty gc n agkzgxbd qtnthkhbt" Ob kntfhkntoaq tfh|h oq
qhidgk kxaf tg n|mxh nlgxt }otf |hmn|d tg t|xtf) lxt fg} dg }h mx|h ot gxt7 ]hii qtn|t}otf tfh qokzihqt }ny tg cg|k n bh} qtnthkhbt) tfh bhmntogb" Nq tfh bnkh qxmmhqtq) tfh
bhmntogb gc n qtnthkhbt fnq tfh gzzgqoth t|xtf snixh" Fh|h oq tfh t|xtf tnlih cg| n bhmntogb"
N NT C
C T
Qobah }h|h bgt cgaxqhd gb qyklgioa igmoa nq n ag|h gc tfoq agx|qh) }h }oii |hqtnth tfoq nq
nb nvogk"
Nvogk >"=" Oc N oq n qtnthkhbt }otf n moshb t|xtf snixh) tfhb N oq n qtnthkhbt }otf tfhgzzgqoth t|xtf snixh"
Hvh|aoqh >"6" ]|oth tfh bhmntogb gc tfh cgiig}obm zf|nqhq"
>" Zo oq n zgqotosh |hni bxklh|"
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Qyklgioa Igmoa Tfh tfobm tfnt |hniiy qhzn|nthq xq c|gk tfh nzhq" 4
Nvogk >"?" Iht N nbd L lh qtnthkhbtq" Tfhb tfh qtnthkhbt NL oq t|xh oc nbd gbiy oc lgtfN nbd L n|h t|xh"
Nvogk >">:" Iht N nbd L lh qtnthkhbtq" Tfhb tfh qtnthkhbt N L oq t|xh xbihqq lgtf Nnbd L n|h cniqh"
Hvh|aoqh >">>" Dhth|kobh }fnt obcg|kntogb }gxid lh bhahqqn|y tg dhth|kobh }fhtfh| hnaf
gc tfh cgiig}obm qtnthkhbtq oq t|xh g| cniqh" Tfhb) dhth|kobh tfh t|xtf snixhq"
>" Tfh anzotni gc Qznob oq Ln|ahigbn nbd tgdny oq ]hdbhqdny"
< &DhKg|mnbq In}q/" IhtN nbdL lh qtnthkhbtq nbd hqtnlioqf tfh cgiig}obm0
>" &NL/ oq igmoaniiy h~xosnihbt tg &N/ &L/
">1 &Tfh Agkkxtntosh Z|gzh|ty/" Z|gsh hnaf gc tfh cgiig}obm0
>" NL oq igmoaniiy h~xosnihbt tg LN
4 &Tfh Nqqgaontosh Z|gzh|ty/" Z|gsh hnaf gc tfh cgiig}obm0
>" &NL/Aoq igmoaniiy h~xosnihbt tg N &LA/
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Qyklgioa Igmoa Tfh tfobm tfnt |hniiy qhzn|nthq xq c|gk tfh nzhq" 8
Z|glihk >">8 &Tfh Doqt|olxtosh Z|gzh|ty/" Z|gsh hnaf gc tfh cgiig}obm0
>" N &LA/ oq igmoaniiy h~xosnihbt tg &NL/ &NA/
3" Iht N nbd L lh qtnthkhbtq" Tfhb tfh qtnthkhbt Oc N) tfhb L oq t|xh xbihqq
N oq t|xh nbd L oq cniqh"
Hvh|aoqh >">=" Dhth|kobh tfh t|xtf g| cniqoty gc tfh cgiig}obm qtnthkhbtq"
>" Ocv oq nb obthmh|) tfhb v1 2 :"
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Qyklgioa Igmoa Tfh tfobm tfnt |hniiy qhzn|nthq xq c|gk tfh nzhq" 3
3" Oc tfh Hn|tf oq tfh ahbth| gc tfh xbosh|qh) tfhb 1 ; 8"
Nq ob bgb+kntfhkntoani Hbmioqf) tfh|h oq gcthb kg|h tfnb gbh }ny tg qny }fnt ygx }nbttg qny" Tfh cgiig}obm z|glihk moshq xq nb nddotogbni }ny tg hvz|hqq tfh qtnthkhbt oc N)
tfhb L" ]h }oii qhh kg|h nlgxt nith|bntosh }nyq tg hvz|hqq n qtnthkhbt inth|" Qtny txbhd"
Z|glihk >">6" Z|gsh tfnt tfh cgiig}obm qtnthkhbtq n|h h~xosnihbt0
>" Oc N) tfhb L" UNL[
">?" Z|gsh tfnt tfh cgiig}obm qtnthkhbtq n|h h~xosnihbt0
>" Ot oq bgt tfh anqh tfnt N okziohq L" U &NL/[
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Qyklgioa Igmoa Tfh tfobm tfnt |hniiy qhzn|nthq xq c|gk tfh nzhq" =
Z|glihk >""" Nii knkkniq fnsh fno|"
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Qyklgioa Igmoa Tfh tfobm tfnt |hniiy qhzn|nthq xq c|gk tfh nzhq" 6
Zxt nbgtfh| }ny) ob n qg|t gc hvthbdhd igmoani qyqthk) n cg| nii qtnthkhbt oq ioeh tfh
agb`xbatogb gc n sh|y in|mh bxklh| gc qokzih| qtnthkhbtq nbd n tfh|h hvoqtq qtnthkhbt oq
ioeh tfh doq`xbatogb gc n sh|y in|mh bxklh| gc qokzih| qtnthkhbtq"
Hvh|aoqh >""" Nii q~xn|hq n|h |hatnbmihq"
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Afnzth| >
Ob g|dh| tg mnob qgkh z|natoah xqobm tfh khtfgdq doqaxqqhd nlgsh) }h }oii qtn|t }otf n
ch} qtnthkhbtq obsgisobm bxkh|oani z|gzh|tohq tfnt ygx n|h cnkoion| }otf" Cg| hnaf gc tfh
Z|glihkq ob tfoq qhatogb) Z|gsh) g| Doqz|gsh nbd Qnisnmh Oc Zgqqolih"
Dhbotogb /< ; &y % >/
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Kntfhkntoani obdxatogb Tfh dgkobg hcchat" >1
Bgth tfnt }fhb }h }|oth Z&e/ }h khnb tfh qtnthkhbt Z&e/ oq t|xh) nbd bgtqgkh zgiybgkoni Z" Cg| obqtnbah oc }h }oqf tg z|gsh tfnt cg| hsh|y b B) tfh
qxk > % < % % b ; b&b%>/< ) tfhb }h anb iht Z&e/ lh tfh qtnthkhbt tfh qxk
gc tfh |qt ebntx|ni bxklh|q oqe&e%>/
Qobah > ;
>&/ oq
t|xh"< &Tfoq tnehq an|h gc tfh lnqh anqh) bg} }h bhhd tg z|gsh tfh obdxatosh qthz"/
Bg} nqqxkh tfnt Z&e/ oq t|xh cg| qgkh bntx|ni bxklh| e" Tfnt oq
> % < % % e;e&e% >/
/ oq t|xh" Tfh|hcg|h) ly tfh nvogk gc obdxatogb) tfh qxk gc tfh |qt b bntx|ni
bxklh|q oq moshb lyb&b%>/
/
|> "
Z|glihk 1"?" Ocb oq n bntx|ni bxklh|) tfhb
< 3 >: >4 &4b:" Ocv \ }otf v 2> nbd b oq n bntx|ni bxklh|) tfhb
&> %v/b > % bv"
Qgkhtokhq tfh lnqh anqh dghq bgt ag||hqzgbd tg tfh bntx|ni bxklh| >" Tfoq kny lh tfh
anqh }fhbhsh| qgkh qtnthkhbt oq bgt t|xh cg| qgkh bxklh| gc anqhq" Tfh cgiig}obm tf|hh
z|glihkq oiixqt|nth tfoq"
Z|glihk 1">>" Oc b oq n bntx|ni bxklh| nbd b 4) tfhb 1b 2
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Kntfhkntoani obdxatogb Tfh dgkobg hcchat" >8
Nvogk 1">1 &Qt|gbm Kntfhkntoani Obdxatogb/" Iht Z&b/ lh n qtnthkhbt cg| hnaf bntx|nibxklh| b"1 Oc0
&o/ Z&>/) nbd
&oo/ oc k oq n bntx|ni bxklh|) tfhb UZ&`/ cg| nii ` k[ Z&k % >/
tfhb Z&b/ oq t|xh cg| hsh|y b B"
Bgth tfh docch|hbah lht}hhb tfh g|omobni obdxatogb nvogk nbd tfoq gbh" Ob tfoq anqh) }h
n|h bgt gbiy nqqxkobm tfnt Z&b/ tg qfg} Z&b % >/) lxt |ntfh| tfnt Z&`/ oq t|xh cg| nii ` c|gk> tg b"
Z|glihk 1">4" Hsh|y bntx|ni bxklh|m|hnth| tfnb > oq hotfh| z|okh g| tfh z|gdxat gc z|okhq"
Z|glihk 1">8" Iht n> ; >) n< ; 1) nbd cg| b < iht nb ; nb> % nb ; >) n< ; % nb< % nb1" Z|gsh tfnt nb 9 ?>6{ nbd gx| xbosh|qni qht X agxid lh tfh yhn|q lht}hhb >?:> nbd???)" N ; ugdd z|okh bxklh|q ihqq tfnb >:{ &Anb ygx |h}|oth tfoq qht ob n docch|hbt }ny7/
" NL >" OcNL) tfhb La
Na
"Dhbotogb 4">):{) L ; u:{) A; u
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Qht tfhg|y ]fnt dg ygx anii n lgv }otf nb hkzty lgv ob ot7 >6
4"< Shbb donm|nkq
]h anb qgkhtokhq |hz|hqhbt tfh gzh|ntogbq gb qhtq m|nzfoaniiy" Oc }h fnsh t}g qhtq) tfhb}h anb xqh tfh cgiig}obm Shbb donm|nk tg agkzxth tfh qht gzh|ntogbq c|gk tfh z|hahdobm
qhatogb" Bgtoah tfnt tfh t}g ao|aihq l|hne tfh xbosh|qni qht obtg cgx| doqtobat |hmogbq" Tfh|h
n|h t}g |hmogbq tfnt agbtnob tfh hihkhbtq ob hotfh| N g| L lxt bgt ob lgtf" &\hmogbq > nbd
8" Kntaf tfh cgiig}obm qhtq }otf tfh |hmogbq gc tfh Shbb donm|nk nlgsh"
>" NL =" Xqh qht bgtntogb tg dhqa|olh hnaf gc tfh |hmogbq ob tfh tf|hh qht Shbb don+
m|nk"
\gb Tnyig| @gx|bni gc Ob~xo|y+Lnqhd Ihn|bobm ob Kntfhkntoaq
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Qht tfhg|y ]fnt dg ygx anii n lgv }otf nb hkzty lgv ob ot7 >?
Hvh|aoqh 4">6" D|n} n Shbb donm|nk cg| hnaf gc tfh cgiig}obm qhtq"
>" &NLA/a
?" Anb ygx bd Shbb donm|nkq cg| cgx| g| kg|h qhtq7
4"1 Qht gzh|ntogbq
]h anb agiihat qht gzh|ntogbq tfnt n|h nbnigmgxq tg tfh gzh|ntogbq }h fnd ob Qhatogb >
}otf |hmn|d tg igmoani hvz|hqqogbq" ]h anb xqh Shbb donm|nkq tg mht qgkh obtxotogb nlgxt
z|gsobm qtnthkhbtq nlgxt qhtq) tfgxmf tfhqh zoatx|hq dg bgt qxcah tg kneh n z|ggc" Tfh
|qt cgx| z|glihkq agiihat qhsh|ni cnatq nlgxt qhtq tfnt qfgxid fgzhcxiiy agkh nq bg qx|z|oqh
hshb tfgxmf tfhy komft lh agxbth|obtxotosh nt |qt minbah"
Z|glihk 4"" NX ; N
" N &LA/ ; &NL/A/
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Qht tfhg|y ]fnt dg ygx anii n lgv }otf nb hkzty lgv ob ot7 " NL ; LN
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Qht tfhg|y ]fnt dg ygx anii n lgv }otf nb hkzty lgv ob ot7
Hvh|aoqh 4"13" Cg| tfh qhtq N ; u)){ nbd L ; u)){ cg|k tfh z|gdxatq NN)NL) LN nbd LL" Oq NL ; LN7 ]fy7
]h }oii qhh tfoq odhn nmnob }fhb }h qtn|t tnieobm nlgxt cxbatogbq nbd |hintogbq" Ot oq
tfh cgxbdntogb gc fg} tfhqh agbahztq }g|e nbd oq tfh lnqoq cg| knby gtfh| qt|xatx|hq ob
nimhl|n) nbniyqoq) tgzgigmy nbd mhgkht|y"
Z|glihk 4"1=" Iht N) L) A nbd D lh qhtq" OcNL nbd AD) tfhb &NA/ &LD/"
Z|glihk 4"16" Iht N) L nbd A lh qhtq" Tfhb &NL/A; &NL/ &LA/"
Z|glihk 4"1?" Iht N) L nbd A lh qhtq" Tfhb N &LYA/ ; &NL/Y &NA/"
Z|glihk 4"4:" Iht N) L) A nbd D lh qhtq" Tfhb &N YL/ &AYD/ ; &NA/ Y U&ND/&LA/["
Hvh|aoqh 4"4>" Moshb tf|hh qhtq N) L nbd A) fg} dg ygx tfobe tfh qht NLAqfgxid lhdhbhd7 Fg} }gxid tfoq qht agkzn|h tg tfh qht N &LA/7 &NL/A7
Hvh|aoqh 4"4
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Qht tfhg|y ]fnt dg ygx anii n lgv }otf nb hkzty lgv ob ot7 " Tfh cnkoiyN agbqoqtq gc t}g qhtq0 N; uN>)N" ]h anb dhbh hnaf qht nq cgiig}q0 zoae n |ndoxq) |) nbd tfh ao|aih oq
&v)y/ \< yv< %y< ; |[
A| nbd
|&:)>[
A|"
Hvh|aoqh 4"8?" Dhbh n cnkoiy gc qhtq C) }foaf anb lh obdhvhd ly tfh bntx|ni bxklh|q)
qg tfnt0 bB
Cb ;\ nbd
bB
Cb ;"
\gb Tnyig| @gx|bni gc Ob~xo|y+Lnqhd Ihn|bobm ob Kntfhkntoaq
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Afnzth| 8
Cxbatogbq nbd |hintogbq Tfh obq
nbd gxtq gc }fg ebg}q }fg nbd
cnsg|otoqk
Tfh cgxbdntogb cg| aniaxixq) obdhhd cg| nii gc kgdh|b kntfhkntoaq) oq tfh inbmxnmh gc
cxbatogbq nbd qhtq" Nq z|hzn|ntogb cg| tfh igbm |gnd gc aniaxixq) tfh qtxdhbt kxqt fnsh
obth|bniophd tfhqh odhnq qg tfnt fh'qfh anb xqh tfhk agkcg|tnliy nbd bntx|niiy" Tfh
qtxdhbt kxqt lh nlih tg |hndoiy nzz|hfhbd qtnthkhbtq &lgtf g|ni nbd }|otthb/ kndh ob
tfoq lnqoa kntfhkntoani inbmxnmh nbd) kg|h okzg|tnbtiy) tfh qtxdhbt kxqt niqg lh nlih
tg cg|kxinth foq'fh| g}b qtnthkhbtq"
L|onb Linbe # Qthshb E|nbtp) Aniaxixq
_gx n|h ioehiy cnkoion| }otf tfh agbahzt gc n cxbatogb" Ot oq }fnt d|oshq tfh odhnq ob aniaxixq
nbd tfh nimhl|n ygx fnsh qtxdohd qobah fomf qafggi" Ob tfoq qhatogb }h }oii kneh z|haoqh
}fnt ygx fnsh n mggd xbdh|qtnbdobm gc ni|hndy" ]h }oii lhmob ly dhbobm n |hintogb nbd
tfhb xqobm tfoq odhn tg cg|kxinth tfh bgtogb gc n cxbatogb" ]fnt ygx obtxotoshiy xbdh|qtnbd
tfh }g|d |hintogb tg khnb oq hvnatiy }fnt ot khnbq kntfhkntoaniiy"
8"> \hintogbq nbd h~xosnihbah |hintogbq
Hvnkzih 8">" Agbqodh| tfh zhgzih ob n ainqq gb tfh |qt dny gc tfh qhkhqth|" Hnaf qtxdhbt
ob tfh ainqq kny g| kny bgt ebg} tfh |qt bnkh gc nbgtfh| qtxdhbt ob tfh ainqq" Kntfhknt+
oaniiy }h anb dhqa|olh tfoq qgaoni zfhbgkhbgb xqobm n |hintogb" Qzhaoaniiy) oc }h }nbt tg
dhqa|olh tfh cnat tfnt Ahd|oa ebg}q Nic|hdq |qt bnkh) tfhb }h anb xqh nb g|dh|hd zno|"]h anb }|oth tfh g|dh|hd zno| &Ahd|oa) Nic|hd/ tg obdoanth tfnt Ahd|oa ebg}q Nic|hdq |qt
bnkh" &]fy dg }h |h~xo|h tfh g|dh|7/ Fhbah) tfh |hintogb ebg}q tfh |qt bnkh gc oq tfh
qht gc g|dh|hd zno|q &v)y/ }fh|h zh|qgb v ebg}q zh|qgb yq |qt bnkh"
Dhbotogb 8"
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Cxbatogbq nbd |hintogbq Tfh obq nbd gxtq gc }fg ebg}q }fg nbd cnsg|otoqk 3/Hvzinob ygx| nbq}h|q"
Dhbotogb 8"8" Qxzzgqh n |hintogb \ oq dhbhd gb Q nbd T" Tfhb tfh dgknob gc\ oq tfh
qht gc nii q Q qxaf tfnt &q) t/ \ cg| qgkh t T" Tfh qht T oq aniihd tfh agdgknob gc tfh|hintogb nbd tfh |nbmh gc\ oq tfh qht gc nii t T qxaf tfnt &q)t/ \ cg| qgkh q Q"
Hvh|aoqh 8"3" Iht Q ; u>)" oq qnod tg lh |hhvosh oc cg| nii v V }h fnsh &v)v/ " Tfnt oq vv"
):" Iht _ ; un)l)a)d)h{" Dhbh n |hintogb N gb _ tfnt oq |hhvosh nbd qyk+kht|oa) lxt bgt t|nbqotosh" Oc tfoq oq bgt zgqqolih) hvzinob }fy bgt"
Z|glihk 8">>" Iht _ ; un)l)a)d)h{" Dhbh n |hintogbL gb _ tfnt oq |hhvosh nbd t|nbqo+tosh) lxt bgt qykkht|oa" Oc tfoq oq bgt zgqqolih) hvzinob }fy bgt"
Z|glihk 8">
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Cxbatogbq nbd |hintogbq Tfh obq nbd gxtq gc }fg ebg}q }fg nbd cnsg|otoqk =" ]fnt n|h tfh h~xosnihbah ainqqhq ob Hvh|aoqh 8"=7 Z|glihk 8">87
Z|glihk 8">6" Dhbh n |hintogb gb \ ly) v y oc vy oq |ntogbni" Z|gsh tfnt oq nbh~xosnihbah |hintogb"
Z|glihk 8">?" Qxzzgqh oq nb h~xosnihbah |hintogb gb n qht Q" Ocn l cg| qgkh n)l Q)tfhb Hn ; Hl"
Z|glihk 8"
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Cxbatogbq nbd |hintogbq Tfh obq nbd gxtq gc }fg ebg}q }fg nbd cnsg|otoqk " Qxzzgqh c oq n |hintogb gb V nbd _" Tfhb }h qny tfnt c oq n cxbatogb oc
>" cg| hnaf v V) tfh|h hvoqtq n y _ qxaf tfnt &v)y/ c) nbd &}fg ebg}q }fg/
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Cxbatogbq nbd |hintogbq Tfh obq nbd gxtq gc }fg ebg}q }fg nbd cnsg|otoqk " OcNL) tfhb cUN[ cUL["
" cUNL[ cUN[ cUL[" Mosh nb hvnkzih }fh|h h~xnioty cnoiq"
" OcAD) tfhb c>UA[ c>UD["
" c>UAD[ ; c>UA[ c>UD[
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Cxbatogbq nbd |hintogbq Tfh obq nbd gxtq gc }fg ebg}q }fg nbd cnsg|otoqk +> &g| ob`hatosh/ oc c&n/ ; c&l/ okziohq n ; l"
N cxbatogb c tfnt oq lgtf gbh+tg+gbh nbd gbtg oq aniihd n gbh+tg+gbh ag||hqzgbdhbah g| n
lo`hatogb g| oq qnod tg lh lo`hatosh"
]otf tfhqh t}g bgtogbq gc eobdq gc cxbatogbq }h anb dhth|kobh tfobmq ioeh }fhtfh| t}g
qhtq fnsh tfh qnkh qoph g| }fhtfh| t}g docch|hbt iggeobm kntfhkntoani gl`hatq fnsh tfh
qnkh obfh|hbt qt|xatx|h"
Hvnkzih 8"4:" Qxzzgqh c 0 \ \ oq moshb ly c&v/ ; 1v % 8" Oq c gbh+tg+gbh7 Gbtg7
Qgixtogb" Zoae y \ nbd agbqodh| v ; y81
" Tfhb
c&v/ ; c
y81
; 1
y8
1
% 8 ; y8 % 8 ; y"
Qg c oq gbtg" Kg|hgsh|) oc c&n/ ; c&l/ tfhb }h qhh 1n % 8 ; 1l % 8" Tfnt oq 1n ; 1l g|n ; l) nbd qg c oq gbh+tg+gbh"
Z|glihk 8"4>" Mosh nb hvnkzih gc hnaf gc tfh cgiig}obm nbd z|gsh tfh z|gzh|tohq ygx
ainok"
>" N cxbatogb c 0\\ tfnt oq gbh+tg+gbh lxt bgt gbtg"
nbd 8"4< fhiz ygx
xbdh|qtnbd tfh agbahztq gc gbh+tg+gbh nbd gbtg7
Z|glihk 8"44" Iht N ; un)l)a)d)h{ nbd L ; u})v)y)p{" Oq tfh|h n gbh+tg+gbh cxbatogbc|gk N obtg L7 Hvzinob"
Z|glihk 8"48" Iht A; ue))k)b{ nbd D ; uz)~)|)q) t{" Oq tfh|h nb gbtg cxbatogb c|gk Aobtg D7 Hvzinob"
Hvh|aoqh 8"43" ]fnt) ob mhbh|ni) anb ygx qny nlgxt tfh |hintosh qophq gc tfh dgknob nbd
agdgknob gc nb gbtg cxbatogb7 N gbh+tg+gbh cxbatogb7
Z|glihk 8"4=" Qxzzgqh c 0 V_ nbd iht NV nbd L _" Tfhb
>" Oc c oq gbh+tg+gbh) tfhb c>UcUN[[ ; N"
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Cxbatogbq nbd |hintogbq Tfh obq nbd gxtq gc }fg ebg}q }fg nbd cnsg|otoqk
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Cxbatogbq nbd |hintogbq Tfh obq nbd gxtq gc }fg ebg}q }fg nbd cnsg|otoqk 1:
Bgth tfnt qobah cUV[ _) }h ebg} tfnt hnaf gxtzxt gc c oq n sniod obzxt cg| m"
Hvh|aoqh 8"88" Qxzzgqh c 0 V _ nbd m 0 _ P n|h cxbatogbq" Hvz|hqq tfh agkzgqothcxbatogb m c nq n qht gc g|dh|hd zno|q"
Hvh|aoqh 8"83" Qxzzgqh c 0 Q T nbd m 0 V_ n|h cxbatogbq" ]fnt agbdotogb }gxid }hbhhd ob g|dh| tg cg|k tfh agkzgqoth cxbatogb cm 0 V T7
Hvh|aoqh 8"8=" Iht c)m 0\\ lh cxbatogbq dhbhd ly c&v/ ; v1 %v< nbd m&v/ ; 4v?"Cobd cm nbd cm" ]fnt anb ygx agbaixdh nlgxt tfh agkkxtntosoty gc tfh gzh|ntogb 7
Z|glihk 8"86" Qxzzgqh c 0 V_ nbd m 0 _P n|h cxbatogbq"
>" Ocm c oq gbh+tg+gbh) z|gsh tfnt c kxqt lh gbh+tg+gbh"
" Qxzzgqh c 0 V _ nbd m 0 _P n|h cxbatogbq" Oc c nbd m n|h gbtg) tfhbqg oq m c"
Qgkhtokhq oc tfh dgknob nbd agdgknob gc gbh cxbatogb n|h tfh agdgknob nbd dgknob
gc nbgtfh| cxbatogb) tfh t}g cxbatogbq anb xbdg tfh natogb gc hnaf gtfh|" Tg kneh tfoq
z|haoqh }h fnsh tfh cgiig}obm dhbotogb0
Dhbotogb 8"3"
Z|glihk 8"31" Agbqodh| qhtq N) L nbd A moshb ly N ; u>)" Cobd m c"
nq n qhtgc g|dh|hd zno|q moshb tfnt c ; u&n) c&n// y n N{"
\gb Tnyig| @gx|bni gc Ob~xo|y+Lnqhd Ihn|bobm ob Kntfhkntoaq
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Cxbatogbq nbd |hintogbq Tfh obq nbd gxtq gc }fg ebg}q }fg nbd cnsg|otoqk 1>
Bgth tfnt hshb tfgxmf }h xqh tfh qnkh bgtntogb cg| tfh obsh|qh oknmh gc n qht nbd tfh
obsh|qh gc n cxbatogb) tfhy n|h bgt tfh qnkh tfobm" Tfh obsh|qh gc n cxbatogb oq nbgtfh|
cxbatogb nbd tfh obsh|qh oknmh gc n qht oq nbgtfh| qht" Hshb tfgxmf }h anb tfobe gc ncxbatogb nq n qht) tfh|h oq n qomboanbt docch|hbah" Tfh obsh|qh oknmh gc n qht oq n qht tfnt
ni}nyq hvoqtq hshb oc ot oq tfh hkzty qht lxt tfh obsh|qh gc n cxbatogb dghqbt ni}nyq
hvoqt" Ob cnat) tfh obsh|qh gc n cxbatogb }oii gbiy hvoqt oc tfh cxbatogb oq lgtf gbh+tg+gbh nbd
gbtg"
Hvh|aoqh 8"38" Ob iomft gc tfh z|hahdobm doqaxqqogb) dhqa|olh tfh docch|hbah lht}hhb c>&y/nbd c>Uuy{["
Z|glihk 8"33" Qxzzgqh c 0 NL oq n lo`hatogb" Z|gsh tfnt0
>" &c> c/&n/ ; n cg| nii n N
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Nzzhbdov N
Kntfhkntoani ]|otobm
Uly Bhni An|gtfh|q[
Kntfhkntoaq oq qxcch|obm c|gk n lnd zxlioa oknmh" Tfoq oq natxniiy n |hahbt zfhbgkhbgb0
Cocty yhn|q nmg kntfhkntoaq fnd bg zxlioa oknmh nt nii) iht nigbh n zgg| gbh" Lxt n igt fnq
afnbmhd ob tfgqh cty yhn|q" Aniaxixq) cg| hvnkzih) }nq nt gbh tokh tnxmft gbiy tg fomfiy
qzhaoniophd qaohbtoqtq nbd hbmobhh|qbg} otq tnxmft ob kgqt fomf qafggiq" Kntfhkntoaq
hcchatq n in|mh| zg|togb gc gx| qgaohty tfnb hsh| lhcg|h nbd yht) qgkhfg}) hioaotq kg|h doq+
dnob tfnb hvaothkhbt" Gx| qgaohty oq lhagkobm kg|h kntfhkntoaniiy ioth|nth) lxt hsodhbtiy
bg kg|h qykzntfhtoa tg kntfhkntoaq" ]fy7
A|otoaq zgobt tg n m|g}obm obnloioty &g| xb}oiiobmbhqq/ gc kntfhkntoaq thnafh|q tg agk+
kxboanth" Tfgqh kgqt nlih tg hvz|hqq tfho| obth|hqt ob kntfhkntoaq n|h nzzn|hbtiy cnoiobm
tg dg qg" Nbd oc gbh mhbh|ntogb gc thnafh|q dghq n zgg| `gl ob agkkxboantobm kntfhknto+ani odhnq) tfh bhvt mhbh|ntogb gc thnafh|q qxcch|q" Ob gtfh| }g|dq) igsh nbd hbtfxqonqk cg|
kntfhkntoaq oq agbt|nathd c|gk gx| thnafh|q) kxaf ioeh n so|xq" Gbiy tfgqh obchathd anb
znqq ot gb"
Nt tfh fhn|t gc qgaohtyq koqagbahztogbq nlgxt kntfhkntoaq oq tfh cnoix|h tg |hagmboph
kntfhkntoaq nq n fxknb hbdhnsg|" Fxknb lhobmq qtxdy kntfhkntoaq lhanxqh ot zihnqhq
tfhk tg dg qg" Bgt lhanxqh ot lxoidq lhtth| kgxqh t|nzq" ]h qtxdy kntfhkntoaq cg| tfh qnkh
|hnqgbq tfnt }h qtxdy n|t) g| kxqoa) g| ioth|ntx|h" Tfnt kntfhkntoaq oq c|h~xhbtiy xqhcxi
tg hbmobhh|q nbd lxqobhqqkhb oq tyzoaniiy gc kg|h obth|hqt tg hbmobhh|q nbd lxqobhqqkhb
tfnb kntfhkntoaonbq" Ob kxaf tfh qnkh }ny tfnt n|t) kxqoa) nbd ioth|ntx|h n|h xqhcxi tg
nb ndsh|toqh| z|gdxaobm thihsoqogb agkkh|aoniq) kntfhkntoaq oq xqhcxi tg hbmobhh|q nbd
lxqobhqqkhb5 lxt otq xtoioty oq zh|ozfh|ni tg tfh |hni gl`hat gc qtxdy" Tfh xbhbiomfthbhd
gcthb agkzinob nlgxt tfoq zgobt gc soh}"
Gx| afniihbmh nq kntfhkntoaonbq oq tg agkkxboanth tfh hihmnbah nbd lhnxty gc kntfh+
kntoaq tg tfh xbhbiomfthbhd }otfgxt |hiyobm gb otq xtoioty nq n a|xtaf" _gx| mgni nq n qtxdhbt
gc kntfhkntoaq oq tg ihn|b otq inbmxnmh nbd otq axitx|h }hii hbgxmf tg khht tfoq afniihbmh"
Tfh nith|bntosh oq nb xbcxiiihd ioch ob }foaf ygx| }g|e oq koqxbdh|qtggd nbd xbnzz|hao+
nthd" Gbh gc tfh mgniq gc tfoq agx|qh oq tg fhiz ygx nsgod tfoq lihne z|gqzhat ly qfn|obm n
ch} odhnq nlgxt fg} kntfhkntoaq oq }|otthb nbd fg} ot oq qzgehb"
1
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Kntfhkntoani ]|otobm
Uly Bhni An|gtfh|q[ 11
Tfh cgiig}obm qxmmhqtogbq kny z|gsh xqhcxi ob okz|gsobm ygx| agkkxboantogb qeoiiq"
>" Kntfhkntoaq oq }|otthb ob agkzihth qhbthbahq" Nby kntfhkntoaniiy ioth|nth |hndh|}otf tfh nloioty tg t|nbqinth tfh qyklgiq qfgxid lh nlih tg xbdh|qtnbd hnaf qtnthkhbt"
N qtxdhbt tneobm tfoq agx|qh ob) qny) Kgbtnbn qfgxid lh nlih tg |hnd nbd xbdh|qtnbd
ygx| }|otobm" _gx n|h bgt}|otobm qokziy cg| ky lhbht. Ot komft fhiz oc ygx oknm+
obhd tfnt ygx }h|h }|otobm cg| tfh lhbht gc qgkh kytfoani zh|qgb &}fg kny bgt
fnsh naahqq tg n zn|toaxin| |hch|hbah g| thvtlgge/"
>Cg| kg|h gb tfoq qhh Nzzhbdov L Agkkhbtq gb Qtyih"
\gb Tnyig| @gx|bni gc Ob~xo|y+Lnqhd Ihn|bobm ob Kntfhkntoaq
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Nzzhbdov L
Agkkhbtq gb Qtyih
Uly @nkhq \" Kxbe|hq[
Tfh z|glihkq n|h tg lh }|otthb gxt an|hcxiiy nbd ag||hatiy) ob mggd kntfhkntoani qtyih" Tfoq
khnbq0>
>" ]|oth ob agkzihth qhbthbahq"
Tfh cggtbgthq n|h kobh) bgt Kxbe|hq"
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Agkkhbtq gb Qtyih
Uly @nkhq \" Kxbe|hq[ 18
a|nkz8/ ly afhaeobm hnaf toby dhtnoi inlg|+gxqiy ob }|otobm" Nt gbh hvt|hkh gc qtyih
&lnd/ n|h tfgqh thvtq }|otthb qg agbaoqhiy tfnt tfh |hndh| kxaf ii ob kgqt gc tfhdhtnoiq fokqhic" Nt tfh gtfh| hvt|hkh &niqg lnd/ n|h tfh z|glihk qht qgixtogbq }|otthb
ly ygx| kgqt agbqaohbtogxq chiig} qtxdhbt) c|gk }foaf ot oq nikgqt okzgqqolih tg
hvt|nat tfh lnqoa odhn) lhanxqh gc tfh }hnitf gc dhtnoi obaixdhd. T|y tg fot qgkh}fh|h
ob tfh koddih"
3" Obaodhbtniiy) nb oiihmolih z|ggc oq obag||hat ly dhbotogb. 3
=" N agkkgb h||g| oq tg }|oth ob }fnt O anii qt|hnk gc agbqaogxqbhqq qtyih) n in
]oiionk Cnxiebh|" ]fhb ygx boqf n tfgxmft) qtgz) zxt dg}b n zh|ogd) nbd tneh
n mggd l|hntf lhcg|h ygx lhmob tfh bhvt qhbthbah &}otf n anzotni ihtth|) zihnqh/" =
8g| an|zni txbbhi qybd|gkh3_gx anb hiokobnth tfh zgqqoloioty gc tfoq z|glihk oc ygx z|hzn|h ygx| z|ggcq ob INTHV"=Ot kny lh n mggd odhn tg |hniiy hkl|nah tfh qzo|ot gc tfoq oc ygx n|h dgobm z|hqhbtntogbq nt tfh lgn|d" Nq ygx
n|h }|otobm dg}b ygx| z|ggc) ygx qfgxid hvzinob ot iobh ly iobh nq ygx n|h t|nbqa|olobm ot gb tfh lgn|d" Oc ygx }|oth
ot nii dg}b ob ndsnbah nbd tfhb hvzinob ot) ygx| ainqqknthq kny bgt lh nlih tg ehhz xz }otf }fnt ygx n|h dgobm oc
tfhy n|h t|yobm tg }|oth dg}b }fnt ygx dod }foih tfhy ioqthb tg ygx| hvzinbntogb" Gc agx|qh) ygx qfgxid nlodh ly
tfh |xihq qht dg}b ly ygx| thnafh|"
\gb Tnyig| @gx|bni gc Ob~xo|y+Lnqhd Ihn|bobm ob Kntfhkntoaq
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Loliogm|nzfy
U>[ Qthzfhb Nllgtt) Xbdh|qtnbdobm Nbniyqoq) Qz|obmh|+Sh|inm) Bh} _g|e) "
U:[ Znt|oae @" Fx|ihy) N Agbaoqh Obt|gdxatogb tg Igmoa) ]ndq}g|tf Zxlioqfobm) >?68"
U>>[ Qthshb M" E|nbtp) Tfh Hihkhbtq gc Ndsnbahd Kntfhkntoaq) Afnzknb # Fnii'A\A
Z|hqq) Lgan \ntgb) 1[ @nkhq \" Kxbe|hq) Tgzgigmy0 N Co|qt Agx|qh) Z|hbtoah+Fnii) >?=8"
U>4[ @nkhq \" Kxbe|hq) Agkkhbtq gb Qtyih) xbzxlioqfhd agx|qh fnbdgxt"
U>8[ Tfh Gvcg|d Gid Himioqf Doatogbn|y) }}}"ghd"agk"
U>3[ Ln|ln|n H" \hybgidq) QDQ # ]oiionk H" Chbtgb) Agiihmh Mhgkht|y0 Xqobm Tfh Mh+
gkhth|q Qehtafznd) Z|hiokobn|y Hdotogb) Ehy Agiihmh Z|hqq) Hkh|ysoiih) Aniocg|bon)
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LOLIOGM\NZF_ 1=
U>=[ An|gi Qafxknafh|) Fg} tg thnaf qtxdhbtq tg }|oth z|ggcq) KNN Z|g`hat BHvT Qhko+
bn|) Xbosh|qoty gc Sh|kgbt) Qxkkh|