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ikajzg H # Abhdho At|gfig
Tgx R`goet rf r`a Gqr`fztDihde `rr|>&&{{{/de7:/fzk&tgxr`goet
(Of thko ho zawqhzab
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Rf gddatt g dqtrfch~gjia }azthfo fm r`ht jffe) gt {aii gt fr`azhorazgdrh}a dforaor) }hthr {{{/de7:/fzk
DE#7: Mfqobgrhfo ht g ofo#|zfr fzkgoh~grhfo {hr` g chtthfo rfzabqda r`a dftr fm raprjffe cgrazhgit mfz r`a E#7: cgzear jfr`ho r`a Q/T/ gob {fzib{hba/ Qthok go f|ao#dforaor) {aj#jgtabdfiigjfzgrh}a cfbai razcab r`a MiapJffe) DE#7: horaobt rf|hfoaaz r`a kaoazgrhfo gob bhtrzhjqrhfo fm `hk`#wqgihrx abqdgrhfogidforaor r`gr {hii taz}a jfr` gt dfza rapr gt {aii gt |zf}hba gogbg|rh}a ao}hzfocaor mfz iagzohok) |f{azab r`zfqk` r`a MiapJffe\igrmfzc/
Df|xzhk`r :&&{{{/de7:/fzk&tgxr`goet (|igdab ho g }hthjia ifdgrhfo hogbbhrhfo rf r`a mfiif{hok razct/
Apda|r gt fr az{hta ofrab) gii DE#7: Dforaor (hodiqbhokDE#7: Dqzzhdqiqc Cgrazhgi ht cgba g}ghigjia rf Qtaztho gddfzbgoda {hr` r`a Dzagrh}a Dfccfot Grrzhjqrhfo&Ofo#Dfccazdhgi&T`gza Gihea 4/< Qo|fzrab (DD JX#OD#TG Ihdaota(`rr|>&&dzagrh}adfccfot/fzk&ihdaotat&jx#od#tg&4/&&{{{/de7:/fzk&razct/
\zhorab> Nqix 77) :
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h} {{{/de7:/fzk
Dforaort
7 Adqgdhfoat x Mqodhfoat 77/7 Ap|zathfoat ]gzhgjiat / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / :7/: Fzbao ba igt F|azgdhfoat Gikajzghdgt / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / 7
G 3 i { G 3 i { G 3 i{
Ofrg> Qo anac|if ba ap|zatho }gzhgjia at :i % :{5 qo anac|if ba qog adqgdho at \ 3 :i % :{/ Ig bhmazaodhg|zhodh|gi aorza adqgdhfoat x ap|zathfoat at ig |zataodhg ba qo thkof hkqgi wqa (f thkof ba hkqgibgb (3/
Ao ai anac|if gorazhfz) of `gx mfzcgt ct thc|iat |gzg igt ap|zathfoat ba |azcarzf x zag/ Aiigt tfo) thoacjgzkf) ap|zathfoat |azmadrgcaora kaoazgiat |gzg ai |azcarzf x ai zag ba qo zadrokqif/ Aiigt bgzo zatqirgbftdfzzadrft |gzg dqgiatwqhazg }gifzat oqczhdft ba ig ifokhrqb x ai god`f ba qo zadrokqif |gzrhdqigz/ Gt) rq rhaoat)taodhiigcaora) wqa tqtrhrqhz ift }gifzat at|addft ba ig ifokhrqb x god`f ba qo zadrokqif zagi baorzf ba oqatrzgtadqgdhfoat ba |azcarzf x zag/ Atra |zfdabhchaorf at g caoqbf dfofdhbf dfcf tqtrhrqxaobf (fz zaac|ig~gobf}gifzat ao qog ap|zatho/ Ao atra dg|rqif qrhih~gzacft ai |zfdatf ba tqtrhrqdho |gzg a}giqgz ap|zatthfoat dqgobfta bht|fokg ba }gifzat |gzg igt }gzhgjiat ho}fiqdzbgbgt/
D`g|raz 7/ Adqgdhfoat x Mqodhfoat
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2 {{{/de7:/fzk
A}giqgdho ba Ap|zathfoat Gikajzghdgt
Dqgobf ta rhaoa qog ap|zatho gikajzghdg) qof ba ift |zfdabhchaorft ct dfcqoat wqa raobzacft wqa zagih~gz dfoaiig at a}giqgzig |gzg giko }gifz ocazhdf ba ig }gzhgjia dforaohbg ao ig ap|zatho/ Ai thkqhaora anac|if hiqtrzgatra |zfdatf/
Anac|if :Tag p 3 7:/ Aodqaorzg ai }gifz ba :p ;/\gzg aodfozgz ig tfiqdho) tqtrhrqhcft 7: ao p baorzf ba ig ap|zatho bgbg/ Dgbg }a~ wqa rq aodqaorzat qog p)aorfodat bajat zaac|ig~gzig |fz 7:/ Ofrg> Ao atrg arg|g dfifdgcft bhd`f }gifz aorza |gzoratht>
:p ; 3 :(7: ;3 :2;3 7;
Ig zg~o |fz ig wqa dfifdgcft ai }gifz tqtrhrqrf aorza |gzoratht at bfjia>
7/ Ra `gz ct mdhi dfc|zaobaz ift |zfjiacgt zatqairft/:/ Ra a}hrgz dfomqthfoat wqa |fbzgo tqzkhz dqgobf ta fchra ai thkof ba ig cqirh|ihdgdho> : 7: 3 :(7: 3 :7:/
Anac|if 4
Tag p 3 7/ Aodqaorzg ai }gifz ba 8p % :/Tfiqdho
8(7 % : 3 8 % :3 77
Anac|if 2
Tag x 3 :/ Aodqaorzg ai }gifz ba ;x 77x % :/Tfiqdho
;
(: 77(
: % : 3
4
7
:% :: % :
3 :247:
3 : ifokhrqb (i x god`f ({/ Ao atrft dgtft bajat taz dqhbgbftf gi tqtrhrqhz ai }gifz g|zf|hgbf ao ig}gzhgjia g|zf|hgbg/
Anac|if 1
7/7/ Ap|zathfoat ]gzhgjiat
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{{{/de7:/fzk 1
Ai zag ba qo rzg|a~fhba atr bgbg |fz ig adqgdho G 3 : (g % j/ Aodqaorzg ai zag ba qo rzg|a~fhba dfo jgtatg 3 7< dc) j 3 71 dc x girqzg ` 3 0 dc/
\gzg aodforzgz ig tfiqdho g atra |zfjiacg) thc|iacaora rfcgcft ift }gifzat |zf|fzdhfogbft |gzg dgbg }gzhgjia)g) j x `) x ift dfifdgcft ao ig ap|zatho ba G>
G 3`:
(g % j Ta tqtrhrqxa 7< ao g) 71 ao j x 0 ao `/
G 30:
(7< % 71 Ta a}giqg dgbg |gzra/ (7< % 71 3 :150:
3 2
G 3 2(:1 3 7 Ai zag bai rzg|a~fhba at 7
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= {{{/de7:/fzk
A}giqgdho ba Ap|zathfoat Gikajzghdgt wqa ho}fiqdzgo Ap|foaorat
Cqd`gt mzcqigt x adqgdhfoat ao cgracrhdg dforhaoao ap|foaorat/ Ift ap|foaorat tfo qrhih~gbft dfcf qogofrgdho dfc|gdrg ba qog cqirh|ihdgdho za|arhbg/ \fz anac|if>
: : 3 ::: : : 3 :4
Ai ap|foaora hobhdg igt }adat wqa ai ocazf at qrhih~gbf dfcf mgdrfz (at badhz) igt }adat wqa ta `g cqirh|ihdgbf |fzt chtcf/ Dqgobf rzgjgngcft ohdgcaora dfo ocazft aorazft) at qtqgicaora ct mdhi ai thc|ihdgz ig ap|zatho/Gt) |fbacft thc|ihdgz>
:: 3 2
x
:4 3 0
Tho acjgzkf) oadathrgcft ift ap|foaorat dqgobf rzgjgngcft dfo }gzhgjiat/ Atrf at gt |fzwqa at cqd`f ct mdhiatdzhjhz p0 wqa p p p p p p p p/\gzg a}giqgz ap|zathfoat dfo ap|foaorat) bajat tqtrhrqhz ift }gifzat oqczhdft bgbft ao dgbg }gzhgjia) x iqakfthc|ihdgz/ At at|adhgicaora hc|fzrgora ao atra dgtf qtgz |gzoratht |gzg amadrqgz ig tqtrhrqdho/ Atrf ta `gda dfoai o ba kgzgorh~gz wqa ig thc|ihdgdho ta zagih~gz dfzzadrgcaora/
Anac|if 0
Ai zag ba qo dzdqif atr bgbf |fz ig mzcqig G 3 z:/ Aodqaorzg ai zag ba qo dzdqif ba zgbhf z3 7; hod`at/
Tqtrhrqxa ift }gifzat oqczhdft ao ig adqgdho/
G 3 z: Ta tqtrhrqxa 7; ao z/
G 3 (7;: 7; 7; 3 8
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{{{/de7:/fzk ;
1p: 2x 3 1(2: 2(1 Ta tqtrhrqxa p 3 2 x x 3 1/3 1(7= 2(1 Ta a}giqg ai ap|foaora (2: 3 7=/3 0
:p: 4p: % 1 3 :(14 4(1: % 1 Ta tqtrhrqxa 1 ao p/3 :(7:1 4(:1 % 1 Ta a}giqgo ift ap|foaorat
(14 3 (1(1(1 3 7:1 x (1: 3 (1(1 3 :13 :1 (:: 3 (:(: 3 2 x (:4 3 (:(:(: 3 0/
(2: 3 (2(2 3 7= x (24 3 (2(2(2 3 =2/
Anac|if 7:
Ig girqzg (` wqa gidgo~g qog |aifrg (f jgio ao }qaif dfomfzca g}go~g) |gzg qo hotrgora at|addf (r) atr bgbg|fz ig mzcqig> ` 3 4:r: % =
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0 {{{/de7:/fzk
7/ :77p:/ 7/41 x4/ 4 722/ 72 ~
A}gig igt thkqhaorat ap|zathfoat |gzg g 3 4) j 3 :) d 3 1 x b3 2/
1/ :g % 4j=/ 2d % b;/ 1gd:j0/ :gdb8/ 4jb
7
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{{{/de7:/fzk 8
77/ #77:/ 47
A}giqgz ap|zathfoat gikajzghdgt wqa dforhaoao tcjfift ba gkzq|gdho/ A}giqgz ap|zathfoat gikajzghdgt wqa ho}fiqdzgo jgzzgt ba mzgddhfoat/ A}giqgz ap|zathfoat gikajzghdgt dfo qog dgidqigbfzg wqa |ftag cfbf kzdf/
HorzfbqddhoFjtaz}g x a}gig ig thkqhaora ap|zatho>
: % 2 ; 7 36
Ba dqorgt mfzcgt bhmazaorat |fbacft horaz|zargz atra |zfjiacg6) x Dqorgt zat|qatrgt bhmazaorat |fbzg gikqhaoaodforzgz gi zatfi}azif6
Ig mfzcg ct thc|ia ba a}giqgz bhd`g ap|zatho at thc|iacaora dfcao~gz batba ig h~wqhazbg x rzgjgngz g rq cgoazgigt f|azgdhfoat) fjraohaobf x qrhih~gobf dqhbgbftgcaora ift zatqirgbft |gzdhgiat wqa dfomfzcgzo ai rfrgi g cabhbg
wqa g}go~gt ao ai |zfdatf ba a}giqgdho ba ig ap|zatho>
: % 2 3 =
= ; 3 2:2: 7 3 27
Th rq horzfbqnazgt ig ap|zatho fzhkhogi ao qog dgidqigbfzg of dhaordg wqa rgc|fdf rhaoa cfbf ba kzdft) |zfjg#jiacaora fjraobzt 27 dfcf zat|qatrzg/ Th) |fz frzf igbf horzfbqnazgt ig ap|zatho ao qog dgidqigbfzg dhaordg) fwqa |qaba kzgdgz) |zfjgjiacaora fjraobzt :8 dfcf zat|qatrg/
Ao cgracrhdg) ai fzbao ao wqa ta zagih~go igt bhmazaorat f|azgdhfoat (rgiat dfcf tqcgz) cqirh|ihdgz) ard/ athc|fzrgora/ Ao ig ap|zatho ba gzzhjg) ig f|azgdho ba cqirh|ihdgdho rhaoa |zadabaodhg (at badhz) wqa baja zagih~gztagorat wqa ig gbhdho) gt wqa ig a}giqgcft |zhcazf/ Rfcgobf ao dqaorg atrg zakig ba |zadabaodhg) za#atdzhjgcft igap|zatho fzhkhogi) |azf dfifdgobf g`fzg ig cqirh|ihdgdho aorza |gzoratht) ( ) |gzg hobhdgz wqa baja taz a}giqgbg|zhcazf/
: % (2 ; 7 36
Gt) a}giqgzacft |zhcazf ig ap|zatho baorzf ba ift |gzoratht> 2 ; 3 :0/ Aorfodat) oqatrzg ap|zatho ta dfo}hazraao>
7/:/ Fzbao ba igt F|azgdhfoat Gikajzghdgt
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{{{/de7:/fzk 77
: % (:0 7 36
\gzg ai dgtf bfoba ohdgcaora aphtrgo gbhdhfoat x tqtrzgddhfoat) taodhiigcaora dfcao~gcft batba ig h~wqhazbg)fjraohaobf x qrhih~gobf ift zatqirgbft |gzdhgiat g cabhbg wqa g}go~gcft ao ig a}giqgdho ba ig ap|zatho>
: % :0 3 4
g 2 ; 77:j 2 (; 77 % :d 2 U; (77 % :SDgbg qog ba atrgt ap|zathfoat dforhaoa ift chtcft ocazft x igt chtcgt f|azgdhfoat cgracrhdgt) x ao ai chtcffzbao/ Tho acjgzkf) ig aphtraodhg ba }gzhft tcjfift ba gkzq|gdho thkohdg wqa bajacft a}giqgz igt ap|zathfoatao qo fzbao bhmazaora |gzg dgbg ihrazgi/ ]agcft dcf a}giqgzacft dgbg qof ba atrft anac|ift/
g Atrg ap|zatho of dforhaoa |gzoratht/ Ba gdqazbf g \ACBGT) bajacft a}giqgz gbhdhfoat x tqtrzgddhfoat)rzgjgngobfba h~wqhazbg g bazad`g) ao ai fzbao ba g|gzadhchaorf ba bhd`gt f|azgdhfoat) (\ACBGT OF baja horaz|zargzta
D`g|raz 7/ Adqgdhfoat x Mqodhfoat
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7: {{{/de7:/fzk
dfcf `gdaz |zhcazf ig tqcg x iqakf ig tqtrzgddho) thof wqa taodhiigcaora bajacft a}giqgzigt ao ai fzbao ao wqag|zadao bhd`gt f|azgdhfoat/
Tfiqdho
2 ; 77 % : 3 4 77 % :3
(4 % 77 % :
3 72 % :3 7:
j Atrg ap|zatho rhaoa |gzoratht/ Gt) bajacft a}giqgz |zhcazf ig ap|zatho wqa ta aodqaorzg baorzf ba aiift);77 3 2/ Zadqazbg wqa zatrgz qo ocazf oakgrh}f awqh}gia g tqcgz qo ocazf |fthrh}f>Tfiqdho
2 (;77 % : 3 2 (2 % :3 0 % :
3 7 4 1 3 715 ; : 3 4/1/ (OFRG> \ACBGT of baja horaz|zargzta dfcf zagih~gz|zhcazf ig cqirh|ihdgdho x iqakf ig bh}htho) thof wqa taodhiigcaora bajacft a}giqgzigt ao ai fzbao ao wqag|gzadao bhd`gt f|azgdhfoat G dforhoqgdho zagih~gcft ig tqtrzgddho>
Tfiqdho
4 1 ; : 3 714/13 77/1
j \zhcazf) a}giqgcft ig ap|zatho baorzf bai |gzoratht> 1 ; 3 :/ Iqakf rzgjgngcft ig ap|zatho zatqirgora bah~wqhazbg g bazad`g/
7/:/ Fzbao ba igt F|azgdhfoat Gikajzghdgt
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{{{/de7:/fzk 74
Tfiqdho
4 (1; : 3 4 (: :3 (= :3 4
d \zhcazf) a}giqgcft igt ap|zathfoat baorzf ba ift |gzoratht> 4 1 3 71) ; : 3 4/1/ Iqakf rzgjgngcft igap|zatho zatqirgora ba h~wqhazbg g bazad`g/
Tfiqdho
(4 1 (; : 3 71 4/13 77/1
Ofrg wqa ao ig |gzra (d ai zatqirgbf of dgcjh dfo ai qtf ba |gzoratht) \azf ig ap|zatho at ct mdhi ba iaaz/ Aokaoazgi) ift |gzoratht |qabao taz qtgbft ao bft mfzcgt bhtrhorgt>
\gzg girazgz ai fzbao ba igt f|azgdhfoat ao qog ap|zatho bgbg \gzg digzhdgz ig ap|zatho x `gdazig ct mdhi ba dfc|zaobaz
Gikqogt ap|zathfoat dgzadao ba |gzoratht) frzgt dforhaoao cqd`f dfonqorft ba aiift/ Gikqogt }adat igt ap|zathfoatraobzo dfonqorft ba |gzoratht baorzf ba frzft dfonqorft ba |gzoratht/ Dqgobf ra aodqaorzat ao dgtft dfcf atrairhcf) dfofdhbft dfcf dgtft ba |gzoratht gohbgbft) dfchao~g |fz ai |gzoratht ct horazof x) iqakf) rzgjgng`gdhg gmqazg/
Anac|if 4
Qrhih~g ai fzbao (|zadabaodhg ba igt f|azgdhfoat |gzg a}giqgz>
0 U78 (: % 1 ;S
Thkqhaobf \ACBGT |zhcazf ift |gzoratht) dfcao~gcft dfo ift |gzoratht ct horazoft |zhcazf>
Tfiqdho
0 (78 (: % 1 ; 3 0 (78 ; ;3 0
1
3 4
Ao ikajzg) qrhih~gcft ai fzbao ba igt f|azgdhfoat dqgobf `acft tqtrhrqhbf }gifzat baorzf ba ap|zathfoat ba}gzhgjiat/ Ao atgt thrqgdhfoat raobzacft qog ap|zatho gikajzghdg bgbg) ig dqgi ho}fiqdgzg qog f ct }gzhgjiat)x rgcjho raobzacft ift }gifzat oqczhdft g tqtrhrqhz ao igt bhmazaorat }gzhgjiat dforaohbgt ao bhd`g ap|zatho/Qog }a~ tqtrhrqcft bhd`ft }gifzat oqczhdft ao igt }gzhgjiat dfzzat|fobhaorat) |zfdabacft dfcf ao ift anac|iftgorazhfzat) g|ihdgobf igt zakigt ba |zadabaodhg ba \ACBGT/
Anac|if 2
Qrhih~g ai fzbao ba igt f|azgdhfoat |gzg a}giqgz ig thkqhaora ap|zatho gikajzghdg>
D`g|raz 7/ Adqgdhfoat x Mqodhfoat
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72 {{{/de7:/fzk
g : (4p % : dqgobf p 3 :j 4x: % :x 7 dqgobf x 3 4d : (r ;: (q4 } dqgobf r3 78) q 3 2 x } 3 :g Ai |zhcaz |gtf at tqtrhrqhz ai }gifz oqczhdf at|addf ba p baorzf ba ig ap|zatho bgbg/ Dfo ai o ba `gdaz ctdigzg ig ap|zatho zatqirgora) bajacft dfifdgz bhd`f }gifz baorzf ba |gzoratht/
Tfiqdho
: (4(: % : 4(: at if chtcf wqa 4 :Thkqa ig zakig ap|zatgbg ao \ACBGT \zhcazf ift |gzoratht/ Iqakf) baorzf ba ift |gzoratht) thkqa oqa}gcaoraigt zakigt ba |zadabaodhg ba \ACBGT/
: (4 : % : 3 : (= % : Baorzf ba ift |gzaoratht) a}giqgcft |zhcazf ig cqirh|ihdgdhfo/: 0 3 = g`fzg dfc|iargcft ig a}giqgdhfo bai |gzaoratht/
j Ai |zhcaz |gtf at wqa tqtrhrqxgcft ai }gifz oqczhdf ba x baorzf ba ig ap|zatho/
Tfiqdho4 (4: % : (4 7Ba gdqazbf dfo \ACBGT> Of |fbacft bajacft a}giqgz ift ap|foaorat (x of |fbacft thc|ihdgzift
3 4 (4: % : (4 7 A}giqgcft ift ap|foaorat > (4: 3 83 48 % : (4 7 A}giqgcft ig cqirh|ihdgdhfo > 48 3 :;5:4 3 =3 :; % (= 7 A}giqgcft ig gbhdhfo x tqtrzgddhfo) ao ai fzbao
wqa g|gzadao) ba h~wqhazbg g bazad`g/
3 :;
=
7
3 :
: (78 ;: (24 :Thkqhaobf igt zakigt ba \ACBGT>
3 : (78;: (24 : A}giqgobf |gzaoratht > (78 ; 3 7:5(24 : 3 (=2 : 3 =:3 : 7:: =: A}giqgobf ap|foaorat > 7:: 3 7223 : 722=: A}giqgobf ig cqirh|ihdgdhfo > 722 =: 3 08:03 : 08:0 A}giqgobf ig tqtrzgddhfo/3 08:=
Ao ig |gzra (j cgorq}hcft |gzoratht gizababfz ba ocazft oakgrh}ft |gzg digzhdgz ai |zfjiacg/ Bhd`ft |gzorathtof gmadrgo ai fzbao ba igt f|azgdhfoat) |azf gxqbgo g a}hrgz dfomqthfoat dqgobf cqirh|ihdgcft ocazft oakgrh}ft/
Ig |gzra (d ao ai irhcf anac|if cqatrzg frzf |qorf horazatgora/ Dqgobf raoacft qog ap|zatho baorzf ba |gzoratht)qrhih~gcft \ACBGT |gzg barazchogz ai fzbao ao wqa ta a}giqgzo ift dforaohbft ba bhd`ft |gzoratht/
7/:/ Fzbao ba igt F|azgdhfoat Gikajzghdgt
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{{{/de7:/fzk 71
A}giqgobf Ap|zathfoat Gikajzghdgt wqa dforhaoao Jgzzgt ba Mzgddhfoat
Igt jgzzgt ba mzgddhfoat dqaorgo dfcf tcjfift ba gkzq|gdho |gzg \ACBGT) x |fz rgorf bajazgo taz a}giqgbgt|zhcazf dqgobf ta atr zatfi}haobf qog ap|zatho/ Qo bargiia cqx hc|fzrgora at wqa wqa rfbft ift oqcazgbfzatx baofchogbfzat |qabao rzgrgzta dfcf th atrq}hazgo baorzf ba |gzoratht ho}hthjiat/ Dqgobf ift |gzoratht zagiatrgcjho atro |zataorat) bajat zadfzbgz wqa ift tcjfift ba gkzq|gdho ct horazoft bajazgo taz a}giqgbft |zhcazf/
Th) |fz anac|if) ift |gzoratht g|gzadao ao qo oqcazgbfz) aiift rhaoao cgxfz |zadabaodhg wqa ig jgzzg ba mzgddho/Th ift |gzoratht g|gzadao mqazg ba ig mzgddho) aorfodat ig jgzzg ba ig mzgddho raobz ig |zadabaodhg cgxfz/
Anac|if 1
Qtg ai fzbao (|zadabaodhg ba igt f|azgdhfoat |gzg a}giqgz igt thkqhaorat ap|zathfoat>
g ~%42 7Dqgobf ~ 3 :j
g%:j%2 7
% jDqgobf g 3 4 gob j 3 7
d :
{%(p:~(x%::
7
Dqgobf { 3 77) p 3 4) x 3 7 x ~ 3 :g Tqtrhrqhcft ai }gifz oqczhdf at|addf ba ~ baorzf ba ig ap|zatho/
Tfiqdho>:%4
2 7Gqowqa atrg ap|zatho of |ftaa |gzoratht) ig zaatdzhjhzacft |gzg cftrzgz ai amadrf ba ig jgzzg ba mzgddho/(:%4
2 7Qrhih~gobf \ACBGT) a}giqgcft |zhcazf ig ap|zatho bai oqcazgbfz/12 7\fbacft dfo}azrhz 12 ao qo ocazf chprf>12 3 7
72
Iqakf a}giqgcft ig ap|zatho>12 7 3 7 72 7 3 72j Tqtrhrqhcft ift }gifzat ba g x j ao ig ap|zatho>
Tfiqdho>4%:7%2 7
7Atrg ap|zatho |ftaa |gzoratht gohbgbft (bajat zadfzbgz ai amadrf ba ig jgzzg ba mzgddho ao ai oqcazgbfz xbaofchogbfz/ Ai tcjfif ba gkzq|gdho ct horazof at |zadhtgcaora ig jgzzg ba mzgddho/ \fz if rgorf) a}giqgzacft|zhcazf ai oqcazgbfz (4 % : x ai baofchogbfz (7 % 2/
11
7
7 G`fzg a}giqgcft ai horazhfz ba ift |gzaoratht) dfcao~gobf dfo ig bh}hthfo/
(77 7 G dforhoqgdhfo a}giqgcft ig tqtrzgddh fo/
Tfiqdho>
Atrg dfc|ihdgbg ap|atho rhaoa }gzhgt dg|gt ba |gzoratht gohbgbft/ Qo crfbf |gzg gtakqzgzoft ba wqa dfcao#
D`g|raz 7/ Adqgdhfoat x Mqodhfoat
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7= {{{/de7:/fzk
~gcft dfo ai |gzoratht ct horazof at `gdhaobf qtf ba ct thkoft ba gkzq|gdho/ Gt) |fbacft zaatdzhjhz atrgap|zatho) dfifdgobf bhmazaorat thkoft ba gkzq|gdho baorzf bai at|gdhf baohbf |fz ig jgzzg ba mzgddho/ Ao|gzrhdqigz) ift thkoft ba gkzq|gdho ct aprazoft tazo |gzoratht ( / G dforhoqgdho ta dfifdgzo ift dfzd`aratho}hthjiat ao ig jgzzg ba mzgddho/ Aiift tazo atdzhrft dfcf U S/Mhogicaora) ai razdaz oh}ai (ct horazof ba ift|gzoratht gohbgbft tazo igt iig}at / Gt chtcf) bangzacft ift ocazft oakgrh}ft baorzf ba |gzoratht/
: U77 % u 4 :(: sS
Uu 7 % : s:S 7
Dfcao~gzacft dfo ai thkof ba gkzq|gdhfo cgt horazofus /
u 7 % : s 3 45u 4 :(: s 3 4 % 2 3 ;
:
U77 % ;S
U4:S7
Ai thkqhaora oh}ai rhaoa bft dfzd`arat g a}giqgz/
:
708
7
G`fzg a}giqgzacft ift |gzaoratht) dfcao~gobf |fz ig bh}hthfo/
:(:7 Mhogicaora) dfc|iargcft ig gbhdhfo x ig tqtrzgddhfo/:(7 3 :
A}giqgdho ba Ap|zathfoat Gikajzghdgt dfo ig mgchihg RH#04&02 ba DgidqigbfzgtKzgdgbfzgt
Qog dgidqigbfzg kzgdgbfzg at qog `azzgchaorg cqx rhi |gzg a}giqgz ap|zathfoa gikajzghdgt/ Ao kaoazgi qogdgidqigbfzg kzgdgbfzg thkqa igt zakigt ba |zadabaodhg bgbgt |fz \ACBGT/ Ao atrg taddho ap|ihdgzacft bftmfzcgt |gzg a}giqgz ap|zathfoat dfo qog dgidqigbfzg kzgdgbfzg/
Crfbf 7> Tqtrhrqxa |zhcazf ao ig }gzhgjia/ Iqakf) a}gig ig ap|zatho oqczhdg dfo ig dgidqigbfzg
Anac|if =
A}gig U4(p: 7: p2 % 7:S % 1p4 7dqgobf p 3 4
Tfiqdho>
Tqtrhrqhcft ai }gifz p 3
4ao ig ap|zatho/
U4((4: 7: (42 % 7:S % 1(44 7
Horfbqdhcft atrg ap|zatho ao ig dgidqigbfzg) rgi dfcf at) x |zathfogcft UAORAZS/ (Ofrg) qrhih~g _ |gzg iftap|foaorat
Ig zat|qatrg at #74/
Crfbf :> \zhcazf horzfbqda ig ap|zatho gikajzghdg fzhkhogi ao ig dgidqigbfzg) x iqakf a}gigig/ ]agcft ai chtcfanac|if/
7/:/ Fzbao ba igt F|azgdhfoat Gikajzghdgt
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{{{/de7:/fzk 7;
A}giqgzU4(p: 7: p2 % 7:S % 1p4 7dqgobf p 3 4
\zhcazf) ta kqgzbg ai }gifz p 3 4ao ig dgidqigbfzg bhkhrgcft #4 UTRFS p(Ig iarzg p|qabacft horzfbqdhzigqtgobf ai jfro p#U]GZS f UGI\@GS % UTRFS/ Aorfodat bhkhrgcft ig ap|zatho ao ig dgidqigbfzg x |zathfogcftUAORAZS/
Ig zat|qatrg at #74/
Ai takqobf crfbf at canfz |fzwqa |qabat a}giqgz mdhicaora ig chtcg ap|zatho |gzg dqgiwqhaz }gifz wqa bataat/\fz anac|if) a}giqacft ig chtcg ap|zatho dfo ift }gifzat p 3 : x p 3 :4 /
\gzgp 3 :) Kqgzbgcft ai }gifz bap ao ig dgidqigbfzg> : UTRFSp/ \zathfogcft bft }adat U:obS UAORAZS |gzg |fbazfjraoaz ig ap|zatho |za}hg wqa bhkhrgcft ao ig |gorgiig tho raoaz wqa horzfbqdhzig oqa}gcaora/ Iqakf) |zathfogcftUAORAZS |gzg a}giqgz/
Ig zat|qatrg at =:/
\gzg p 3 :4 ) kqgzbgcft ai }gifz ba p ao ig dgidqigbfzg>:4 UTRFS p/ \zathfogcft U:obS UAORAZS bft }adat |gzg
fjraoaz ig ap|zatho ao ig |gorgiig tho raoaz wqa horzfbqdhzig ba oqa}f/ Iqakf) |zathfogcft UAORAZS |gzg a}giqgz/
Ig zat|qatrg at 74/:7 f 7 4p:2x:%p2(p%x
7:
|gzg p 3 :) x 3 7/
Tfiqdho
D`g|raz 7/ Adqgdhfoat x Mqodhfoat
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70 {{{/de7:/fzk
Kqgzbg ift }gifzat ba p x x/ #: UTRFS p) 7 UTRFS x/ Igt iarzgt p x x |fbacft horzfbqdhzigt ao ig dgidqigbfzg |fzcabhf ba igt radigt UGI\@GS % UEAXS/ G`fzg horzfbqda ig ap|zatho ao ig dgidqigbfzg/ Dqgobf qog ap|zathocqatrzg ig bh}htho ba bft ap|zathfoat gtakzgra ba qrhih~gz |gzoratht> (oqcazgrfz (baofchogrfz\zathfog UAORAZS |gzg fjraoaz ig zat|qatrg /00 f 08 /
Anazdhdhft ba Za|gtf
7/ Qtg ai fzbao ba igt f|azgdhfoat |gzg a}giqgz igt thkqhaorat ap|zathfoat/
g/ 0 (78 (: % 1 ;j/ : % ;777: 4d/ (4 % ; (; 7:b/ :(4%(:72(=%: (4 1
:/ A}gig igt thkqhaorat ap|zathfoat wqa ho}fiqdzgo }gzhgjiat/
g/ nen%e dqgobf n 3 = x e3 7:/
j/ :x: dqgobf p 3 7 x x 3 1
d/ 4p: % :p % 7 dqgobf p 3 1b/ (x: p: dqgobf p 3 : x x 3 7
4/ A}gig igt thkqhaorat ap|zathfoat wqa ho}fiqdzgo }gzhgjiat/
g/ 2p8p:4p%7 dqgobf p 3 :j/ ~
:
p%x %p:
px dqgobf p 3 7) x 3 :) x ~ 3 2/d/ 2px~x:p: dqgobf p 3 4) x 3 :) x ~ 3 1
b/ p:~:
p~:p(~p dqgobf p 3 7 gob ~ 3 42/ Hotazrg ift |gzoratht oadatgzhft ao dgbg ap|zatho |gzg fjraoaz qog adqgdho }ihbg/
g/ 1
:
=
2 % : 3 1
j/ 7:2 % 7
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{{{/de7:/fzk 78
4/ 0=2/ 4
7/ 047:/ 2;44/ #:22/
01
7/ (1 : (= 1 % : 3 1:/ (7: 2 % 7
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:< {{{/de7:/fzk
7/4 \grzfoat x Adqgdhfoat
Fjnarh}ft bai G|zaobh~gna
Ao atrg iaddho g|zaobazt g>
Atdzhjhz adqgdhfoat/ Qrhih~gz ai cfbaif }azjgi |gzg atdzhjhz adqgdhfoat/ Zatfi}az |zfjiacgt cabhgora adqgdhfoat/
Horzfbqddho
Ao cgracrhdgt) x at|adhgicaora ao ikajzg) at dfo}aohaora jqtdgz |grzfoat ao ift ocazft fjtaz}gbft/ Igt `az#zgchaorgt bai ikajzg oft gxqbgo g batdzhjhz atrft |grzfoat dfo |gigjzgt x dfo adqgdhfoat (mzcqigt fz mqodhfoat/Qog adqgdho at dfcf qog zadarg cgracrhdg wqa |zf|fzdhfog ai }gifz ba qog }gzhgjia ao rzchoft ba frzg/
\fz anac|if) th qo |gzwqa ba bh}azthfoat dfjzg "7: |fz gbchtho) Aorfodat ai ocazf ba |aztfogt wqa aorzgo dgbgbg g bhd`f |gzwqa x ig dgorhbgb ba bhoazf zadgqbgbf |fz }aorg ba jfiarft atro zaigdhfogbft cgracrhdgcaora/
Oftfrzft |fbacft atdzhjhz qog zakig |gzg aodforzgz ig dgorhbgb ba bhoazf zadgqbgbf |fz }aorg ba jfiarft/
Gt) ao |gigjzgt) |fbzgcft badhz) Ai bhoazf zadgqbgbf ao bigzat at (hkqgi g bfda }adat ai ocazf ba |aztfogtwqa hokzatgo gi |gzwqa/
Rgcjho |fbzgcft `gdaz qog rgjig/ Ig thkqhaora rgjig zaigdhfog ai ocazf ba |aztfogt wqa }hthrgo ai |gzwqa x airfrgi ba bhoazf zadgqbgbf |fz }aorg ba jfiarft/
Oqcazf ba }hthrgorat 7 : 4 2 1 = ;
Bhoazf zadgqbgbf(" 7: :2 4= 20 =< ;: 02
Digzgcaora) oadathrgzgcft qog rgjig kzgoba th zakhtrzgtacft if wqa fdqzza ao qo bg cqx fdq|gbf bqzgora ai|azfbf ba }gdgdhfoat atdfigzat'
Qog razdazg mfzcg ao ig wqa |fbzgcft zaigdhfogz bft dgorhbbat (}hthrgorat x bhoazf zadgqbgbf at cabhgora qogkzdg/ Th kzgdgcft ai bhoazf zadgqbgbf ao ai ana }azrhdgi x ai ocazf ba }hthrgorat ao ai ana `fzh~forgi) aorfodatraobzgcft qog kzdg wqa iqdhzg thchigz g ig wqa thkqa g dforhoqgdho/ Fjtaz}g wqa atrg kzdg cqatrzg qog ioagdforhoqg |gzg }gifzat zagiat (of bhtdzarft ba p (a/k/) p 3 :/1/ \azf) ao ig }hbg zagi atrf of tazg |fthjia |fzwqa of|qabat raoaz cabhg |aztfog hokzatgobf gi |gzwqa/ Atrf at qo racg ba if wqa ta dfofda dfcf bfchohf x zgokf) racgtba ift wqa `gjigzacft ct gbaigora/
7/4/ \grzfoat x Adqgdhfoat
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{{{/de7:/fzk :7
Ai crfbf wqa apgchogzacft ao bargiia ao atrg iaddho at dazdgof g ig |zhcazg mfzcg caodhfogbg gzzhjg wqa |qabaqtgzta |gzg batdzhjhz ig zaigdho aorza bft dgorhbgbat/ At badhz) dqgobf batdzhjhcft bhd`g zaigdho dfo |gigjzgt/ Gt|fz anac|if) |fbacft badhz wqa Ai bhoazf zadgqbgbf ao bigzat at bfda }adat ai ocazf ba |aztfogt wqa hokzatgo
gi |gzwqa/ \fz frzg |gzra) ao rzchoft cgracrhdft) |fbacft batdzhjhz qog zaigdho ba atra rh|f cabhgora }gzhgjiat/Qog }gzhgjia at qog iarzg qrhih~gbg |gzg za|zataorgz qog dgorhbgb batdfofdhbg/ Igt }gzhgjiat ta qrhih~go |gzg dzagzap|zathfoat cgracrhdgt/ At hc|fzrgora wqa ofrat wa |fbacft }az ai fzhkao ba igt ap|zathfoat cgracrhdgt ao igt|gigjzgt/
Ai bhoazf zadgqbgbf ao bigzat at bfda }adat ai ocazf ba |aztfogt wqa hokzatgo gi |gzwqa/
Atrf |qaba ap|zatgzta dfcf>
(Ai bhoazf zadgqbgbf ao bigzat 3 7: (ai ocazf ba |aztfogt wqa aorzgo gi |gzwqabfoba ta `go dfifdgbf igt dgorhbgbat aorza |gzoratht |gzg `gdazigt ct a}hbaorat/ G`fzg |fbacft }az ctmgdhicaora dqiat dgorhbgbat |qabao za|zataorgzta cabhgora iarzgt (f }gzhgjiat/ \zhcazf) bajacft atrgjiadazdqiat iarzgt (}gzhgjiat dfzzat|fobao g dqiat dgorhbgbat/ Atra |zfdatf ta dfofda dfcf baohdho ba }gzhgjiat>
Tag p 3 ai ocazf ba |aztfogt wqa aorzgo gi |gzwqa/
Tag x 3 ig dgorhbgb rfrgi ba bhoazf zadgqbgbf ao jfiarazg/
G`fzg |fbacft cftrzgz ig dqgzrg mfzcg |gzg batdzhjhz ig zaigdho fzhkhogi) wqa at cabhgora oqatrzg adqgdhogikajzghdg/
x 3 7:p
Atdzhjhz qog adqgdho cgracrhdg g rzg}t }gzhgjiat at cqx dfo}aohaora/ R |qabat zagih~gz rfbgt igt f|azgdhfoatoadatgzhgt |gzg zatfi}az atra |zfjiacg tho raoaz wqa atdzhjhz igt dgorhbgbat dfofdhbgt x batdfofdhbgt) cabhgora|gigjzgt atdzhrgt) qog x frzg }a~/ Gi ogi bai |zfjiacg) ohdgcaoa oadathrgzacft zadfzbgz dqiat dgorhbgbat tfoza|zataorgbgt |fz p x x/
Atdzhjhaobf qog Adqgdho
Qog adqgdho at qo rzchof qrhih~gbf |zg batdzhjhz qog dfiaddho ba ocazft x }gzhgjiat zaigdhfogbft aorza tcabhgora f|azgbfzat cgracrhdft/ Qog adqgdho gikajzghdg dforaobz iarzgt wqa za|zataorgo dgorhbgbat zagiat)f jhao ocazft wqa dfotrhrqxao }gifzat |gzg dgorhbgbat zagiat/ Th) |fz anac|if) wqhthzgcft qtgz ig adqgdhogikajzghdg bai anac|if gorazhfz |gzg aodfozgz ai bhoazf zadgqbgbf |fz qo ocazf at|addf ba }hthrgorat) raobzgcftwqa zaac|ig~gz ata }gifz (ai ocazf ba }hthrgorat ao p) x aorfodat zatfi}az ig adqgdho zatqirgora |gzg x/
D`g|raz 7/ Adqgdhfoat x Mqodhfoat
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:: {{{/de7:/fzk
Anac|if 7
Qo |gzwqa ba bh}azthfoat dfjzg "7: g ift }hthrgorat/ Aodqaorzg ai ocaazf zadgqbgbf th 7:8= |aztfogt }hthrgo ai|gzwqa/
Bh}hbgcft ig tfiqdho g atra |zfjiacg ao qo ocazf ba |gtft/ Atrf oft gxqbgz g zatfi}az rfbft ift |zfjiacgt baatrg iaddho/
\gtf 7 Fjro ig homfzcgdho hc|fzrgora/
(bhoazf zadgqbgbf ao bfigzat 3 7: (oqcazf ba }hthrgorat(oqcazf ba }hthrgorat 3 7:8=
\gtf : Dfo}hazra bhd`g homfzcgdho ao qog adqgdho cgracrhdg/
@gdacft atrf baohaobf }gzhgjiat x tqtrhrqxaobf ao aiigt }gifzat dfofdhbft/
Tag x 3 (bhoazf zadgqbgbf ao bfigzat
x 3 7:7:8= ATRG AT OQATRZG ADQGDHFO/
\gtf 4 Zatqai}a ig adqgdho/
x 3 7111: Zat|qatrg> Ai bhoazf zadgqbgbf at "7111:
\gtf 2 Dfc|zqajg ai zatqirgbf/
Th "7111: tfo zadgqbgbft ao }aorg ba jfiarft x dgbg jfiarf dqatrg "7:) aorfodat |fbacft bh}hbhz ig dgorhbgb rfrgibai bhoazf zadgqbgbf aorza ai |zadhf ba dgbg jfiarf hobh}hbqgi/
(ocazf ba |aztfogt 37111:
7:3 7:8=
Atra zatqirgbf at hborhdf gi ocazf ba |aztfogt wqa hokzatgzfo gi |gzwqa/ \fz if rgorf ig zat|qatrg `g thbfdfc|zfjgbg/
Anac|if :
Ig thkqhaora rgjig cqatrzg ig zaigdho aorza bft dgorhbgbat/ \zhcazf) atdzhja qog adqgdho wqa batdzhjg bhd`gzaigdho/ Iqakf) aodqaorzg ai }gifz ba j dqgobf g at ;1 < 7< :< 4< 2< 1 :< 2< =< 0< 7
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{{{/de7:/fzk :4
RGJIA 7/7>
Raprf ta rzgbqda g ig ap|zatho cgracrhdg\gzg aodforzgz j j 3ai bfjia bai }gifz ba g :gtqcgz :
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:2 {{{/de7:/fzk
\gtf 7 Fjro ig homfzcgdho hc|fzrgora/
\fbacft }az ba ig rgjig wqa x at dhodf }adat ct kzgoba wqa p/ Ai }gifz ba x at oakgrh}f dqgobf p at |fthrh}f) x at|fthrh}f dqgobf p at oakgrh}f/ \fz rgorf) ig zakig wqa zaigdhfog p x x/
xat ai hkqgi g ai oakgrh}f ba dhodf }adat ai }gifz ba p
Tra| : Dfo}hazra ai thkqhaora aoqodhgbf ao qog adqgdho cgracrhdg/
RGJIA 7/4>Raprf Ta dfo}hazra ao ig Ap|zatho Cgracrhdgx at hkqgi g x 3ai oakgrh}f ba 1 }adat ai }gifz ba
p 1p
x 3 1p ATRG AT OQATRZG ADQGDH FO/
\gtf 4 Ogbg `gx wqa zatfi}az ao atra |zfjiacg/ \fbacft takqhz dfo ai \gtf 2/\gtf 2 Dfc|zqajg ai zatqirgbf/
Ao atra dgtf) ig mfzcg ba dfc|zfjgz ai zatqirgbf at kaoazgobf oqatrzft |zf|hft |gzat px `gdhaobf qtf ba oqatrzgadqgdho/ Th bhd`ft |gzat dfhodhbao dfo ift }gifzat wqa aodforzgcft ao ig rgjig) aorfodat oqatrzg adqgdho atdfzzadrg/ \gzg kaoazgz bhd`ft |gzat) zaac|ig~gcft ao p ift }gifzat #:) x 3 1(: x 3 %7
x 3 1( x 3 1(: x 3 7
x 3 1(2 x 3 :
x 3 1(= x 3 4 Dqgobf (ai ocazf ba ig tacgog 3 7) (ai jgigoda 3 7
Tag ai ocazf ba ig tacgog 3 o
Tag ai jgigoda 3 j
RGJIA 7/1>
Raprf Ta dfo}hazra ao ig Ap|zatho CgracrhdgG cabhbg wqa o ta hodzacaorg ao 7)
j badzada ao ::
j 3 ::o%6
Ai thkof6 hobhdg wqa oadathrgcft frzf rzchof/ Tho bhd`f rzchof ai jgigoda tacgogi tazg #::) #22) #==)///) ifdqgi dforzgbhda ai `ad`f ba wqa ai jgigoda ao ig |zhcazg tacgog at 7
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:= {{{/de7:/fzk
Zatfiqdho ba \zfjiacgt qtgobf Adqgdhfoat
Zatfi}gcft ai thkqhaora |zfjiacg bai cqobf zagi/ \gzg aiif qtgzacft ig homfzcgdho |zf|fzdhfogbg |gzg dzagz qogadqgdho cgracrhdg wqa |qaba taz zatqairg |gzg aodforzgz qog tfiqdho/
Anac|if 1
Qo kzq|f ba atrqbhgorat atr ao qo tgio/ Iqakf wqa :1 atrqbhgorat tgiao) ta fjtaz}g wqa :4 bai kzq|f fzhkhogiwqabg baorzf bai tgio/ Dqorft atrqbhgorat ta aodforzgjgo hohdhgicaora baorzf bai tgio6
\gtf 7 Fjro ig homfzcgdho hc|fzrgora
Tgjacft wqa :1 atrqbhgorat tgiao bai tgio/
Rgcjho tgjacft wqa :4 bai ocazf fzhkhogi ba atrqbhgorat wqabgo baorzf bai tgio/
Oadathrgcft aodforzgz dqorft atrqbhgorat ta aodforzgjgo hohdhgicaora baorzf bai tgio/
\gtf : Dfo}hazra ig homfzcgdho ao qog adqgdho cgracrhdg/
Hohdhgicaora raoacft qo ocazf batdfofdhbf ba atrqbhgorat baorzf bai tgio/ Oft |fbacft zamazhz g aiift dfcf aiocazf fzhkhogi ba atrqbhgorat/
Baogcft ig }gzhgjia p 3 ai ocazf fzhkhogi ba atrqbhgoat baorzf bai tgio/
:1 atrqbhgorat tgihazfo bai tgio/ Aorfodat ai ocazf ba atrqbhgorat wqa |azcgoadao baorzf bai tgio at>
RGJIA 7/=>
Raprf Ta dfo}hazra ao Ap|zatho CgracrhdgAi ocazf fzhkhogi ba atrqbhgoratao ai tgio
p
:1 atrqbhgorat tgiao bai tgio p:1:4 bai ocazf fzhkhogi |azcgoadabaorzf bai dqgzrf
:4p
p :1 3 :4p ATRG AT OQATRZG ADQGDHFO/
\gtf 4 Zatqai}a ig adqgdho/
Tqcg :1 ao gcjft chacjzft ba ig adqgdho/
p :1 3 :4p
p :1 % :1 3:
4p % :1
p 3:4p % :1
Tqtrzga :4pba gcjft chacjzft/
p :4p 3
:4p :
4p % :1
74p 3 :1
7/4/ \grzfoat x Adqgdhfoat
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{{{/de7:/fzk :;
Cqirh|ihdg gcjft chacjzft |fz4/
4 74p 3 :1 4p 3 ;1
Zadqazbg wqa p za|zataorg ai ocazf fzhkhogi ba atrqbhgorat baorzf bai tgio/ \fz rgorf)Zat|qatrg Hohdhgicaora gjgo ;1 atrqbhgorat baorzf bai tgio/
\gtf 2 Dfc|zqajg ig zat|qatrg>
Th dfcao~gcft dfo ;1 atrqbhgorat baorzf bai tgifo x :1 ba aiift tgihazfo) aorfodat wqabgo ;1 :1 3 1< baorzf baitgio/:4 bai ocazf fzhkhogi ba atrqbhgorat at
:4 ;1 3 1
Bg Kgogodhg7 : ta gihcaorg ig dgng dfo qo dfonqorf ba ocazft (bhd`f dfonqorf|qaba) tho acjgzkf) atrgz dfomfzcgbf |fz qo tfif ocazf/ G dforhoqgdho) ig f|azgdho cgracrhdg wqa atrbaorzf ba ig dgng rzgotmfzcg bhd`ft ocazft) ba cgoazg wqa ta fjrhaoa frzf dfonqorf ba ocazft wqa tgia |fz aiigbf f|qatrf ba ig dgng/ Gt |fz anac|if) |gzg ai dgtf bai |gzwqa ba bh}azthfoat) |fbacft gihcaorgz ig dgng dfo
bhmazaorat }gifzat wqa dfzzat|fobgo g ift |gtaft zagih~gbft |fz Nft` ao bhmazaorat bgt/ Ba ig dgng tgibzo ift dftrft|fz bg gtfdhgbft g bhd`ft }gifzat/
Ig aorzgbg ta baofchog dfcf ig }gzhgjia hoba|aobhaora |fzwqa tq }gifz |qaba taz dqgiwqhaz ocazf |fthjia/ Igtgihbg ta fjrhaoa iqakf ba g|ihdgz ig f|azgdho cgracrhdg x ta dfofda dfcf ig }gzhjia ba|aobhaora |fzwqa tq }gifzba|aoba bai }gifz ba aorzgbg/
7/1/ Igt Mqodhfoat dfcf Zakigt x Rgjigt
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G caoqbf igt mqodhfoat tfo ct dfc|ihdgbgt wqa ig ba atra anac|if/ Igt mqodhfoat qtqgicaora dforhaoao ct baqog f|azgdho cgracrhdg/ Gwq rhaoat qog thrqgdho ihkazgcaora ct dfc|ihdgbg/
Ngtfo }g g qo |gzwqa ba bh}azthfoat bfoba |gkg "0 |fz bazad`f ba gbchtho x ": |fz dgbg |gtaf/
Atrg mqodho za|zataorg ig dgorhbgb rfrgi wqa Ngtfo |gkg/ Ig zakig wqa kfjhazog ig mqodho at cqirh|ihdgz ai oczfba }hgnat |fz :) x ggbhz 0 gi zatqirgbf ba bhd`g cqirh|ihdgdho/
Horzfbqdhcft bhmazaorat }gifzat |gzg ai ocazf ba |gtaft |gzg fjraoaz bhmazaorat tgihbgt (dftrft/
Atrft bhgkzgcgt ba qnf tfo jgtrgora rhiat |gzg }htqgih~gz if wqa at qog mqodho/ Tho acjgzkf) tq qtf |qaba zatqirgzrzgjgnftf a hodcfbf ao ig |zdrhdg/ At |fz aiif wqa qrhih~gzacft) ao tq iqkgz) ig thkqhaora ofrgdho dfc|gdrg/
\zhcazf) baohcft igt }gzhgjiat/
p 3 ai ocazf ba |gtaft zagih~gbft |fz Ngtfo
x 3 ig dgorhbgb rfrgi ba bhoazf wqa Ngtfo |gk ao ai |gzwqa ba bh}azthfoat
Gt) p za|zataorg ig aorzgbg x x za|zataorg ig tgihbg/ Ig ofrgdho> m( za|zataorg ig mqodho) f awqh}giaoracaora) igtf|azgdhfoat cgracrhdgt g igt wqa tfcaracft ig aorzgbg |gzg |fbaz fjraoaz ig tgihbg/ Ao ai irhcf anac|if) ai dftrfat : }adat ai ocazf ba |gtaft ct 0/ Atrf |qhaba taz atdzhrf dfcf qog mqodho/
m(p 3 :p % 0
Ig tgihbg }haoa bgbg |fz ig mzcqig m(p 3 :p % 0/ Igt ofrgdhfoat x x m(p |qabao dfothbazgzta awqh}giaoaratx qtgzta hobhtrhorgcaora) |azf rao |zataora wqa x za|zataorg ai }gifz ba tgihbg) chaorzgt wqa m(p za|zataorg igtf|azgdhfoat cgracrhdgt g igt wqa tfcaracft ig aorzgbg |gzg fjraoaz ig tgihbg/
Hbaorhdgz ai Bfchohf x ai Zgokf ba qog Mqodho
Ao ai irhcf anac|if) }hcft wqa |fbacft hokzatgz ai ocazf ba |gtaft baorzf ba ig mqodho |gzg fjraoaz ai dftrfrfrgi ba hz gi |gzwqa ba bh}azthfoat/ Ai dfonqorf ba rfbft ift }gifzat |fthjiat |gzg ig aorzgbg ta dfofda dfcf ai
D`g|raz 7/ Adqgdhfoat x Mqodhfoat
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bfchohf ba ig mqodho/ Ai dfonqorf ba rfbft ift |fthjiat }gifzat |gzg ig tgihbg ta dfofda dfcf ai zgokf ba igmqodho/ Ao cqd`gt thrqgdhfoat rgorf ai bfchohf dfcf ai zgokf ba qog mqodho atrgzo mfzcgbft |fz ai dfonqorfba rfbft ift ocazft zagiat) |azf of thac|za taz ai dgtf/ ]agcft oqa}gcaora g oqatrzf anac|if bai |gzwqa babh}azthfoat
Anac|if 7
Aodqaorzg ai bfchohf x zgokf ba ig mqodho wqa batdzhja ig thrqgdho thkqhaora>
Ngtfo }g g qo |gzwqa ba bh}azthfoat bfoba |gkg "0 |fz bazad`f ba gbchtho x ": |fz dgbg |gtaf/Tfiqdho
@a gwq ig mqodho wqa batdzhja atrg thrqgdho/
m(p 3 :p % 0 3 x
Ao atrg mqodho) p at ai ocazf ba |gtaft x x at ai dftrf rfrgi/ \gzg aodforzgz ai bfchohf ba ig mqodho) oadathrgcftbarazchogz dqiat }gifzat ba p tfo }ihbgt dfcf aorzgbgt/
Ift }gifzat ba p rhaoao wqa taz dazf f |fthrh}ft |fzwqa Ngtfo of |qaba zagih~gz qo ocazf oakgrh}f ba |gtaft/ Ift }gifzat bajao taz aorazft |fzwqa) |fz anac|if) Ngtfo of |qaba zagih~gz :/:1 }hgnat/ Ba cgoazg zagihtrg) baja `gjaz qo ocazf cphcf ba |gtaft wqa |qaba zagih~gz Ngtfo |fzwqa ai |gzwqa
baja dazzgz g dhazrg `fzg) |fzwqa Ngtfo razchog dfo rfbf tq bhoazf) ard/ Tho acjgzkf) bgbf wqa of raoacfthomfzcgdho gikqog gdazdg ba atrf) |fbacft gtqchz wqa rfbft ift aorazft of oakgrh}ft tfo |fthjiat aorzgbgt(ofrgz wqa ta hodiqxa ai dazf) xg wqa of at |fthrh}f) |azf rgc|fdf oakgrh}f) tho hc|fzrgz if kzgobat wqa|qabgo taz tqt }gifzat/
Zat|qatrg \gzg atrg mqodho) ai bfchohf at ai dfonqorf ba rfbft ift aorazft of oakgrh}ft) at badhz (
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Ig }gzhgjia p |qaba rfcgz dqgiwqhaz }gifz zagi cgxfz wqa dazf/
Ig }gzhgjia x rgcjho |qaba rfcgz dqgiwqhaz }gifz zagi cgxfz wqa dazf/
Zat|qatrg Ai bfchohf at ai dfonqorf ba rfbft ift ocazft zagiat cgxfzat wqa dazf/
Ai zgokf at ai dfonqorf ba rfbft ift ocazft zagiat cgxfzat wqa dazf/
j Bgbf wqa of raoacft qo |zfjiacg ap|zatgbf }azjgicaora gtfdhgbf g atrg adqgdho) |fbacft gtqchz wqa|fbacft qtgz dqgiwqhaz ocazf zagi dfcf qo }gifz |fthjia ba p/
Bgbf wqa x 3 p:) ai }gifz ba x taz thac|za of oakgrh}f) tho hc|fzrgz wqa p tag |fthrh}f) oakgrh}f f dazf/
Zat|qatrg Ai bfchohf ba atrg mqodho tfo rfbft ift ocazft zagiat/
Ai zgokf ba atrg mqodho atr mfzcgbf |fz rfbft ift ocazft zagiat of oakgrh}ft/
Zadfzbacft wqa) |gzg qog mqodho) ig }gzhgjia p ta baofchog dfcf ig }gzhjia hoba|aobhaora |fzwqa |qaba rfcgzdqgiatwqhazg }gifzat bai bfchohf/ Ig }gzhgjia x ta baofchog dfcf ig }gzhgjia ba|aobhaoa |fzwqa tq }gifz ba|aobaba p/ \fbacft qrhih~gz tcjfift dqgiatwqhazg |gz za|zataorgz igt }gzhjiat ba|aobhaorat a hoba|aobhaorat/ Gwq rhaoatrzat bhmazaorat anac|ift/
x 3 m(p 3 4p
Z 3 m({ 3 4{
} 3 m(r 3 4r
Rfbgt atrgt ap|zathfoat za|zataorgo g ig chtcg mqodho/ Ig }gzhgjia ba|aobhaora at rzat }adat ig }gzhjia hoba|ao#bhaora/ Ao ig |zdrhdg) ift tcjfift wqa tfo qrhih~gbft |gzg igt }gzhgjiat hoba|aobhaorat x ba|aobhaorat ta atdfkaoba gdqazbf gi qtf dfco kaoazgih~gbf/ \fz anac|if> r ta qrhih~g |gzg za|zataorgz rhac|f) b |gzg bhtrgodhg) } |gzg}aifdhbgb) ard/ Ift tcjfift atrobgz (f kaozhdft wqa ta qrhih~go tfo x |gzg ig }gzhjia ba|aobhaora x p |gzg ig}gzhgjia hoba|aobhaora/
Qog mqodho>
ohdgcaoa gda|rg ocazft wqa |azraoa~dgo g tq bfchohf \gzg dgbg aorzgbg aphtra apgdrgcaora qog tgihbg/ Ai dfonqorf ba rfbgt igt tgihbgt dfzzat|fobhaorat gi bfchohf
dfotrhrqxao ai zgokf
Cqirhcabhg Ihoe \fz frzf }htrg~f gi bfchohf ba qog mqodho) }a ai thkqhaora }hbaf bfoba ai ogzzgbfz zatqai}a qo|zfjiacg ba cqatrzg ba ig \zqajg ba Atrobgzat ba Dgihmfzohg gdazdg ba aodforzgz ai bfchohf ba qog mqodho hoqtqgiE`go Gdgbacx DG Gikajzg H Mqodrhfot (=>42
CABHG
Dihde hcgka rf r`a iamr mfz cfza dforaor/
/
D`g|raz 7/ Adqgdhfoat x Mqodhfoat
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@gdaz qog Rgjig |gzg qog Mqodho
Qog rgjig at qog mfzcg cqx rhi |gzg fzkgoh~gz ift bgrft za|zataorgbft |fz qog mqodho/ \fbacft nqorgz ift }gifzatba aorzgbg x ba tgihbg) bht|fohobfift ao mfzcg ba rgjig/ Rfcacft ba oqa}f ai anac|if bai |gzwqa ba bh}azthfoat
Ngtfo }g g qo |gzwqa ba bh}azthfoat bfoba |gkg "0 |fz bazad`f ba gbchtho x ": |fz dgbg |gtaf/
Xg `acft }htrf wqa |gzg fjraoaz ig tgihbg dfzzat|fobhaora g qo }gifz ba aorzgbg ta iia}go g dgjf igt f|azgdhfoat: aorzgbg % 0/ \fz anac|if) th |foacft g ig aorzgbg ift }gifzat
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{{{/de7:/fzk 24
RGJIA 7/7
p m(p 3 7p 3 x7 77 3 7#
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22 {{{/de7:/fzk
Aodforzgz qog zakig mqodhfogi at |zfjgjiacaora ig rgzag ct bhmdhi ba zagih~gz ao cgracrhdgt/ Ao atra ihjzf) rbajazt aodforzgz x atdzhjhz zakigt mqodhfogiat cgxfzhrgzhgcaora |gzg zaigdhfoat ihoagiat) igt dqgiat tfo ai rh|f ctthc|ia ba igt mqodhfoat/
Za|zataorgz qog Thrqgdho bai Cqobf Zagi cabhgora qog Mqodho
Bacft qo }htrg~f g qogt dqgorgt thrqgdhfoat bai cqobf zagi wqa |qabao taz za|zataorgbgt cabhgora qog mqodho/
Anac|if 1
Cgxg dforzgrg qo taz}hdhf ba Horazoar wqa rhaoa gdrqgicaora qo dgzkf caotqgi ba "77/81 ct qo dgzkf ba " qog rgzhmg ng (|igogba "77/81 x qo dgzkf |fz
`fzg ba dfoapho ba "
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anac|if ;
Qog ac|zatg ba raimfoft daiqigzat }aoba bft chiifoat ba raimfoft ao tq |zhcaz gf ba f|azgdhfoat/ Ai ocazf baraimfoft wqa aiift }aobao ta bq|ihdg dgbg gf/ Atdzhja qog mqodho wqa |zf|fzdhfoa ai ocazf ba raimfoft wqatfo }aobhbft dgbg gf dfcf qog mqodho ba ig abgb ba ig ac|zatg//
Tfiqdho
Baohz Tag p 3 abgb ba ig ac|zatg ao gft
Tag x 3 ocazf ba raimfoft wqa tfo }aobhbft |fz gf
@g~ qog rgjig
Abgb ba ig ac|zatg(goft 7 : 4 2 1 = ;
Oqcazf ba raiamfoft (chiifoat : 2 0 7= 4: =2 7:0
Atdzhjhz qog zakig mqodhfogi
Ai ocazf ba raimfoft }aobhbft |fz gf ta bq|ihdg dgbg gf/ Dfcao~gcft dfo bft chiifoat ba aiift ai |zhcaz gf>
Gof 7 > : chiifoat
Gof : > : : 3 2 chiifoatGof 4 > : : : 3 0 chiifoatGof 2 > : : : : 3 7= chiifoat
\fbacft dforhoqgz cqirh|ihdgobf |fz bft |gzg aodforzgz ai ocazf ba raimfoft }aobhbft ao ift |zphcft gft/ Rq|zfjgjiacaora zadqazbat wqa) dqgobf cqirh|ihdgcft qo ocazf |fz t chtcf }gzhgt }adat) |fbacft qtgz ig ofrgdhoap|foaodhgi/
: 3 :7
: : 3 ::: : : 3 :4
Ao atra |zfjiacg) ai ap|foaora za|zataorg ig abgb ba ig ac|zatg/
Zat|qatrg x 3 m(p 3 :p
Anazdhdhft ba Za|gtf
Hbaorhdg ai bfchohf x ai zgokf ba igt thkqhaorat mqodhfoat/
7/ Bqtrho dfjzg "7< ig `fzg |fz dfzrgz dt|abat/:/ Cgzg dfjzg ":1 ig `fzg |fz digtat |gzrhdqigzat (g bfchdhihf ba cgracrhdgt) dfo qo dgzkf cohcf ba "71/4/ m(p 3 71p 7:2/ m(p:p: % 11/ m(p 3 7p=/ Dqi at ai zgokf ba ig mqodho x 3 p: 1 dqgobf ai bfchohf at #:) #7)
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2= {{{/de7:/fzk
;/ Dqi at ai zgokf ba ig mqodho x 3 :p 42 dqgobf ai bfchohf at #:/1) 7/1) 160/ Gokha kgog "=/1< ig `fzg dqgobf rzgjgng dfcf dgnazg ao qog rhaobg ba dfcatrhjiat/ @g~ qog rgjig wqa cqatrza
tq tgigzhf |gzg ift thkqhaorat }gifzat ba aorzgbg (ao `fzgt 1) 7 ocazft zgdhfogiat of oakgrh}ft/:/ Bfchohf> ocazft zgdhfogiat of oakgrh}ft5 Zgokf> ocazft zgdhfogiat cgxfzat f hkqgiat wqa 71/4/ Bfchohf> rfbft ift ocazft zagiat5 Zgokf> Rfbft ift ocazft zagiat/2/ Bfchohf> rfbft ift ocazft zagiat5 Zgokf> ocazft zagiat cgxfzat f hkqgiat wqa 1/1/ Bfcgho> rfbft ift ocazft zagiat apda|rf rfbft ift ocazft zagiat
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{{{/de7:/fzk 2;
p 7 < 7 : 4 2 1x 7 7/;4 :/:2 :/=1 4 4/4: 4/=
77/ x 3 p:
7:/ x 3 71 % 1p
74/ x 3:2:p
72/ m(p 3 p 771/ x 3 2< % :1p5 "7717=/ :
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7/= Kzdgt ba Mqodhfoat
Fjnarh}ft bai G|zaobh~gna
Ao atrg iaddho g|zaobazt g>
Kzgdgz qog mqodho g |gzrhz ba qog zakig mqodhfog f ba qog rgjig/ Atdzhjhz qog zakig mqodhfogi g |gzrhz ba qog kzdg/ Gogih~gz ig kzdg ba qog thrqgdho bai cqobf zagi/ Barazchogz th qog zaigdho at) f of) qog mqodho/
Horzfbqddho
Ig za|zataorgdho kzdg ba igt mqodhfoat dfothtra) jthdgcaora) ao bhjqngz |qorft tfjza qo \igof Dffzbaogbf(ai dqgi rgcjho ta baofchog dfcf ai \igof Dgzrathgof / Batba qog |azt|adrh}g |qzgcaoa kzdg) ai |igofdffzbaogbf at qog zanhiig f dqgbzdqig mfzcgbg g |gzrhz ba bft zadrgt oqczhdgt |zhodh|giat) qog `fzh~forgi x ig frzg}azrhdgi) wqa ta dzq~go ao qo |qorf iigcgbf ai fzhkao/ Ai fzhkao at ai |qorf (
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{{{/de7:/fzk 28
Aorfodat oft cf}acft 2 qohbgbat `gdhg ig bazad`g/
Iqakf oft cf}acft : qohbgbat `gdhg gzzhjg) |gzrhaobf ba ig irhcg |fthdho/
Anac|if 7
Kzgwqa ift thkqhaorat |qorft dffzbaogbft ao ai |igof Dgzrathgof/
(g (1) 4
(j (#:) =
D`g|raz 7/ Adqgdhfoat x Mqodhfoat
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(d (4) #2
(b (#1) #;
Tfiqdho
Cftrzgcft rfbft ift |qorft dffzbaogbft ao ig chtcg kzdg
Bajacft ofrgz wqa>
\gzg qo }gifz |fthrh}f ba p oft cf}acft `gdhg ig bazad`g/
\gzg qo }gifz oakgrh}f ba p oft cf}acft gdhg ig h~wqhazbg/
\gzg qo }gifz |fthrh}f ba x oft cf}acft gdhg gzzhjg/
\gzg qo }gifz oakgrh}f ba x oft cf}acft `gdhg gjgnf/
Ift anat pgpht x x bh}hbao ai |igof dffzbaogbf ao 2 dqgbzgorat/ Ift dqgbzgorat ta oqcazgo ao ai taorhbfgorh#`fzgzhf (taorhbf ba khzf dforzgzhf gi ba igt cgoadhiigt ba qo zaifn) dfcao~gobf batba ai dqgbgzgora tq|azhfz
bazad`f/ Gt) ai |qorf kzgdgbf dfzzat|fobhaora gi ihrazgi (g atr qjhdgbf ao ai \zhcaz dqgbzgora) ai ba (j atr aoai takqobf dqgbzgora) ai ba (d ta aodqaorzg ao ai Dqgzrf dqgbzgora) x ai ba (b atr ao ai Razdaz dqgbzgora/
Kzdg ba qog Mqodho fjraohbg g |gzrhz ba qog Zakig Mqodhfogi f ba qog Rgjig
Th ig zakig mqodhfogi at dfofdhbg) f th bht|foacft ba qog rgjig ba }gifzat wqa batdzhja g qog mqodho) |fbacft`gdaz qog kzdg ba ig mqodho/ Qog rgjig ba }gifzat oft |zf|fzdhfog |qorft dffzbaogbft wqa |fbacft bhjqngz aoai |igof Dgzrathgof/
Anac|if :
Kzgdg ig mqodho wqa rhaoa ig rgjig ba }gifzat thkqhaora/
p : 7 < 7 :x = 0 7< 7: 72
Tfiqdho
Ig rgjig oft |zf|fzdhfog dhodf dfonqorft ba dffzbaogbgt p) x (at badhz) dhodf |qorft dffzbaogbft> (#:) =) (#7) 0)(
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{{{/de7:/fzk 17
\gzg kzgdgz ig mqodho) bhjqngcft rfbft ift |qorft dffzbaogbft/ Bgbf wqa of ta oft jzhobg homfzcgdho tfjza aibfchohf ba ig mqodho f bai dforaprf bfoba g|gzada) |fbacft gtqchz wqa ai bfchohf at ai dfonqorf ba rfbft iftocazft zagiat/ \gzg cftrzgz wqa ig mqodho at }ihbg |gzg rfbft ift }gifzat bai bfchohf) dfoadrgcft ift |qorftdfo qog ioag dforhoqg/ Ao atra taorhbf) rgcjho bajacft bgzoft dqaorg wqa ig ioag ta aprhaoba hobaohbgcaora aogcjgt bhzaddhfoat/
Anac|if 4
Kzgdg ig mqodho g ig wqa dfzzat|foba ig thkqhaora rgjig ba }gifzat/
Ifokhrqb bai igbf bai dqgbzgbf < 7 : 4 2
Gzag bai dqgbzgbf < 7 2 8 7=
Ig rgjig oft |zf|fzdhfog dhodf |qorft dffzbaogbft> (
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Kzgdg ig mqodho wqa rhaoa ig thkqhaora rgjig ba }gifzat/
Oqcazf ba kifjft 7: 74 72 71 7=
Dftrf 27 22 2; 1< 14
Atrg mqodho za|zataorg ai dftrf rfrgi ba ift kifjft iia}gbft g rq dgtg/ Dgbg kifjf dqatrg "4 x ig rhaobg ift iia}g g rqdgtg |fz ig dfc|zg ba qog bfdaog gbhdhfogi ba kifjft/ Ig aorzakg g bfchdhihf rhaoa qog rgzhmg ng (|igogba "1/
Tfiqdho
Ig rgjig oft |zf|fzdhfog dhodf |qorft dffzbaogbft (7:) 27) (74) 22) (72) 2;) (71) 1
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{{{/de7:/fzk 14
Tfiqdho
@g~ qog rgjig ba }gifzat/ Taiaddhfog qog }gzhabgb ba }gifzat aorazft oakgrh}ft x |fthrh}ft |gzg ig }gzhgjia hoba|ao#bhaora/ Qrhih~g ig zakig mqodhfogi |gzg aodforzgz ai }gifz ba ig }gzhgjia dfzzat|fobhaora g dgbg }gifz ba ig }gzhgjiahoba|aobhaora/ Iqakf kzgdg dgbg qof ba ift |qorft dffzbaogbft gt fjraohbft/
RGJIA 7/77>
p x 3 m(p 3 yp :y2 y2:y3 y=y3 =#4 y4:y3 y1y3 1#: y::y3 y2y3 2#7 y7:y3 y4y3 4< y
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12 {{{/de7:/fzk
At gdfotangjia wqa rzgjgnat dfo cqd`ft }gifzat dqgobf ac|ha~gt g mgchihgzh~gzra dfo ig dzagdho ba kzdgt bamqodhfoat/ Iqakf) dfomfzca }gxgt g|zaobhaobf gdazdg ba ift bhmazaorat rh|ft ba mqodhfoat) ra bgzt dqaorg wqa|fbzt dzagz kzdgt jgtrgora |zadhtgt dfo rgjigt ba }gifzat wqa dforaokgo |fdft |qorft/
Anac|if =
Kzgdg ig thkqhaora mqodho> m(p 3
p
Tfiqdho
@g~ qog rgjig ba }gifzat/ Of |fbacft qrhih~gz oqcazft oakgrh}ft |fzwqa of |fbacft fjraoaz ig zg~ dqgbzgbg baqo ocazf oakgrh}f/ Ao kaoazgi) ig mqodho zg~ dqgbzgbg of |zf|fzdhfog tgihbgt zagiat |gzg aorzgbgt oakgrh}gt/Ai bfchohf) |fz rgorf) at ai dfonqorf ba rfbft ift ocazft zagiat |fthrh}ft/ Gt wqa bajacft taiaddhfogz bh}aztft}gifzat aorazft |fthrh}ft |gzg ig }gzhgjia hoba|aobhaora/ Iqakf qrhih~g ig zakig mqodhfogi |gzg aodforzgz ai }gifz baig }gzhgjia ba|aobhaora |gzg dgbg }gifz ba ig }gzhgjia hoba|aobhaora/
RGJIA 7/7:>
p x 3 m(p 3
p
@gdacft qog rgjig ba }gifzat dfzzat|fobhaorat g }gzhft |qorft dffzbaogbft |gzg }az th |fbacft hbaorhdgz ai |grzowqa cqatrzg dcf ta zaigdhfogo igt }gzhgjiat ba|aobhaora a hoba|aobhaora aorza t/
p 2 4 : 7 < 7 : 4 2x 0 2/1 : /1 < /1 : 2/1 0
Ofrgcft wqa dgbg }gifz ba x at ig chrgb bai dqgbzgbf |azmadrf ba p/ \fz rgorf) zaatdzhjhcft ig rgjig ba }gifzatdfcf>
p 2 4 : 7 < 7 : 4 2x
7=:
8:
2:
7:
]fiqcao 3 1 7:
Bg : > ]fiqcao 3 1 7:
7:
Bg 4 > ]fiqcao 3 1 7:
7:
7:
\fz rgorf) ig adqgdho ba ig mqodho at m(p 3 1
7:
p
Gogih~gz ig kzdg ba qog Thrqgdho bai Cqobf Zagi
Igt kzdgt tfo qrhih~gbgt |gzg za|zataorgz bgrft ao rfbgt igt zagt ba ig }hbg/ \fz anac|if) |qabat aodforzgz kzdgt
ao |azhbhdft) dgc|ggt |firhdgt) |qjihdgdhfoat dhaordgt x |zataorgdhfoat ba oakfdhft/@a gwq qo anac|if ba qog kzdg wqa |fbzgt }az za|fzrgbg ao igt ofrhdhgt/ Ig cgxfzg ba dhaordft dzaa wqaigt dzadhaorat achthfoat ba kgtat ba ho}azogbazf) |gzrhdqigzcaora ba bhphbf ba dgzjfof) atro dforzhjqxaobf gidgiaorgchaorf ba oqatrzf |igoarg/ Atrg kzdg cqatrzg dcf ift oh}aiat ba bhphbf ba dgzjfof ta `go hodzacaorgbfdfomfzca ai cqobf ta `g hobqtrzhgih~gbf/
Ba atrg kzdg) |fbacft aodforzgz ig dfodaorzgdho ba bhphbf ba dgzjfof ao ig grctmazg |gzg bhmazaorat gft/
78
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{{{/de7:/fzk 18
Barazchogz th qog Zaigdho at qog Mqodho
Xg }hcft wqa qog mqodho at qog zaigdho aorza igt }gzhgjiat hoba|aobhaora x ba|aobhaora/ Tgjacft rgcjho wqa atqog zakig wqa qrhih~g ift }gifzat ba ig }gzhgjia hoba|aobhaora |gzg bgz ift }gifzat ba ig }gzhgjia ba|aobhaora/ Qogzakig mqodhfogi |qaba taz ap|zatgbg ao |gigjzgt) rgcjho dfcf qog adqgdho) f dfcf qog rgjig ba }gifzat) f jhaodfcf qog kzdg/ Rfbgt atrgt za|zataorgdhfoat tfo rhiat x oadatgzhgt |gzg aoraobaz ig zaigdho aphtraora aorza igt
}gzhgjiat ba|aobhaora a hoba|aobhaora/ Cgracrhdgcaora) qog mqodho at qo rh|f at|adhgi ba zaigdho/Igt thkqhaora dfobhdho oft gxqbgz g barazchogz th qog zaigdho cgracrhdg at) f of) qog mqodho/
Ao qog mqodho) |gzg dgbg }gifz ba aorzgbg) aphtra apgdrgcaora qo }gifz ba tgihbg/
Atrf thkohdg qtqgicaora wqa dgbg }gifz ba p rhaoa gthkogbf qo ohdf }gifz ba x/ Tho acjgzkf) at hc|fzrgoratgjaz wqa of rfbgt igt mqodhfoat ho}fiqdzgo }gifzat bhtrhorft ba x |gzg }gifzat bhtrhorft ba p/ At badhz) wqa bft f ct}gifzat ba p |qabao raoaz gthkogbf qo chtcf }gifz ba x/ Ao rfbf dgtf) if wqa qog mqodho of |azchra at gthkogzcirh|iat }gifzat x g dgbg }gifz ba p/
Dfcf hiqtrzgdho) dfothbazg ig zaigdho wqa cqatrzg igt atrgrqzgt ba rfbft ift atrqbhgorat ba qog digta/ Ai bfchohfat ai dfonqorf ba |aztfogt ao ig digta x ai zgokf at ai dfonqorf ba atrgrqzgt/ Dgbg |aztfog ao ig digta of |qaba raoazct ba qog atrgrqzg g ig }a~/ \fz rgorf) atrg zaigdho at qog mqodho |fzwqa |gzg dgbg |aztfog aphtra apgdrgcaoraqog atrgrqzg wqa ia |azraoada/
Fjtaz}g) tho acjgzkf) wqa ao qog mqodho qo }gifz bai zgokf |qaba |azraoadaz g ct ba qo aiacaorf bai bfchohf/At badhz) wqa ct ba qog |aztfog ao digta |qaba raoaz ig chtcg atrgrqzg/ \azf if f|qatrf of at |fthjia) at badhz) wqaqog |aztfog raokg cirh|iat atrgrqzgt/
Anac|if 77
Barazchog th ig thkqhaora zaigdho at qog mqodho/
g (7) 4) (#7) #:) (4) 1) (:) 1) (4) 2j (#4) :
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p : 7 < 7 :
x 7: 7< 0 = 2
Tfiqdho
Ig cgoazg ct mdhi ba barazchogz th qog zaigdho at qog mqodho at fjta}gz g rfbft ift }gifzat ba p
ao ig ihtrg f
rgjig/ Th qo }gifz ba p g|gzada ct ba qog }a~ x ift }gifzat wqa ia dfzzat|foba ba xtfo bhmazaorat) aorfodat igzaigdho of at qog mqodho/
g (7) 4) (#7) #:) (4) 1) (:) 1) (4) 2
\qabat }az wqa ao atrg zaigdho) `gx bft }gifzat bhmazaorat ba x wqa |azraoadao gi }gifz 4 bap/ Atrf thkohdg wqaatrg zaigdho of at qog mqodrhfo/
j (#4) :
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{{{/de7:/fzk =7
Of at qog mqodho/ Of |gtg ig |zqajg ba ig ioag }azrhdgi
At qog mqodho/ Ohokqog ioag }azrhdqgi dzq~gz ig dqz}g ba ig kzdg ao ct ba qo |qorf/
At qog mqodho/ Ohokqog ioag }azrhdqgi dzq~gz ig dqz}g ba ig kzdg ao ct ba qo |qorf
Of at qog mqodho/ Of |gtg ig |zqajg ba ig ioag }azrhdgi
D`g|raz 7/ Adqgdhfoat x Mqodhfoat
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Anazdhdhft ba Za|gtf
7/ Bhjqng ift |qorft dffzbaogbft ao ai |igof Dgzrathgof/
g/ (2) #2j/ (:) ;d/ (#4) #1b/ (=) 4a/ (#2) 4
:/ Atdzhja igt dffzbaogbgt |gzg dgbg |qorf cftrzgbf ao ai |igof Dgzrathgof/
4/ Kzgdg ig mqodho wqa rhaoa ig thkqhaora rgjig ba }gifzat/ (g
p 7< 1 < 1 7Ai crfbf @gdaz qog Rgjig at rhi dqgobf ta zatqai}ao |zfjiacgt wqa rhaoao wqa }az dfo zaigdhfoat oqczhdgt/Dqgobf ift bgrft ta fzkgoh~go ao qog rgjig) at ct mdhi zadfofdaz |grzfoat x zaigdhfoat aorza ocazft/ G|ihwqacftatrg atrzgrakhg gi thkqhaora anac|if/
Anac|if :
Nftha badhba dfcao~gz g |zgdrhdgz ai rzfra (nfkkhok/ Bqzgora ig |zhcazg tacgog) aiig rzfrg 7< choqrft dgbg bg5 aoig takqobg tacgog) rzfrg 7: choqrft dgbg bg/ Dgbg tacgog) aiig wqhaza hodzacaorgz tq rhac|f ba rzfra bhgzhf ao :choqrft/ Th aiig rzfrg = bgt dgbg tacgog) Dqi taz ai rhac|f rfrgi ba rzfra bqzgora ig taprg tacgog6
Tfiqdho
\gtf 7Aoraobaz
Tgjacft wqa bqzgora ig |zhcazg tacgog Nftha rzfrg 7< choqrft dgbg bhg) bqzgora = bgt/
Tgjacft wqa bqzgora ig takqobg tacgog Nftha rzfrg 7: choqrft dgbg bg) bqzgora = bgt/
Dgbg tacgog) aiig hodzacaorg ao : choqrft tq rhac|f ba rzfra bhgzhf/ Gbact) aiig thac|za |zgdrhdg ai rzfra = }adatg ig tacgog/
Wqazacft dfofdaz ai rhac|f rfrgi ba rzfra ao ig taprg tacgog/
\gtf :
D`g|raz 7/ Adqgdhfoat x Mqodhfoat
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Atrzgrakhg
Qog jqaog atrzgrakhg at `gdaz dfifdgz ift bgrft wqa oft |zf|fzdhfog ai aoqodhgbf bai |zfjiacg ao qo rgjig/ Iqakfbajacft qtgz ig homfzcgdho |zf|fzdhfogbg |gzg aodforzgz oqa}g homfzcgdho/ \fbacft `gdaz ig rgjig dfo iftthkqhaorat aodgja~gbft/
Tacgog Choqrft |fz bg Choqrft |fz Tacgog
Ai aoqodhgbf bai |zfjiacg oft bhda wqa Nftha rzfrg 7< choqrft gi bg) |fz = bgt bqzgora ig |zhcazg tacgog/ Rgcjhooft bhda wqa aiig rzfrg 7: choqrft gi bg) |fz = bgt ao ig takqobg tacgog/ \fbacft aorfodat ggbhz rfbg atrghomfzcgdho ao oqatrzg rgjig>
RGJIA 7/71>
Tacgog Choqrft |fz bg Choqrft |fz tacgog7 7< =
Tacgog Choqrft |fz bg Choqrft |fz tacgog7 7< =
Jqtdgz qo \grzo at qog atrzgrakhg wqa |qabat qrhih~gz |gzg jqtdgz |grzfoat ao ift bgrft dfo ig ogihbgb ba zatfi}az|zfjiacgt/ Ig ogihbgb ba bhd`g atrzgrakhg at jqtdgz bgrft f ocazft wqa ta za|hrao) f jhao jqtdgz a}aorft wqa taza|hrao/ Ai thkqhaora |zfjiacg |qaba zatfi}azta g rzg}t ba ig rdohdg ba aodforzgz qo |grzo/
Anac|if 4
Rq bht|foat |aifrgt ba raoht ao gzzakift rzhgokqigzat) dfcf ta cqatrzg/ Dqorgt |aifrgt `gjzo ao qo rzhokqifwqa rhaoa 0 igt ba |aifrgt6
Tfiqdho
\gtf 7
Aoraobaz
Tgjacft wqa bht|foacft igt |aifrgt ba raoht ao gzzakift rzhgokqigzat dfcf ta cqatrzg/
Wqazacft tgjaz dqorgt |aifrgt `gx ao qo rzhokqif wqa rhaoa 0 igt ba |aifrgt/
\gtf :
Atrzgrakhg
Qog jqaog atrzgrakhg at `gdaz qog rgjig wqa dforaokg qog ihtrg ba dqorgt |aifrgt aphtrao ao rzhokqift wqa |ftaaobhmazaorat ocazft ba igt/
Qog ig/ At thc|ia fjtaz}gz wqa qo rzhokqif dfo qog ig rhaoa tfigcaora qog |aifrg/
Bft igt/ \gzg qo rzhgokqif dfo : igt) tqcgcft igt |aifrgt ba ig ig tq|azhfz dfo igt ba ig ig homazhfz/ At rhi`gdaz qo jftwqanf ba igt bhmazaorat igt bai rzhokqif/
3 : % 7 3 4
Rzat igt Tqcgcft igt |aifrgt bai rzhokqif tq|azhfz dfo igt |aifrgt ba ig ig homazhfz/
D`g|raz 7/ Adqgdhfoat x Mqodhfoat
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;0 {{{/de7:/fzk
3 4 % 4 3 =
\fbacft aorfodat dfc|iargz igt |zhcazgt rzat igt ba ig rgjig/RGJIA 7/7;>
Ocazf ba igt Ocazf ba |aifrgt7 7: 44 =
\fbacft fjtaz}gz wqa aphtra qo |grzo' At badhz>
\gzg dzagz ai thkqhaora rzhokqif) ggbhcft qog oqa}g ig homazhfz gi rzhokqif aphtraora/
Ig oqa}g ig homazhfz rhaoa qo ocazf ba |aifrgt hkqgi gi ocazf ba igt aphtraorat ao ai oqa}f rzhokqif (bhd`focazf) |fz tq|qatrf) ta baja rfcgz ao dqaorg ig oqa}g ig homazhfz/
# Qo rzhokqif dfo 4 igt rhaoa 4 |aifrgt ao ig ig homazhfz/
\gzg fjraoaz ai ocazf rfrgi ba |aifrgt |gzg ai oqa}f rzokqif) tqcgcft ai ocazf ba |aifrgt bai rzhokqif fzhkhogigi ocazf ba |aifrgt ba ig oqa}g ig homazhfz/
bgbf wqa) dfcf ta caodhfo gzzhjg) ai ocazf ba |aifrgt ba ig oqa}g ig homazhfz at hkqgi gi ocazf rfrgi ba igtbai oqa}f rzhokqif) rgcjho ta |qaba badhz wqa
\gzg fjraoaz ai ocazf rfrgi ba |aifrgt |gzg ai oqa}f rzokqif) tqcgcft ai ocazf ba |aifrgt bai rzhokqif fzhkhogigi ocazf ba igt bai oqa}f rzhokqif/
\gtf 4G|ihdgz ig atrzgrakhg&zatfi}az>
\fbacft dfc|iargz ig rgjig thkqhaobf ai |grzo wqa `acft batdqjhazrf/
Ocazf ba |aifrgt 3 ocazf ba |aifrgt ao ai rzhokqif fzhkhogi % ocazf ba igt bai oqa}f rzhokqif
RGJIA 7/70>
Ocazf ba igt Ocazf ba \aifrgt7 7: 44 =2 = % 2 3 7 @gdaz qog Rgjig f Jqtdgz qo \grzo
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{{{/de7:/fzk ;8
Dgbg ig ba qo rzhokqif rhaoa qog |aifrg ct wqa ig ig |za}hg/ Gt) ao qo rzhokqif ba 0 igt)
ig ig 7 rhaoa 7 |aifrg5 ig ig : rhaoa : |aifrgt5 ig ig 4 rhaoa 4 |aifrgt5 ig ig ig 2 rhaoa 2 |aifrgt5 ig ig 1 `gt 1 jgiit5ig ig = rhaoa = |aifrgt5 ig ig ; rhaoa ; |aifrgt5 ig ig 0 rhaoa 0 |aifrgt/
Dqgobf tqcgcft rfbgt atrgt dgorhbgbat) raoacft> 7 % : % 4 % 2 % 1 % = % ; % 0 3 4= |aifrgt
Ig zat|qatrg ta `g dfc|zfjgbf/
Ofrg wqa ao atra anac|if `hdhcft rgjigt x bhjqngcft bhgkzgcgt |gzg gxqbgzoft g fzkgoh~gz ig homfzcgdho xaodforzgz qo |grzo/ Ai qtf thcqiroaf ba }gzhft crfbft at qog |zdrhdg dfco x at cqx rhi |gzg zatfi}az|zfjiacgt/
Atrgjiadaz x Dfc|gzgz Aomfwqat Girazogrh}ft |gzg Zatfi}az \zfjiacgt
Ao atrg taddho) dfc|gzgzacft ift crfbft @gdaz qog rgjig x Jqtdgz qo \grzo qrhih~gobf dgbg crfbf g ig }a~|gzg zatfi}az qo |zfjiacg bgbf/
Apgc|ia 2
Gobza{ `gda amadrh}f qo d`awqa ba "70< x |hba ai bhoazf ao jhiiarat ba "7< x ba ": @gdaz qog Rgjig
\gtf 7
Aoraobaz
Gobza{ ia bg gi dgnazf bai jgodf qo d`awqa ba "70
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0< {{{/de7:/fzk
RGJIA 7/78> (dforhoqab
Jhiiarat ba "7< Jhiiarat ba ":< Dgorhbgb Rfrgi0 2 "7
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{{{/de7:/fzk 07
RGJIA 7/:
Jhiiarat ba "7< Jhiiiarat ba ":< Dgorhbgb Rfrgi7: < "7
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Aorfodat aiig bfjig ift igbft ba ig dgng x nqorg ift jfzbat gbgxgdaorat qtgobf |akgcaorf/ Dqo kzgobat bajaotaz ift dqgbzgbft wqa aiig dfzrg ba igt atwqhogt |gzg fjraoaz ig dgng dfo ai cphcf }fiqcao |fthjia6
Tfiqdho
\gtf 7
Aoraobaz
Gooa `gda qog dgng g |gzrhz ba qog |ha~g ba dgzro dqgbzgbg ba :< |ik
:< |ik/
Aiig dfzrg dqgzf dqgbzgbft hkqgiat ba igt atwqhogt ba ig |ha~g ba dgzro/
Aiig bfjig ift igbft x |akg tqt jfzbat gbxgdaorat/
Dqo kzgobat bajazo taz ift dqgbzgbft wqa aiig dfzrg |gzg `gdaz qog dgng dfo ai cphcf }fiqcao |fthjia6
\gtf :
Atrzgrakhg
Oadathrgcft zadfzbgz ig mzcqig ba qog dgng
]fiqcao 3 zag ba ig jgta girqzg]fiqcao 3 god`f
ifokhrqb
girqzg
@gdaz qog rgjig ba }gifzat taiaddhfogobf bhmazaorat }gifzat |gzg ift igbft ba ift dqgbzgbft wqa ta }go g dfzrgz) |gzgiqakf dgidqigz ai }fiqcao/
\gtf 4
G|ihdgz ig atrzgrakhg&zatfi}az
@gkgcft qog dgng dfzrgobf dqgrzf dqgbzgbft dfo igbft ba ifokhrqb hkqgi g 7 |qikgbg/ Ai bhgkzcg iqda dfcf tra>
\qabat fjtaz}gz wqa dqgobf bfjigcft ift igbft x ift nqorgcft |gzg `gdaz ig dgng) ig girqzg at 7 |qikgbg) ai god`f atba 70 |qikgbgt chaorzgt wqa ig ifokhrqb ig dgng at ba 70 |qikgbgt/
]fiqcao 3 god`f ifokhrqb girqzg]fiqcao 3 70 70 7 3 4:2 |ik4
@gkgcft qog rgjig wqa cqatrza ai }gifz ba ig dgng |gzg bhmazaorat igbft bai dqgbzgbf>
7/0/ Atrzgrakhgt |gzg Zatfiqdho ba \zfjiacgt> @gdaz qog Rgjig f Jqtdgz qo \grzo
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{{{/de7:/fzk 04
RGJIA 7/:7>
Igbf baiDqgbzgbf
Girqzg ba ig Dgng God`f ba ig Dgng Ifokhrqb ba igDgng
]fiqcao
7 7 70 70 70 707 3 4:2: : 7= 7= 7= 7=: 3 17:4 4 72 72 72 724 3 1002 2 7: 7: 7:
7:
2 3 1;=
1 1 7< 7< 7
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02 {{{/de7:/fzk
RGJIA 7/::> (dforhoqab
Igbf baiDqgbzgbf
Girqzg ba ig Dgng God`f ba ig Dgng Ifokhrqb ba igDgng
]fiqcao
4/1 4/1 74 74 74 74 4/1 3187/1
Ofrg wqa ai cphcf }fiqcao of fdqzza dqgobf ai igbf bai dqgbzgbf at ba rzat |qikgbgt) thof dqgobf ai igbf baidqgbzgbf at ba 4/4 |qikgbgt/
Oqatrzg zat|qatrg fzhkhogi of azg hodfzzadrg) |azf fj}hgcaora of azg rgo |zadhtg dfcf if |fbzg taz/ Ba `ad`f)|qabat fjraoaz qog zat|qatrg gqo ct |zadhtg th rfcgt hodzacaorft ct |awqaft wqa ift ba ig rgjig gorazhfz |gzgig ifokhrqb ba ift igbft bai dqgbzgbf/ \gzg atra dgtf) |fbacft qrhih~gz cabhbgt wqa tfo caofzat f cgxfzat wqa 4/4|qikgbgt/
\fz rgorf) ig zat|qatrg wqabg dfc|zfjgbg th ig wqazacft zabfobagbg g dazf dhmzgt badhcgiat) |azf Qog zat|qatrgct |zadhtg at 4/4 |qikgbgt/
Anazdhdhft ba Za|gtf
7/ Zakzatg x aodqaorzg ig tfiqdho gi |zfjiacg bai Anac|if 7/:/ Jzhrr rhaoa ":/:1 ao cfoabgt ba dhodf x bha~ daorg}ft/ Th aiig rhaoa 2< cfoabgt ao rfrgi Dqorgt cfoabgt ba
dgbg rh|f rhaoa64/ Qo |grzo ba bhgkzgcgt ba dqgbzgbft ta cqatrzg g dforhoqgdho/ Dqorft dqgbzgbft gx ao ai 7:rf bhgkzgcg6
2/ Ft{gib atr rzgrgobf ba bhtchoqhz tq dfotqcf ba dgm/ Tq carg at jgngz tq dfotqcf `gtrg = rg~gt |fz tacgog/Th i dfchao~g dfo :2 rg~gt ig |zhcazg tacgog5 iqakf jgng tq dfotqcf g :7 rg~gt ig takqobg tacgog5 x iqakfg 70 rg~gt ig razdazg tacgog Ao dqorgt tacgogt gidgo~gz tq carg6
1/ Rgxifz |zatr qo ihjzf ao ig jhjihfradg x nqtrf g`fzg rhaoa 1 bgt ba zarzgtf ao ig ba}fiqdho bai chtcf/ Ai }gifzba ig cqirg |fz ba}fiqdho rgzbg at ba 7< daorg}ft bhgzhft/ Dgorf rhaoa wqa |gkgz ba cqirg th ba}fi}hazg aiihjzf g`fzg6
=/ Dqorgt `fzgt ia rfcgz g qo gqrfc}hi wqa g}go~g g ;1 chiigt |fz `fzg gidgo~gz g frzf gqrfc}hi wqa }hgngg 11 chiigt |fz `fzg) th ai gqrfc}hi ct iaorf gzzgodg bft `fzgt gorat wqa ai ct z|hbf6
;/ Kzgda gzzgodg ao tq jhdhdiarg g qog }aifdhbgb ba 7: chiigt |fz `fzg/ Qog `fzg bat|qt) Bgo gzzgodg ao igtqxg qog `fzg bat|qt g qog }aifdhbgb ba 71 chiigt |fz `fzg) thkqhaobf ig chtcg zqrg/ Tq|fohaobf wqa igt}aifdhbgbat hohdhgiat ba gcjft ta cgorhaoao dfotrgorat Dqorf ia rfcgz g Bgo gidgo~gz g Kzgda6
0/ Iacqai wqhaza atrgjiadaz ift ichrat ba qo razzaof zadrgokqigz dfo qog dazdg/ Ai rhaoa cgrazhgi tqdhaora |gzgdfotrzqhz qog dazdg wqa raokg qog ifokhrqb ba :2 |hat/ Dqi at ig cphcg zag |fthjia ba razzaof wqa i |qabaaodazzgz dfo bhd`g dazdg6
Zat|qatrgt g ift Anazdhdhft ba Za|gtf
7/ "4 @gdaz qog Rgjig f Jqtdgz qo \grzo
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{{{/de7:/fzk 01
4/ :4 dqgbzgbft2/ ; tacgogt1/ 1< daorg}ft=/ 1/1 `fzgt;/ 1 `fzgt0/ 4= |hat:5 ai razzaof dazdgbf at qo dqgbzgbf
D`g|raz 7/ Adqgdhfoat x Mqodhfoat
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0= {{{/de7:/fzk
7/8 Zadqztft Gbhdhfogiat
\gzg cgrazhgi gbhdhfogi tfjza zatfiqdho ba |zfjiacgt }az ao Kafzka \ixg [heh|abhg `rr|>&&ao/{heh|abhg/fzk&
{heh&KafzkaV\!D4!J4ixg [heh|abhg aorzx
7/8/ Zadqztft Gbhdhfogiat
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{{{/de7:/fzk 0;
D@G\RAZ : Ocazft ZagiatD`g|raz Fqrihoa
:/7 AORAZFT X OCAZFT ZGDHFOGIAT
:/: GBHDHO BA OCAZFT ZGDHFOGIAT:/4 TQTRZGDDHO BA OCAZFT ZGDHFOGIAT
:/2 CQIRH\IHDGDHO BA OCAZFT ZGDHFOGIAT
:/1 IG \ZF\HABGB BHTRZHJQRH]G
:/= BH]HTHO BA OCAZFT ZGDHFOGIAT
:/; ZG^ DQGBZGBG X OCAZFT ZAGIAT
:/0 ATRZGRAKHGT \GZG ZATFIQDHO BA \ZFJIACGT> TQ\FTHDHO X ZA]HTHO)
RZGJGNF HO]AZTF/
D`g|raz :/ Ocazft Zagiat
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00 {{{/de7:/fzk
:/7 Aorazft x Ocazft Zgdhfogiat
Fjnarh}ft ba G|zaobh~gna
Kzgdgz x dfc|gzgz Aorazft/ Digthdgz x fzbaogz ocazft zgdhfogiat/ Aodforzgz ift f|qatrft ba ift ocazft/ Aodforzgz }gifzat gjtfiqrft/ Dfc|gzgz mzgddhfoat |gzg barazchogz dqgi at ig ct kzgoba/
Kzgdgz x Dfc|gzgz AorazftIft Aorazft tfo ift ocazft ba dforaf (7) :) 4///) ift ocazft ba dforaf oakgrh}ft (#7) #:) #4///) x dazf/ Aphtraqo ocazf hoohrf ba aorazft/ Anac|if ba aorazft tfo
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{{{/de7:/fzk 08
Bat|qt ba qo tgirf ig zgog |fbzg atrgz ao ai 8 f ai 1 (|azf of ao ai ;/ Bat|qt ba bft tgirft ig zgog |fbzg atrgzao ai 77) ; f 4/ Dforgobf ai ocazf ba }adat wqa ig zgog tgirg g ig bazad`g f g ig h~wqhazbg) |fbzgcft barazchogzbfoba grazzh~g ig zgog/ Bat|qt ba dhodf tgirft) `gx }gzhgt |fthjiat qjhdgdhfoat |gzg ig zgog/ Aphtra qog cgoazgthtracrhdg |gzg dgidqigz igt |fthjiat qjhdgdhfoat ba|aobhaobf ba dqgorgt }adat ig zgog tgir g ig bazad`g) x dqgorgt}adat ig zgog tgir g ig h~wqhazbg/
ZZZZZ 3 1 tgirft g ig bazad`g qjhdgdho 3 ; % (1 : 3 7;ZZZZI 3 2 tgirft g ig bazad`g) 7 tgirf g ig h~wqhazbg qjhdgdho 3 ; % (4 : 3 74ZZZII 3 4 tgirft g ig bazd`g) : tgirft g ig h~wqhazbg qjhdgdho 3 ; % (7 : 3 8
ZZIII 3 : tgirft g ig bazad`g) 4 tgirft g ig h~wqhazbg qjhdgdho 3 ; (7 : 3 1ZIIII 3 7 tgirf g ig bazad`g) 4 tgirft g ig h~wqhazbg qjhdgdho 3 ; (4 : 3 7IIIII 3 1 tgirft g ig h~wqhazbg qjhdgdho 3 ; (1 : 3 4
Atrgt tfo igt |fthjiat qjhdgdhfoat ba ig zgog apgdrgcaora bat|qt ba dhodf tgirft/ \qabat ofrgz wqa ai fzbao ofhc|fzrg> rzat tgirft g ig bazad`g) qof g ig h~wqhazbg x qof g ig bazad`g at if chtcf wqa dqgrzf tgirft g ig bazad`g xqof g ig h~wqhazbg/
Digthdgdho ba ift Ocazft ZgdhfogiatDqgobf bh}hbhcft qo aorazf |fz frzf aorazf (of dazf fjraoacft if wqa iigcgcft ocazf zgdhfogi/ At iigcgbfgt |fzwqa at ig zaigdho ba qo ocazf g frzf/ \fz anac|if) th bh}hbhcft qo aorazf g |fz qo takqobf aorazf j aiocazf zgdhfogi wqa fjraoacft at gj ) |zf}htrf wqa j of at dazf/ Dqgobf atdzhjhcft qo ocazf zgdhfogi dfcf atra)ai ocazf ao ig |gzra ba gzzhjg at iigcgbf oqcazgbfz/ Ai ocazf ao ig |gzra homazhfz at iigcgbf baofchogbfz/ R|qabat |aotgz gdazdg ba ift ocazft zgdhfogiat dfcf ig mzgddho ba qo |gtrai/ Th dfzrgt ai |gtrai ao j zajgogbgt) rq|gzra at g ba atgt zajgogbgt/
\fz anac|if dqgobf }acft ai ocazf zgdhfogi 7: ) oft hcgkhogcft dfzrgobf ai |gtrai ao bft |gzrat/ Oqatrzg |gzra atqof ba atft |abg~ft/ Ai ocazf zgdhfogi 7: ta }a dfcf atrf>
Dfo ai ocazf zgdhfogi 42 ) dfzrgcft ai |gtrai ao dqgrzf |gzrat x oqatrzg |gzra at rzat ba atft |abg~ft/ Ai ocazfzgdhfogi 42 ta }a dfcf atrf>
D`g|raz :/ Ocazft Zagiat
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8< {{{/de7:/fzk
Ai ocazf zgdhfogi8
7< za|zataorg oqa}a zajgogbgt ba qo |gtrai wqa `g thbf dfzrgbf ao bha~ |gzrat/ Ai ocazf zgdhfogi87< ta }a dfcf atrf>
Mzgddhfoat \zf|hgt tfo ocazft zgdhfogiat bfoba ai oqcazgbfz (ai ocazf ba gzzhjg at caofz wqa ai baofchogbfz
(ai ocazf ba gjgnf/ Qog mzgddho |zf|hg za|zataorg qo ocazf caofz wqa qof/ Dfo qog mzgddho |zf|hg thac|zarazchogzt dfo caoft ba qo |gtrai aorazf'
Mzgddhfoat Hc|zf|hgt tfo ocazft zgdhfogiat bfoba ai oqcazgbfz at cgxfz wqa ai baofchogbfz/ Igt mzgddhfoathc|zf|hgt |qabao taz zaatdzhrgt dfcf qo ocazf chprf qo aorazf ct qog mzgddho |zf|hg/ Qog mzgddho hc|zf|hgza|zataorg qo ocazf cgxfz wqa qof/
Mzgddhfoat Awqh}giaorat tfo bft mzgddhfoat wqa bgo ai chtcf }gifz oqczhdf dqgobf tfo a}giqgbgt/ \fz anac|if)fjtaz}g ig za|zataorgdho }htqgi bai ocazf zgdhfogi :2 >
R |qabat }az wqa ig zakho tfcjzagbg at hborhdg ao rgcgf g ig bai ocazf zgdhfogi qo cabhf 7: / \fbacft atdzhjhzift mgdrfzat |zhcft ba gcjft) ai oqcazgbfz x ai baofchogbfz) dgodaigcft mgdrfzat dfhodhbaorat wqa g|gzadao aogcjft/
:
2 3: 7
: : 7 Iqakf cqirh|ihdgcft ba oqa}f ift mgdrfzat zatrgorat/ :
2 37
:Atra |zfdatf at iigcgbf zabqddho ba ig mzgddho) f atdzhjhz ig mzgddho ao rzchoft ct jgnft/ Zabqdhz ig mzgddhoof dgcjhg ai }gifz ba ig mzgddho/ Tfigcaora thc|ihdg ig mfzcg ao wqa ig atdzhjhcft/ Dqgobf `acft dgodaigbfrfbft ift mgdrfzat dfcqoat) raoacft qog mzgddho ao tq mfzcg ct thc|ia/
Anac|if 4
Digthdgz x thc|ihdgz ift thkqhaorat ocazft zgdhfogiat
g
4;
j
84
:/7/ Aorazft x Ocazft Zgdhfogiat
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{{{/de7:/fzk 87
d
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Tfiqdho7: 9
:4 9
42
Dfo mzgddhfoat thc|iat) at cqx mdhi fzbaogzigt/ \haotg ao ai anac|if gorazhfz/ Tgjacft wqa qo cabhf at cgxfzwqa qo dqgzrf) x tgjacft wqa bft razdhft at cgxfz wqa qo cabhf/ Dfo mzgddhfoat ct dfc|iangt) oadathrgcft qogcanfz cgoazg |gzg dfc|gzgz/
Anac|if 1
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Ao fzbao ba barazchogz atrf) oadathrgcft aodforzgz qog cgoazg ba zaatdzhjhz oqa}gcaora igt mzgddhfoat gt |fba#cft dfc|gzgzigt canfz/ Tgjacft wqa |fbacft atdzhjhz mzgddhfoat awqh}giaorat |gzg gcjgt/ Th `gdacft iftbaofchogbfzat hkqgiat ao oqatrzgt mzgddhfoat awqh}giaorat) aorfodat |fbacft dfc|gzgzigt bhzadrgcaora/ Atrgcftjqtdgobf ai cirh|if dfco ct jgnf ba dgbg baofchogbfz/ G atrf ta ia iigcg aodforzgz ai cohcf dfcobaofchogbfz (cdb/
Ai cohcf dfco cirh|if ba ; x 8 at =4/ Oqatrzg mzgddho atrgz za|zataorgbg |fz qog mfzcg bh}hbhbg ao =4taddhfoat/ Atrg }a~ qtgzacft qo zadrokqif dfzrgbf ao 8 |fz ; 3 =4 |abg~ft>
; bh}hba g =4 oqa}a }adat aorfodat>
D`g|raz :/ Ocazft Zagiat
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8: {{{/de7:/fzk
4;
3
88
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Ofrg wqa cqirh|ihdgz |fz 88 at if chtcf wqa cqirh|ihdgz |fz 7/ \fz rgorf):;=4 at qog mzgddho awqh}giaora g
4; / Gwq ta
cqatrzg if gorazhfz>
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28
3
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:0=4 at qog mzgddho awqh}giaora g
28 / Gwq rhaoat dfcf ta fjtaz}g/
Atdzhjhaobf ig mzgddho tfjza qo dfco baofchogbfz ba =4) |qabat mdhicaora dfc|gzgzigt/ Gwq rfcgcft :0 baift dqgbzft tfcjzagbft ba =4 (ba oqatrzg hcgkao ba 28 ba gzzhjg x fzkgoh~gbgt ba cgoazg wqa tag mdhi dfc|gzgzigdfo oqatrzg za|zataorgdho ba 4; / Ofrg wqa `gx qo |awqaf dqgbzf wqa tfjzg/
Tfiqdho
Xg wqa :0=4 at cgxfz wqa:;=4 )
28 at cgxfz wqa
4; /
Zadqazbg
\gzg dfc|gzgz ocazft zgdhfogiat bajat zaatdzhjhzift dfo qo dfco baofchogbfz/
:/7/ Aorazft x Ocazft Zgdhfogiat
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{{{/de7:/fzk 84
Aodforzgz ift F|qatrft ba ift Ocazft
Dgbg ocazf rhaoa qo f|qatrf/ Ao ig zadrg oqczhdg) qo ocazf x tq f|qatrf tfo f|qatrft aorza t/ Ao frzgt|gigjzgt) atro g ig chtcg bhtrgodhg g |gzrhz ba dazf) |azf atro ao igbft f|qatrft ba ig zadrg oqczhdg/
\fz baohdho) ai f|qatrf g dazf at dazf/
Anac|if =
Aodforzgz ai }gifz ba ift f|qatrft ba dgbg qog ba igt thkqhaorat ap|zathfoat/
g 4 % (
4
j 1 % (1d (77/1 % (77/1b 4; %
4;
Dgbg qog ba igt |gzangt ba ocazft ao ift anac|ift gorazhfzat tfo f|qatrft/ Ai f|qatrf ba 4 at (#4) ai f|qatrf ba1 at (#1) ai f|qatrf ba (#77/1 at 77/1 x ai f|qatrf ba 4; at
4; /
Tfiqdho
ai }gifz ba dgbg tqcg ao atra |zfjiacg at g 78/=
j 28d p
b px:
a (p 4Xg wqa tgjacft wqa ift ocazft f|qatrft atro ao igbft f|qatrft g |gzrhz bai dazf) |fbacft thc|iacaora cqirh#|ihdgz dgbg ap|zatho |fz #7/ Atrf dgcjhg ai thkof bai ocazf g tq f|qatrf/
g TfiqdhoAi f|qatrf ba 78/= at #78/=/
j Tfiqdho
Ai f|qatrf ba 28 at 28 /d Tfiqdho
Ai f|qatrf ba p at p/b Tfiqdho
Ai f|qatrf ba px: at px:/
D`g|raz :/ Ocazft Zagiat
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82 {{{/de7:/fzk
a Tfiqdho
Ai f|qatrf ba (p 4 at (p 4 3 4p/Ofrg> Dfo ai irhcf anac|if rq bajat cqirh|ihdgz ig ap|zatho dfc|iarg |fz #7/ Qo azzfz dfco ao atra anac|ifat gtqchz wqa ai f|qatrf ba (p 4 at (p % 4/ OF DFCARGT ATRA AZZFZ'
Aodforzgz ]gifzat Gjtfiqrft
Dqgobf `gjigcft gdazdg ba }gifz gjtfiqrf) atrgcft `gjigobf gdazdg ba bhtrgodhgt ao ig zadrg oqczhdg/ \fz anac|if)ai ocazf ; atr ; qohbgbat giangbgt ba dazf/ Ai ocazf #; atr rgcjho ; qohbgbat giangbgt bai dazf/ Ai }gifzgjtfiqrf ba qo ocazf at ig bhtrgodhg g ig wqa atr g |gzrhz ba dazf) aorfodat ai }gifz gjtfiqrf ba ; x ai }gifz gjtfiqrfba #; at |gzg gcjft ;/
Oftfrzft iaacft ig ap|zatho ypy gt ai }gifz gjtfiqrf ba p/ f Oftfrzft atdzhjhcft ai }gifz gjtfiqrf ba #; gty;y
Rzgrgz ap|zathfoat ba }gifz gjtfiqrf dfcf |gzoratht/ Th aphtra qog f|azgdho gbaorzf ba ift tcjfift bai}gifz gjtfiqrf |zhcazf bajat a}giqgz ig f|azgdho/
Ai }gifz gjtfiqrf ba qo ocazf f ba qog ap|zatho at thac|za |fthrh}g f dazf/ Of |qaba taz oakgrh}f/ Dfoai }gifz gjtfiqrf) atrgcft horazatgbft ohdgcaora ao wq rgo ianft atr qo ocazf g |gzrhz ba dazf) x of igbhzaddho/
Anac|if 0
A}giqgz igt thkqhaorat ap|zathfoat ba }gifz gjtfiqrf/
g y1 % 2yj 4 y2 8yd y1 77yb
y;
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Tfiqdho
g y1 % 2y3 y8y3 8
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Zatqcao ba ig Iaddho
Aorazft (f Ocazft aorazft tfo ift ocazft ba dforaf (7) :) 4///) ift ocazft ba dforaf oakgrh}f (#7) #:)
:/7/ Aorazft x Ocazft Zgdhfogiat
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{{{/de7:/fzk 81
#4///) x dazf/ Qo ocazf zgdhfogi at ig zaigdho ba qo aorazf zat|adrf g frzf) dfcf gj f
41 / Ai ocazf ao ig |gzra ba gzzhjg
at iigcgbf oqcazgbfz x ai ocazf ao ig |gzra homazhfz (ai dqgi of |qaba taz dazf at iigcgbf baofchogbfz/ Mzgddhfoat \zf|hgt tfo ocazft zgdhfogiat ao igt wqa ai oqcazgbfz at caofz wqa ai baofchogbfz/ Mzgddhfoat Hc|zf|hgt tfo ocazft zgdhfogiat ao igt wqa ai oqcazgbfz at cgxfz wqa ai baofchogbfz/ Mzgddhfoat Awqh}giaorat tfo bft mzgddhfoat wqa |zf|fzdhfogo ai chtcf }gifz oqczhdf dqgobf tfo a}giqgbgt/ \gzg zabqdhz qog mzgddho (atdzhjhzig ao tq mfzcg ct thc|ia Atdzhjhz rfbft ift mgdrfzat |zhcft bai oqcaz#
gbfz x baofchogbfz) dgodaigz mgdrfzat dfcqoat) iqakf atdzhjhz ba oqa}f ig mzgddho ao tq mfzcg thc|ihdgbg/ \gzg dfc|gzgz bft mzgddhfoat at dfo}aohaora atdzhjhzigt dfo qo dfco baofchogbfz> ai chtcf aorazf ao ig|gzra homazhfz (baofchogbfz ba dgbg mzgddho/
Ai }gifz gjtfiqrf ba qo ocazf at ig bhtrgodhg ao ig dqgi atr ao ig zadrg oqczhdg g |gzrhz ba dazf/ Ai }gifzgjtfiqrf ba qo ocazf taz thac|za |fthrh}f f dazf/
Bft ocazft tfo f|qatrft th atro g ig chtcg bhtrgodhg g |gzrhz ba dazf ao ig zadrg oqczhdg x ao igbftf|qatrft gi dazf/ Ai f|qatrf ba qog ap|zatho |qaba taz aodforzgbf cqirh|ihdgobf ig ap|zatho rfrgi |fz #7/
Anazdhdhft ba Za|gtf
7/ Igt cgzdgt ao ig zadrg oqczhdg za|zataorgo aorazft at|gdhgbft qohmfzcacaora/ aodqaorzg ift }gifzat bag) j) d) bx a/
:/ Barazchogz wqa mzgddho bai rfbf za|zataorg dgbg zakho tfcjzagbg/
g/
j/
d/4/ Dfifdgz ift thkqhaorat dfonqorft ba ocazft zgdhfogiat ao fzbao) ba caofz g cgxfz/
g/ 7: )74 )
72
j/ 777: )7:77 )
74772
34 742
34
7:
Aorfodat qog tqcg awqh}giaora |gzg oqatrzf |zfjiacg at =7:
% :7:
% 47:
3 (= % : % 47:
3 777:
Tfiqdho
\abzf |qaba dforgz dfo foda bfdag}ft bai dftrf bai }hgna (":):
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{{{/de7:/fzk 7
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{{{/de7:/fzk 7
Ai zjfi ba mgdrfzat |gzg 8< ta fjtaz}g gt>
8< 3 8 7
7:= 3 8 728 3 4 4
72 3 ; :7:= 3 4 4 ; :
D`g|raz :/ Ocazft Zagiat
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7
\zhcf Mgdrfzat ao 8< Mgdrfzat ao 7:= Rfcgcft: 7 7 7
4 : : :1 7 < 7; < 7 7
Aorfodat oadathrgcft> qo :) bft 4t) qo 1 x qo ;/ Ao frzgt |gigjzgt> : 4 4 1 ; 3 =4 gd jd 3 gjd
Ai ocazf qof at g }adat iigcgbf baofchogbfz ho}hthjia) dfcf dgbg ocazf aorazf |qaba taz |aotgbf dfcfqo ocazf zgdhfogi dqxf baofchogbfz at qof/
Ig bhmazaodhg aorza bft }gifzat at ai dgcjhf ao atg dgorhbgb/
Anazdhdhft ba Za|gtf
7/ tqtrzga ift thkqhaorat ocazft zgdhfogiat/ Gtakzgra wqa rq zat|qatrg atr ao ig mfzcg ct thc|ia/
g/ 17: 870j/ :4 72d/ 42 74b/ 7177 8;a/ :74 777m/
;
:; 8
48k/ =77 4::`/ 74=2 ;2
Dgorhbgb ba @:F: |qzg 3
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{{{/de7:/fzk 77;
\fbacft apgchogz atra |zfjiacg qtgobf ocazft zgdhfogiat/ Cgoraoacft qo rfrgi gdqcqigbf ba wq mzgddho ba igjgzzg wqabg/ Zadqazbg) dqgobf iaacft qog mzgddho takqhbg |fz ba ao ai |zfjiacg) thkohdg wqa oftfrzft bajacftcqirh|ihdgz |fz atg mzgddho/
Dfcao~gcft dfo qog jgzzg dfc|iarg ba d`fdfigra Ai rfrgi dfo ai wqa dfcao~gcf
UQ%
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770 {{{/de7:/fzk
Anazdhdhft ba Za|gtf
7/ Cqirh|ihdgz igt thkqhaorat ap|zathfoat |fz caoft qof/
g/ :1j/ #7
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{{{/de7:/fzk 778
:/1 Ig \zf|habgb Bhtrzhjqrh}g
Fjnarh}ft ba G|zaobh~gna
G|ihdgz ig |zf|habgb bhtrzhjqrh}g/ Hbaorhdgz |gzrat ba qog ap|zatho/ Zatfi}az |zfjiacgt bai cqobf zagi qtgobf ig |zf|habgb bhtrzhjqrh}g/
Horzfbqddho
Gi ogi bai gf atdfigz) qo |zfmatfz ba atdqaig aiacaorgi `gda qog |awqag jfitg ba zakgif |gzg dgbg qof ba tqtatrqbhgorat/ Dgbg jfitg dforhaoa qog mfrfkzgmg ba ig digta) bft |awqagt jfithrgt dfo fjtawqhft x dhodf bqidat/ Ai|zfmatfz bhtrzhjqhz igt jfitgt aorza tqt :0 atrqbhgorat/ Dqorft gzrdqift ba dgbg rh|f oadathrg ai |zfmatfz6
G|ihdgz ig \zf|habgb Bhtrzhjqrh}g
Dqgobf raoacft qo |zfjiacg dfcf ai cftrzgbf ao ig horzfbqddho) Ig \zf|habgb Bhtrzhjqrh}g |qaba gxqbgzoft gzatfi}azif/ \gzg ac|a~gz) |fbacft atdzhjhz qog ap|zatho |gzg ift dforaohbft ba dgbg jfitg/
Dforaohbft 3 (mfrfkzgmg % : jfithrgt ba fjtawqhft % 1 bqidat
Dforaohbft 3 (| % :m% 1d \fbzgcft qtgz qog iarzg |gzg atdzhjhz igt }gzhgjiat ba qog ap|zatho/
Tgjacft wqa ai |zfmatfz rhaoa :0 atrqbhgorat) ba dqgiwqhaz cgoazg |fbacft atdzhjhz ig thkqhaora ap|zatho |gzg aiocazf ba gzrdqift wqa ai |zfmatfz oadathrgz/
gzrdqift 3 :0 (| % :m% 1d :0 }adat ai dforaohbf hobh}hbqgi ba dgbg jfitg/
Kaoazgicaora fchrhcft dqgiwqhaz thkof ba cqirh|ihdgdho wqa of tago atrzhdrgcaora oadatgzhft/
gzrdqift 3 :0(| % :m% 1d
g Ig |zf|habgb Bhtrzhjqrh}g ba ig Cqirh|ihdgdho thkohdg wqa dqgobf aodforzgcft baorzf ba |gzoratht qorzchof cqirh|ihdgobf frzft rzchoft) ai rzchof ba gmqazg ta cqirh|ihdg dfo dgbg qof ba ift rzchoft baorzf bai|gzoratht/
D`g|raz :/ Ocazft Zagiat
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7:< {{{/de7:/fzk
3 :0(| % :m% 1d 3 :0(| % :0(:m % :0(1d 3 :0| % 1=m% 72
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{{{/de7:/fzk 7:7
:;
4x: 77 3 =x:::;
b :p;
4x: 77px
3 :p; (4x
: % :p;
77px
3 =p
:x;
::p;px
Tfiqdho:p;
4x: 77px
3 =px
4::;x
Hbaorhdgz Ap|zathfoat wqa Ho}fiqdzgo ig \zf|habgb Bhtrzhjqrh}g
Ig \zf|habgb Bhtrzhjqrh}g g|gzada dfo mzadqaodhg ao ap|zathfoat) x cqd`gt }adat of rzga |gzoratht dfcf tc#jfift ba gkzq|gchaorf/ Ao ig iaddho 7/:) fjtaz}gcft dfcf ig jgzzg ba ig mzgddho gdrg dfcf qo tcjfif bagkzq|gchaorf/ Ai thkqhaora anac|if ho}fiqdzg ai qtf ba ig \zf|habgb Bhtrzhjqrh}g dfo mzgddhfoat/
Anac|if 2
Thc|ihdgz igt thkqhaorat ap|zathfoat/
g :p%02
j 8x:4d ~%=:Gqowqa atrgt ap|zathfoat of atro atdzhrgt ao qog mfzcg wqa ofzcgicaora gtfdhgcft dfo ig \zf|habgb Bhtrzhjqrh}g)ai `ad`f wqa ai oqcazgbfz ba igt mzgddhfoat bajhazg taz rzgrgbf dfcf th atrq}hazg ao |gzoratht `gda atrf qo |zfjiacgwqa ig \zf|habgb Bhtrzhjqrh}g |qaba gxqbgzoft g zatfi}az/
g :p%02 |qaba zaatdzhjhzta dfcf72 (:p % 0/
\fbacft aorfodat |zfdabaz g bhtrzhjqhz ai 72 /
72(:p % 0 3
:p2 %
02 3
:p: : %
2:
2
Tfiqdho:p%0
2 3p: % :
j 8x:4 |qaba taz zaatdzhrf dfcf74 (8x :/
\fbacft aorfodat |zfdabaz g bhtrzhjqhz ai 74 /
74
(8x : 3 8x4
:4
34 4p
4 :
4
Tfiqdho8x:
4 3 4x :4d ~%=: |qaba taz zaatdzhrf dfcf
7= (~ % =/
\fbacft iqakf |zfdabaz g bhtrzhjqhz 7: /
7:
(~ % = 3~
:%
=:
D`g|raz :/ Ocazft Zagiat
http://www.ck12.org/http://www.ck12.org/http://www.ck12.org/http://www.ck12.org/http://www.ck12.org/7/30/2019 CK-12: lgebra Edicin-Espaola v1 s1
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7:: {{{/de7:/fzk
Tfiqdho~%=
4 3~: % 4
Zatfi}az \zfjiacgt bai Cqobf Zagi Qtgobf ig \zf|habgb Bhtrzhjqrh}g
Ig \zf|habgb Bhtrzhjqrh}g at qog ba igt |zf|habgbat cgracrhdgt ct dfcqoat }htrgt ao ig }hbg bhgzhg/ Wqa gfzgao ift oakfdhft x ao ig Kafcarzg/ Dgbg }a~ wqa ta rhaoao bft f ct kzq|ft ba fjnarft) Ig \zf|habgb Bhtrzhjqrh}g|qaba gxqbgzoft g bat|angz qog hodfkohrg/
Anac|if 1
Qo ehftdf fdrfkfogi `g ba taz dfotrzqhbf dfcf ta cqatrzg ao ig hiqtrzgdho/ Ai zakigcaorf ba dfotrzqddho zawqhazatf|fzrat ba gdazf ba dhodf |hat ba ifokhrqb |gzg taz gkzakgbft g if igzkf ba ig ig jgta x tf|fzrat ba gdazf ba dqgrzf
|hat ba ifokhrqb |gzg taz gkzakgbft g ig ioag bai rad`f bai ehftdf/ Wq ifokhrqb ba gdazf taz zawqazhbg |gzgdfc|iargz ai |zfxadrf6
Dgbg igbf zawqazhz bft ifokhrqbat) qog ba dhodf x qog ba dqgrzf |hat za|adrh}gcaora/ @gx fd`f igbft) gth wqa gwqatr oqatrzg adqgdho/
gdazf zawqazhbf 3 0(2 % 1 |hat/
\fbacft qtgz ig |zf|habgb bhtrzhjqrh}g |gzg aodforzgz ig dgorhbgb rfrgi ba gdazf>
Gdazf zawqazhbf 3 02 % 01 3 4: % 2< |hat/
Tfiqdho
Qo rfrgi ba ;: |hat ba gdazf tfo zawqazhbft |gzg ai |zfxadrf/
:/1/ Ig \zf|habgb Bhtrzhjqrh}g
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{{{/de7:/fzk 7:4
Anac|if =
G dgbg atrqbhgora ia taz bgbf qo awqh|f ba acazkaodhg x tq|az}h}aodhg |gzg qo }hgna gi jftwqa/ Ai awqh|f dforhaoaqog ihorazog) qo awqh|f ba |zhcazft gqphihft) x zgdhfoat ba dfchbg |gzg acazkaodhg/ Igt ihorazogt dqatrgo "7: dgbgqog) ift ehr ba |zhcazft gqphihft ; dgbg qof) x igt zgdhfoat ba dfchbg dqatrgo ": |fz bg/ @gx "1
7 "7: ihorazog/7 "; awqh|f ba |zhcazft gqphihft/
p ": zgdhfoat bhgzhgt/
Ai ocazf ba awqh|ft 3 7;) aorfodat ai dftrf rfrgi at awqh}giaora g ig thkqhaora adqgdho>
Dftrf rfrgi 3 7;(7: % ; % :p
\fbacft qtgz ig \zf|habgb Bhtrzhjqrh}g ao atrg ap|zatho/
7;(7: % ; % :p 3 :
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7:2 {{{/de7:/fzk
Anazdhdhft ba Za|gtf
7/ Qtgz ig \zf|habgb Bhtrzhjqrh}g |gzg thc|ihdgz igt thkqhaorat ap|zathfoat/
g/ (p % 2 :(p % 1j/ 7: (2~ % =d/ (2 % 1
(1 % :
b/ (p % : % ;a/ x(p % ;m/ 74p(4x %~
:/ Qtgz ig \zf|habgb Bhtrzhjqrh}g |gzg zacf}az ift |gzoratht ba igt thkqhaorat ap|zathfoat/
g/ 7: (p x 2j/
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{{{/de7:/fzk 7:1
7/ :p % 4:/ 4p % 24/ 77p: % =2/ x: %
74
1/ :4 :~=/ ;4 :|
:/ Ai atrgora dforhaoa 41 ihjzft ba |fatg x 11 of}aigt/
7/ Gcgz |qaba `gdaz 74 kgiiargt (: f~ tfjzgo/:/ Dgbg kgiiarg rhaoa 2 tachiigt ba cgdgbgchg (0 tfjzgo/
D`g|raz :/ Ocazft Zagiat
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7:= {{{/de7:/fzk
:/= Bh}htho ba Ocazft Zgdhfogiat
Fjnarh}ft ba G|zaobh~gna
Aodforzg
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