Reprezentari matematice ale civilizatiilor antice-Mesopotamia

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^@IE@ ]U^DU

ÊQÊ_EBT Ď^K ILTEILTKME LHE

MKZKHK_LȟKKH@^ MKZKHK_LȟKKH@^ LBTKME )IE]@Q@TLIKL)

Edktu~l ]je~l































Tefb`~edlmtl~e? ^ìe` ]u~du M`qe~tč? ^ìe` ]u~du

De}m~ke~el MKQ l Nknhk`temkk Blŭk`blhe l ^ìîbkek ]U^DU( ^@IE@ êq~eebtč~k ilteiltkme lhe mkzkhklŭkkh`~ lbtkme ? Ie}`q`tlikl / ^ìe` ]u~du" ” Nî~hld ? ]je~l( >1<1 Nknhk`c~" K]NB ;36):1:)615:)35)= 5<&1;<+

« Edktu~l ]je~l( >1<1 ]t~" M" Flilbcku( b~"<5( Nî~hld































Muq~kb}

Muzîbt âblkbte…………………………………… âblkbte…………………………………………………5 ……………5 Q~ejlȗč…………………………………………"……………"""3 K" Lql~kȗkl ilteiltkmkk…………………………………………; <"< ]kin`hu~khe buie~kme dkb q~ek}t`~ke …"……"……""; <"> Lql~kȗkl buie~eh`~ …………………"……"……"""<4 …………………"……"……"""<4 <"= ]k}teie de buie~lȗke" ……………………"………>: <"4 Q~kiehe mlhmuhe ilteiltkme…………"…"………"=3 KK" Bkzehuh cebe~lh lh ilteiltkmkk ie}`q`tlikebe…………"""5< >"< ]mu~t k}t`~km ………………………………………5< >"> ]m~ke~el( lql~kȗkl }kin`hu~kh`~ ilteiltkme" ……""5: >"= @qe~lȗkk l~ktietkme ……"…………………………3= KKK" Lqhkmlȗkk ilteiltkme……………………………"………""63 ="< Cebe~lhktčȗk ………""…"……"……………………63 ="> Q~`nheie de l~ktietkmč …"""……………………"""6; …"""……………………"""6; ="= Emulȗkk de c~lduh K …………"……………………;= …………"……………………;= ="4 L~kk……………"" …………………"……………";: ="5 Z`huie…………………………………………"<14 =": Lqhkmlȗkk lhe te`~eiek huk Qktlc`~l ……………""<1; ="3 Emulȗkk qčt~ltkme ………………………………""<<5 Lbeve…………"……………………………………………"<>< Nknhk`c~ljke }ehemtkzč"………………………………………"<=<































































Muzîbt Âblkbte

L

}m~ke ` ml~te de K}t`~kl Ilteiltkmkk e}te ` il~e q~`z`ml~e Ők l}tl dkb ilk iuhte i`tkze" Q~kiuh e lmehl mč âb ŭl~l b`l}t~č( dlt`~ktč quŭkbuhuk tkiq k}t`~km lh lme}tek dk}mkqhkbe( }un <51 de lbk( k}t`~kl ilteiltkmkk e}te âbmč q~kzktč ml ` MebuŐč~el}č" Ub lh d`khel i`tkz( me ŭkbe de q~kiuh e}te quŭkbčtltel }u~}eh`~ de d`muiebtl~e7 lzei( mu ml~lmte~ cebe~lh d`l~ mîtezl t~ldume~k Ők ` âbme~ml~e l huk Bkm`hle Ikfčkhelbu qhu} mezl i`b`c~ljkk( dedkmlte ub`~ l}qemte ql~tkmuhl~e( dlt`~lte Q~`je}`l~ek keŐebe Jh`~kml T" Mîiqlb" Mfkl~ k}t`~kl ilteiltkmkk ~ìîbeŐtk }tč }un }eibuh ub`~ }hlne lql~kŭkk edkt`~klhe( mehe lhe huk ]" Lbd`bke jkkbd ezkdebt mu iuht deqčŐkte ml qe~k`ldč t~ltltč7 q~`nlnkh ilk }ubt mezl hum~č~k mu ml~lmte~ h`mlh" Bu qutei lkmk ìkte i`b`c~ljkl kiq~e}k`blbtč l Q~`je}`~uhuk Dlb Qlqum âb ml~e }e qube ub lmmebt de`}enkt qe jkh``jkl ilteiltkmkk" Ub lht i`tkz j`l~te q~`jubd e}te hkq}l ub`~ }u~}e ~ìîbeŐtk dedkmlte ubek qe~k`lde k}t`~kme deiuht lqu}e ~e}qemtkz ubek muhtu~k âbdeqč~tlte ml }qlŭku ce`c~ljkm" Dlt`~ktč tutu~`~ lme}t`~ ~lŭkubk( i`b`c~ljkl de jlŭč ie~ktč ` lq~emke~e de`}enktč qebt~u ej`~tuh dequ} âb ~edlmtl~el ek" Ilk iuht( lzîbd âb zede~e evqube~el lbte~k`l~č ~emìlbdči qunhkml~el âbt~)` edktu~č blŭk`blhč" Mktkt`~uh zl jk jl}mkblt de j`~ŭl ub`~ z~eiu~k t~emute Ők zl }kiŭk dkb qhkb zlh`l~el ~lŭkubkk Ők numu~kl de}m`qe~k~kk ub`~ heck de





























































Q~ejlȗč

H

l âbmequtuh k}t`~kek( m`bmeqtehe ilteiltkme lu ~eq~eebtlt ` i`dlhktlte q~kb ml~e `liebkk q~kiktkzk qe~meqelu `nkemtehe țk jebìebehe dkb iedkuh âbm`bou~čt`~( t~lb}j`~iîbdu)he lq`k âb ~eq~eebtč~k ml~e }č âk loute âb zklȗl de k mu k" Âbt~)` q~kič etlqč( }eiebkk b`țt~k bu ~euțelu }č ln}t~lmtkee âb t`tlhktlte b`ȗkubkhe ilteiltkme( de lmeel( qîbč l dezebk țtkkbȗč evlmtč( ilteiltkml `je~el }`huȗkk nllte qe kbtukȗke( qe~meqȗke( `n}e~zl~e( }lu evqe~kiebtl~e q~lmtkmč" Âbmeqîbd mu ikoh`muh }em`huhuk lh Z)hel â"F~" ilteiltkml l mub`}mut ` liqhč dez`htl~e âb qhlb te`~etkm" Dehkiktl~el dejkbktkzč l ilteiltkmkk ilteiltkmkk ml țtkkbȗč te`~etkmč te`~etkmč l j`}t j`}t kiqu}č de mčt~e mčt~e zemfkk c~emk" c~emk" Lmețtkl lu j`}t q~kikk ml~e lu kbt~`du} dei`b}t~lȗkl( ou}tkjkmlu ~kcu~`} }`huȗkkhe q~`nheieh`~( `je~elu iet`de h`ckme me qe~iktelu cebe~lhkč~k țk m`b}emkbȗe jč~č l jlme lqeh hl ~elhktltel âbm`bou~čt`l~e" T`lte lme}te mub`țtkbȗe te`~etkme lu j`}t ~`duh ub`~ lmuiuhč~k ilteiltkme de)l hubcuh ikhebkkh`~( âbmeqîbd mu }kiqhehe dete~ikbč~k qe mlhe eiqk~kmč( țk te~ikbîbd mu ejemtul~el ub`~ mlhmuhe l mč~`~ q~emkke lu ukikt qîbč țk qe ilteiltkmkebkk eq`mkk i`de~be" i`de~be" Lme}te l}qemte q~lciltkme lhe ilteiltkmkk }ubt ilk quȗkb ln`~dlte hl bkzeh edumlȗk`blh" L}tčk( q~`c~liehe țm`hl~e muq~kbd t`t ilk iuhte b`ȗkubk te`~etkme( t~emîbd âb qhlb }emubdl~ ml~lmte~uh q~lmtkm)lqhkmltkz lh ilteiltkmkk" ]č bu uktči t`tuțk( mč ilteiltkml l lqč~ut dkb beme}ktčȗk q~lmtkme7 ` de}q~kbde~e j`~ȗltč dkb qhlbuh q~lmtkm âb meh te`~etkm dume lde}e`~k hl dkjkmuhtčȗk âb âbzčȗl~e"































m`bȗkbut ilteiltkm" El l~e ml `nkemt q~eebtl~el ub`~ l}qemte cebe~lhe lhe k}t`~kek ilteiltkmkk( ilteiltkmkk( âb }qemklh l meh`~ dez`htlte âb Mîiqkl Ie}`q`tlikek( qîbč hl dehkiktl~el dejkbktkzč ml țtkkbȗč te`~etkmč" Q~kiehe q~`nheie mu ml~lmte~ te`~etkm lu lqč~ut mu iuht tkiq âblkbte7 ehe lu j`}t m`bmequte de mčt~e zemfkk nlnkh`bkebk țk eckqtebk lmui =111 de lbk â"F~" Eckqtuh lbtkm l oumlt ub ~`h dejkbkt`~ku âb dez`htl~el ilteiltkmkk ml țtkkbȗč( âb}č âb mlqkt`hehe mč~ȗkk be zì `muql ilk iuht de lqhkmlȗkkhe ilteiltkme lhe ie}`q`tlikebkh`~" Âb q~kiuh mlqkt`h }ubt ln`~dlte mîtezl l}qemte cebe~lhe q~kzkbd lql~kȗkl b`ȗkubkh`~ jubdliebtlhe de ilteiltkmč( âbmeqîbd mu eq`ml q~ek}t`~kmč țk m`btkbuîbd mu eq`ml lbtkmč" Âb lme}t mlqkt`h }ubt kbt~`du}e m`bmeqtehe buie~`h`ckme( ez`huȗkl âb tkiq tkiq l }kin`hu~kh`~ țk }eibeh`~ ilteiltkme mu q~kzk~e hl buič~l~e țk ič}u~l~e" Mlqkt`hehe d`k țk t~ek q~ekbtč ql~tkmuhl~ktčȗk lhe ilteiltkmkk ie}`q`tlikebe( q`~bkbd de hl }kiqhehe ezkdebȗe m`btlnkhe țk loubcîbd qîbč hl ` }e~ke de ~lȗk`bliebte âb qhlb te`~etkm țk q~lmtkm" Lqhkmlȗkkhe }ubt t~ldume~k lhe tčnhkȗeh`~ ilteiltkme lhe ie}`q`tlikebkh`~( ljhlte âb il~khe m`hemȗkk de lbtkmfktčȗk dkb huie" Âb lbeve }ubt q~eebtlte j`t`c~ljkkhe q~kbmkqlheh`~ tčnhkȗe ilteiltkme q~eebtlte âb hum~l~e" Nî~hld( Klbul~ke >1<1 Lut`~uh































Lql~kȗkl ilteiltkmkk

Mlqkt`huh K Lql~kȗkl ilteiltkmkk

<"< ]kin`hu~khe buie~kme dkb q~ek}t`~ke

Q

~kiehe b`ȗkubk eheiebtl~e de ilteiltkmč lu lqč~ut `dltč mu dez`htl~el ilte~klhč țk }qk~ktulhč l uilbktčȗkk" Âb iìebtuh âb ml~e `liebkk q~kiktkzk lu âbmequt }č)țk m`bjemȗk`bee ubehte țk }č)țk q~`mu~e ikoh`lmehe de evk}tebȗč( l lqč~ut beme}ktltel de l ezlhul mlbtktltkz țk mlhktltkz ~euhtltehe iubmkk" Zklȗl âb m`hemtkzktlte l ìuhuk q~kiktkz l kiqu} ubehe ~ecuhk de m`bzkeȗuk~e( ` lbuiktč `~dkbe țk dk}mkqhkbč( ~e}qemtl~el ub`~ ke~l~fkk" T~knu~khe q~kiktkze âțk lhecelu ub lbuikt hkde~( de de ~ecuhč meh ilk evqe~kiebtlt zîbčt`~" Lme}tl t~enukl }č kl ubehe f`tč~î~k âb q~kzkbȗl ~eql~tkč~kk nubu~kh`~ m`hemtkze( q~kb u~il~e( l lqč~ut bez`kl ejemtuč~kk q~kieh`~ mlhmuhe ~udkiebtl~e" Âb q~kzkbȗl m`bjemȗk`bč~kk l~ieh`~( zîbčt`~kk lu `n}e~zlt mč zî~juh ubek }uhkȗe e}te ilk ejkmlme dlmč l~e ` lbuiktč lbuiktč j`~ič


































}m`kmk dem`~lte( dkb }qemkl Bl}}l~ku} cknn`}uhu}" Qe hîbcč jlqtuh mč lme}te }m`kmk e~lu j`h`}kte ml eheiebte de q`d`lnč( duqč ubkk me~metčt`~k( lme}tel e~lu utkhklte țk ml zlh`l~e de }mfkin" Âb iuhte ~eckubk de qe m`btkbebtuh lj~kmlb( }m`kmkhe lu j`}t j`h`}kte qîbč âb eq`ml i`de~bč qe q`}t de i`bede" @ lhtč de}m`qe~k~e kiq`~tlbtč me l }m`} hl huikbl khek `nkemte me lu ` zemfkie de 31111 de lbk( l j`}t jčmutč âb qețte~l Nhìn`} dkb Lj~kml de ]ud" Lkmk lu j`}t de}m`qe~kte }m`kmk dkb lmeelțk }qemke mu mehe de}m`qe~kte âb mlze~bl C~`tte de} Qkce`b} ( ubehte m`bjemȗk`blte dkb `l}e( q~emui țk jkcu~k ceìet~kme de}eblte qe qket~e"
































Q~eebtli ilk o`} ubl dkb q~kiehe `qe~e de lme}t ceb de}m`qe~kte hl Ikt`m( oudeȗuh N`t`țlbk( ^ìlbkl" Qke}l ~eq~ekbtč ` liuhetč m`bjemȗk`bltč dkbt~)ub j~lciebt de `}( qe ml~e lu j`}t kb}m~kqȗk`blte c~uqu~k de hkbkk ql~lhehe" Liuhetl dltelč dkb ikhebkuh >3 â"F~" țk e}te âiqč~ȗktč âb t~ek mld~lbe q~kb kbte~iedkuh l t~ek ubcfku~k" Ubcfkuh dkb d~elqtl muq~kbde âb de}mfkde~el }l bùl hkbkk ql~lhehe( ql~lhehe( kl~ ubcfku~khe dkb ql~tel }tîbcč muq~kbd âbt~e hltu~k t~ek( ~e}qemtkz țl}e hkbkk ql~lhehe" ]eibehe be kbdkmč ` ~ehlȗke ilteiltkm`)ceìet~kmč âbt~e iuhtkqhkk buič~uhuk t~ek" ]e ql~e mč be ljhči âb jlȗl q~kiek tlnhete ilteiltkme l ìebk~kk ubde }ubt mub`}mute qebt~u q~kil dltč mkj~ehe =( : țk ;( ilk iuht demît ltît( }ubtei quțk âb jlȗl q~kiek `qe~lȗkk `qe~lȗkk l~ktietkme "
































mu << qubmte" Kltč mui kbte~lmȗk`belč ilteiltkm lme}te buie~e? :='45'<49<>>( 56'5='<<9<>>( 56'5=9<<<( >4='<>>9=:5" Âb }tlȗkubel qlhe`hktkmč de hl M`}čuȗk &>1"111)<1"111 â"F~ + l j`}t de}m`qe~kt de mčt~e l~fe`h`cuh Khke N`~klm ub `} tunuhl~( âb kbte~k`~uh mč~ukl })l cč}kt ub lm m`bjemȗk`blt t`t dkb `}" Q`~)lmuh e}te țhejukt qe t~ek }uq~ljeȗe evte~k`l~e qe ml~e lu j`}t kbmklte c~uqu~k de m~e}tčtu~k" Qe q~kil }uq~ljlȗč âbtîhbki c~uqu~k de m~e}tčtu~k j`~ilte dkb <4 țk 3 hkbkuȗe( qe l dùl }uq~ljlȗč c~uqu~khe <: țk <1 kl~ qe l t~ekl 3 țk ;" ]e q`lte `n}e~zl mč }uil lme}t`~ ‘buie~e’ e}te eclhč mu q~`du}uh ‒buie~eh`~’ de qe jlȗl l t~ekl 3Ó;9:=" <4'3'<:'<1'3';9:=( kl~ qe~emfel de ‒buie~e’ 3 țk ; ` ~ecč}ki kbmkltč qe j`l~te iuhte qke}e de l~tč dkb qlhe`hktkm" Âb lbuh <;=3 ( âb h`mlhktltel Ze}tkbkme dkb I`~lzkl( l j`}t de}m`qe~kt ub `} de huq q~`zebkbd dkb eq`ml qlhe`hktkmč qe ml~e }ubt zkknkhe 55 de m~e}tčtu~k ql~lhehe" Kbte~e}lbt e}te
































;(<;(>< țk <<"]e q`lte `n}e~zl mč hl evt~eiktčȗk lzei zlh`~khe <1'< țk <1)<( âb ikoh`m zlh`~khe >1'< țk >1)<( kl~ ;'<;'><'<<9:1" Qe hkbkl &m+ âbtîhbki buie~ehe q~kie muq~kb}e âbt~e <1 țk >1 me kbte~lmȗk`belč l}tjeh? <;'<<9=1( <3'<=9=1

@} de}m`qe~kt âb h`mlhktltel K}flbc` ) Lj~kml Mebt~lhč

@liebkk q~kiktkzk lu ~eil~mlt jlqtuh mč zklȗl h`~ he e~l kbjhuebȗltč de jebìebehe teiq`~lhe? }mfkinl~el khek țk l b`qȗkk( lhte~bl~el lb`tkiqu~kh`~( ikțml~el lql~ebtč l l}t~eh`~ etm" Qebt~u l q~ekme lme}te jebìebe( ek lu }kiȗkt bez`kl
































jleh`~ hubkk" Duqč qč~e~el }qemklhkțtkh`~( qe lme}t `} l j`}t khu}t~lt ub mlhebdl~ hubl~" Lțldl~( }kin`hu~khe buie~kme lu j`}t âb~eck}t~lte âbmč dkb qlhe`hktkm( ltît qe m`btkbebtuh eu~`qelb mît țk qe meh lj~kmlb" ]č jke ` }kiqhč âbtîiqhl~e jlqtuh mč buič~uh buič~uh lme}t`~ }kin`hu~k kbte~lmȗk`belč ilteiltkm0 De}m`qe~k~el ubuk buič~ il~e de `nkemte mu l}tjeh de âb}eibč~k( m`bt~lkme lmel}tč kq`teč" @iuh dkb qlhe`hktkmuh }uqe~k`~ l lzut de}tuh tkiq hl dk}q`kȗke qebt~u l }tudkl }eibehe me~uhuk( ~`tlȗkl ]`l~ehuk( l Hubkk( jebìebehe ~eqetlnkhe ml~e kbjhuebȗlu zklȗl m`tkdklbč( kl~ lme}te }eibe lu j`}t iei`~lte țk }t`mlte qe dkje~kte `nkemte de l~tč țk muht" Mu t`lte lme}tel( bu lzei me~tktudkbel mč }kin`hu~khe de}m`qe~kte jlm ql~te dkbt~)ub hkinlo ilteiltkm( âb}č( m`b}t~umȗkkhe ieclhktkme ml~e lu ~čil} qîbč âb khehe b`l}t~e( }ubt ` d`zldč me~tč mč lmețtk `liebk mub`țtelu l}t~ehe( țtklu }č jlmč ič}u~čt`~k țk qutelu ejemtul mlhmuhe ilteiltkme ~udkiebtl~e"


































~ehltl~e l ilteiltkmklbuhuk de `~kckbe hktulbklbč( T`nkl} Dlbtkc " ‒Ub b`nkh j~lbme d`~el }č }mlqe de ub m`~n me h`mukl âb tu~buh ml}tehuhuk( dl~ de jkeml~e dltč mîbd }e lq~`qkl de tu~b ql}č~el nu~l kbt~)ub m`qlm dkb lq~`qke~e( lŐteqtîbd qîbč me q~`q~ketl~uh qč~č}el tu~buh" Zčîbd lme}t hum~u( b`nkhuh l t~kik} d`k }e~zkt`~k âb tu~b( }qubîbdu)he ml duqč ` qe~k`ldč de tkiq ubuh dkb ek }č qč~č}el}mč tu~buh( kl~ mehčhlht }č lŐteqte nu~čt`l~el" M`~nuh bu l j`}t qčmčhkt( l lŐteqtlt qîbč l qhemlt Ők lh d`khel }e~zkt`~" Ltubmk b`nkhuh l ~eqetlt evqe~kebŭl mu t~ek( lq`k mu qlt~u }e~zkt`~k( dl~ m`~nuh lŐteqtl âbt`tdelubl qîbč qhemlu t`ŭk }e~zkt`~kk" Âb iìebtuh âb ml~e


































j`}t țk ~čiîbe âb m`btkbul~e ` ič~kie zl~klnkhč( dkbm`h` de ml~e ìuh bu ilk ilk e}te mlqlnkh }č ejemtuee buič~čt`l~el"


































lbtkme lzelu ub buič~ buič~ ilvkilh ml~e bu qutel jk deqčțkt( kl~ âb z`mlnuhl~uh h`~ bu evk}tl ` evq~e}ke ml~e }č ~eq~ekbte ub buič~ ilk il~e" @dltč mu t~eme~el tkiquhuk( tkiquhuk( `liebkk de de țtkkbȗč lu ~elhklt mč ‘iuht’ e}te ` b`ȗkube ~ehltkzč( l}`mkltč b`ȗkubkk de kbjkbkt" Q~kiuh âbzčȗlt lh lbtkmfktčȗkk ml~e l l~čtlt mč ìuh q`lte buič~l `~kmît de iuht( l j`}t L~fkiede &>63 )><> â"F~ "+ "+" Lme}tl țk)l q~`qu} }č dete~ikbe ub buič~ ilk il~e demît jk~ehe de bk}kq ml~e l~ âbmčqel âb Ubkze~}" &hl lmel dltč( q~kb ubkze~} }e âbȗehecel ` }je~č mu mebt~u âb ]`l~e țk ~ll eclhč mu dk}tlbȗl de hl ]`l~e qîbč hl qhlbetl ]ltu~b+" Eh l ~euțkt }č dete~ikbe ub buič~ de}tuh de il~e?


































buič~čt`l~el l ~čil} âbt~)` jlč kbmkqkebtč" Kltč mîtezl eveiqhe? Âb oubchl lil`bklbč( âb b`~d)ze}tuh N~lkhkek t~čkețte t~knuh Qk~lfl( ` mìubktlte de lq~`vkiltkz =11 de iein~k" M`bj`~i me~metčt`~kh`~( hkinlouh j`h`}kt de lme}t t~kn bu m`bȗkbe m`bmeqte m`bmeqte mhl~e qebt~u evq~kil~el b`ȗkubkk de buič~" Iein~k t~knuhuk j`h`}e}m ` }e~ke de te~iebk qebt~u evq~kil~el lq~`vkiltkzč l mlbtktčȗkh`~( ml de eveiqhu ‒quȗkb( mîtezl( iuht‘"Lmețtkl lu m`b}kde~lt mč buie~ehe bu he }ubt j`h`}kt`l~e âb muhtu~l h`~ țk bu lu âbme~mlt }č he j`h`}el}mč( qebt~u ek buič~čt`l~el }e ~edumel hl ‘ubu’( ’d`k’ țk ’iuht’"


































3 9 < ' >  = 6 9 >  4 ; 9 >  4 ' < <1 9 > ' >  4

bltfedlm mlml{bk mlml{bkhkl bkz`ml blh`tlqeclt bkz`ml blh`tlqqeclt bltfedlm mlml{bk bkz`ml blh`tlqeclt

Q`quhlȗkl lut`ft`bč dkb êqunhkml Zlbultu( buiktč Bes Fen~kde} âb tkiquh qe~k`ldek m`h`bklhe( }ktultč âb @melbuh Qlmkjkm de ]ud( j`h`}ețte u~ičt`l~ehe evq~e}kk qebt~u buie~ehe de hl < hl <1? <

Q~`bubȗke tlk

T~ldume~e ubu




































âbmequt( }t~či`țkk b`țt~k bu e~lu q~e`muqlȗk qebt~u l ŭkbe ezkdebŭl iuhŭkikh`~ mu ub buič~ il~e de eheiebte( âb}č `dltč mu dez`htl~el mìubktčȗkh`~ `liebkk lu j`}t bez`kȗk }č jlmč q~`c~e}e âb q~kzkbȗl b`ȗkubkh`~ de l~ktietkmč eheiebtl~č" M~eŐte~el q`quhlŭkek( dez`htl~el lmtkzktčŭkh`~ q~`dumtkze(




































Ub lht l}qemt lh mub`lŐte~kk mît ilk evlmte l iuhŭkikh`~( âh m`b}tktuke `~d`bl~el eheiebteh`~ }lhe" @iuh q~kiktkz t~enukl }č mub`l}mč ml~e dkbt~e lbkilhehe zîblte e~lu mehe ilk il~k( ml~e e~l zkteokl }eiebkh`~ qe mîiquh de huqtč ) ml~e e~l q~kiuh( lh d`khel( lh t~ekhel etm" Mfkl~ dlmč `




































ln}t~lmtklt( dl~ lmel}tč ~eq~eebtl~e iet~`h`ckmč l }tlt hl nll kdekk de buič~ ml b`ŭkube ln}t~lmtč" Ln}t~lmtkl~el b`ŭkubkk de buič~ l j`}t q`}knkhč builk ltubmk mîbd ìebk~el l ltkb} t~eqtehe }uqe~k`l~e lhe dez`htč~kk" Qebt~u `liebkk q~kiktkzk( q~emui Ők qebt~u ubehe ubehe




































LŐldl~( }t~či`Őkk b`Őt~k lu lzut dkze~}e q`}knkhktčŭk qebt~u l evq~kil b`ŭkubel de buič~( hl âbmequt q~kb kbte~iedkuh hkinlouhuk }lu mu lout`~uh m`~e}q`bdebŭeh`~( ilk tî~ku( mîbd buič~uh e~l qe deqhkb ln}t~lmtklt( mu lout`~uh }kin`hu~kh`~"




































Q~kb lbuh :111 â"F~ " oet`lbehe de l~ckhl e~lu ~č}qîbdkte âb âbt~ecuh @~kebt Ikoh`mku" Âb t`lte }ktu~khe l~fe`h`ckme kiq`~tlbte ljhlte âb K~lg( K~lb( ]k~kl( Tu~mkl }lu K}~leh e~lu de}m`qe~kte de hl mîtezl emk qîbč qîbč hl mîtezl }ute de oet`lbe" Ilk tî~ku( âb lbuh ==11 â"F~ "("( m`bu~khe( }je~ehe(














































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































Bkzehuh cebe~lh lh ilteiltkmkk ie}`q`tlikebe

oet`lbeh`~ qe }je~ehe de hut( lq`k q~kb kiq~kil~el oet`lbeh`~ qe tčnhkȗe de hut" Âb tlnehuh de ilk o`} }e q`lte `n}e~zl i`duh mui lu ez`hult mîtezl dkbt~e }eibehe beme}l~e }m~ke~kk" Oet`b de hut

Kde`c~lič

]m~ke~el mubekj`~ič

]eibkjkmlȗke Buič~( ` ubktlte de ič}u~č &qebt~u `~+ Buič~( eme ubktčȗk de ič}u~č &qebt~u `~+ @zkbč N`zkbč Zl} ȟe}čtu~č

Âb~eck}t~l~e buie~kmč l zl}eh`~ &mu hlqte+ țk n`zkbeh`~

Âb~eck}t~l~e buie~kmč l ȗe}čtu~kh`~

Âb~eck}t~l~e buie~kmč l `kh`~

Kbte~e}lbtč e}te ez`huȗkl buič~uhuk( ml b`ȗkube ln}t~lmtč" Kbkȗklh( oet`buh de j`~il m`buhuk e~l j`h`}kt qebt~u l
































j`h`}kt qebt~u l evq~kil ` mlbtktlte de eme `~k ilk ilk il~e" De me lu j`}t lhe}e oet`lbehe mu ml~e e~lu ič}u~lte mlbtktčȗkhe de me~elhe }č ~eq~ekbte mkj~ehe ln}t~lmte0 Q~lmtkml~el lc~kmuhtu~kk l j`}t ubl dkbt~e mehe ilk zemfk âbdehetbkmk~k lhe `liebkh`~" @dltč mu dez`htl~el mìubktčȗkh`~( mlbtktčȗkhe de me~elhe ~em`htlte lu dezebkt dkb me âb me ilk il~k( q~kb u~il~e l lqč~ut bez`kl }t`mč~kk țk m`btlnkhkč~kk lme}t`~ q~`du}e" Q~kbt~e q~kiehe ič~ju~k ml~e lu j`}t m`btlnkhklte mu lout`~uh ub`~ }eibe( lu j`}t t`milk mlbtktčȗkhe de me~elhe( m`bzebkbdu) }e uhte~k`~ ml lme}te }eibe }č jke }tlbdl~dklte ml ubktčȗk de ič}u~č țk utkhklte qebt~u âb~eck}t~l~el lht`~ q~`du}e" Dkb qe~k`ldl q~`t`)}uie~klbč q~`zkbe mel ilk zemfe j`~ič de }m~ke~e( }m~ke~el mu lout`~uh qkmt`c~lieh`~( m`b}tîbd âbt~)` }umme}kube de kilckbk }kin`hkme l ub`~ jkkbŭe Ők hum~u~k ml~e q~kb }kiqhl lhčtu~l~e }uce~lu ub ie}lo" Dlmč q~kzki tčnhkȗl de ilk o`} `n}e~zči qe q~kiuh ~îbd }ki }kin`hu~kh ~khe?

&mlq mlq+ țk

&~lȗk lȗke+( e+( ` }e~k e~ke de }kin`hu~k

bui buie~km e~kmee q~e q~emu mui i țk }kin }kin`h `huh uh ml~e ml~e âb âb}e }eli libč bč `~" ~" E}te E}te mhl~ mhl~ mč be ljhči âb jlȗl ubek âb~eck}t~č~k m`btlnkhe mu q~kzk~e hl m`b}uiuh de me~elhe"

]m~ke~el mu lout`~uh qkmt`c~lieh`~

]m~ke~el mubekj`~ič

Uhte~k`~( ie}`q`tlikebkk lu }kiqhkjkmlt j`~il qkmt`c~lieh`~ j`h`}kbd kde`c~liehe mubekj`~ie &hlt" mubeu}
































tčnhkŭek de l~ckhč m~udč( mu lout`~uh ubuk neȗkț`~( kl~ ilk tî~ku mu lout`~uh ubuk zî~j ietlhkm debuikt }t{hu}" Lțldl~( qîbč l }e loubce hl }m~ke~el mubekj`~ič lu j`}t ql~mu~}e u~ičt`l~ehe etlqe? ) utkhkl~el oet`lbeh`~ }kiqhe7 ) utkhkl~el oet`lbeh`~ âbmfk}e âb }je~e de hut7 ) kiq~kil~el oet`lbeh`~ qe }je~e de hut7 ) kiq~kil~el oet`lbeh`~ qe tčnhkȗe de hut7 ) utkhkl~el qkmt`c~lieh`~7 ) }m~ke~el mubekj`~ič" Qebt~u }eibehe buie~kme })lu utkhklt hl âbmequt dùč }kin`hu~k? me~muh țk m`buh( de~kzlte dkb oet`lbehe de l~ckhč de j`~il }je~ek țk l m`buhuk" ]m~ke~el e~l ~ehltkz uț`l~č( jkkbdmč me~muh }e `nȗkbel q~kb lqč}l~el ubuk neȗkț`~ qe tčnhkȗl de hut( qe ze~tkmlhč( kl~ m`buh e~l `nȗkbut q~kb lqč}l~el neȗkț`~uhuk }un ub lbuikt ubcfk jlȗč de ze~tkmlhč" Qebt~u l }m~ke buie~e ilk il~k e~l j`h`}kt ub neȗkț`~ ilk c~`} l}tjeh âbmît u~il me~muhuk țk l m`buhuk }č lknč dkieb}kubk ilk il~k" Lmel}tč j`~ič de }m~ke~e e}te mub`}mutč }un debuik~el de }m~ke~e q~`t`)mubekj`~ič țk }e e}tkielč mč l lqč~ut âb ou~uh lbuhuk =111 â"F~" Q~kiehe mlhmuhe lhe }uie~kebkh`~ ejemtulte qe tčnhkȗehe de hut e~lu de bltu~č ldikbk}t~ltkzč" Ehe }e ~edumelu hl }kiqhe ezkdebȗe m`btlnkhe q~kzkbd mlbtktltel de c~îbe( buič~uh lbkilheh`~ }lu zebktuh il~kh`~ c`}q`dč~kk" Ilk tî~ku lql~ tčnhkȗe mu ml~lmte~ qu~ ilteiltkm( ubde e~lu ~e`hzlte q~`nheie de l~ktietkmč }lu ceìet~ke" Qebt~u l buič~l( ie}`q`tlikebkk lu j`h`}kt }k}teiuh de buie~lȗke }evlce}kilh" Ub `nkemt e~l }kin`hklt mu ub m`b ikm( <1 m`bu~k ikmk e~lu âbh`mukte mu ub me~m ikm( : me~mu~k ikmk e~lu âbh`mukte mu ub m`b il~e( <1 m`bu~k il~k e~lu âbh`mukte mu ub m`b il~e mu ub me~m ikm âb kbte~k`~( kl~ țl}e
































il~e" Âb jkbe( <1 me~mu~k il~k e~lu âbh`mukte mu ub me~m il~e me m`bȗkbe âb kbte~ k`~ k`~ ub me~m ikm" L}tjeh( uhtkil ubktlte buič~l <1 Ó : Ó <1 Ó : Ó <1 9 =:"111 `nkemte" ]k}tei de

buie~lȗke }evlce}kilh ]m~ke~e

}evlce}kilhč 3;:

<Ó:11'=Ó:1'<Ó<1':Ó<

]mfekh&<;=5 B~"=<4+( jlȗl

]mfekh&<;=5 B~"=<4+( }qlte

Qe tčnhkȗl ]mfekh &<;=5 B~"=<4+ q`lte jk `n}e~zlt ub mlhmuh }evlce}kilh mu q~kzk~e hl m`btlnkhkl~el zl}eh`~ mu ne~e" Qe jlȗl tčnhkȗek }ubt }m~k}e buič~uh zl}eh`~? =1(>1(<1(<5( kl~ qe qe }qltehe }qltehe tčnhkȗek }uil? 35" Ie}`q`tlikebkk j`h`}elu }k}teie de buie~lȗke dkje~kte( âb jubmȗke de ič~kikhe ič}u~lte( qe~k`ldl k}t`~kmč }lu `bl ce`c~ljkmč" Me~metčt`~kk lu qu} âb ezkdebȗč ilk iuhte }k}teie de buie~lȗke? qebt~u ič}u~l~el me~elheh`~( qebt~u ič}u~l~el mlbtktčȗkh`~ de ietlh( qebt~u ič}u~l~el l~kkh`~ țk
































iuhtkqhkmktlte l }kin`hu~kh`~ e~l dkje~ktč âb jubmȗke de ič~kikhe ič}u~lte( l}tjeh âbmît ub }kin`h qutel }č lknč zlh`~k dkje~kte( âb jubmȗke de }k}teiuh j`h`}kt" ]k}tei de

buie~lȗke nk}evlce}kilh ]m~ke~e nk}evlce}kilhl

3;:

:Ó<>1'<Ó:1'<Ó<1':Ó<

5>1

3>1

61

:1 Tčnhkȗl ]mfekh( <=>5( b~" >3 jlȗč

<=61

Tčnhkȗl ]mfekh( <=>5( b~" >3 }qlte

Qebt~u lbuikte mlhmuhe ilteiltkme q~emui țk qebt~u mlhmuhuh ~lȗkkh`~ ( }uie~kebkk }uie~kebkk j`h`}elu j`h`}elu ub }k}tei }k}tei nk}evlce}kilh âb ml~e jlmt`~kk de iuhtkqhkml~e e~lu <1( :( >( <1( : ( l}tjeh mč }kin`huh qebt~u mlbtktltel mel ilk il~e &ub me~m il~e mu dùč me~mu~k ikmk kbte~k`l~e+ lzel zlh`l~el de : Ó <1 Ó > Ó : Ó <1 9 3">11 3">11 ubktčŭk de nlč" Qe jlȗl tčnhkȗek ]mfekh( <=>5( b~" >3 }ubt m`btlnkhklte qlt~u mlbtktčȗk de c~îu ~eq~eebtlte q~kb buie~ehe 5>1( 3>1(


































}qltehe tčnhkȗek lzei }uil lme}t`~ buie~e( <=61" ]kin`hu~khe buie~kme }ubt mktkte de }u} âb o`}" ]k}tei de

buie~lȗke emkilh ]m~ke~el

emkilhč 3;:

3Ó<11';Ó<1'':Ó< :5

;'>> <:'<6

Tčnhkȗl ]mfekh( <;15( b~" ><> jlȗč

]kin`h qebt~u `lke

Tčnhkȗl ]mfekh( <;15( b~" ><> }qlte

Qe hl }jî~țktuh ikhebkuhuk lh KZ)hel â"F~ " âb mîiqkl ie}`q`tliklbč l mk~muhlt țk ub }k}tei de buie~lȗke zemkilh( j`h`}kt mu q~emčde~e hl buič~l~el lbkilheh`~ dìe}tkme țk l iubmkt`~kh`~" Tčnhkȗehe qe ml~e e~lu kb}m~kqȗk`blte mlhmuhehe mu buie~e emkilhe lu j`}t de}m`qe~kte âb `~lțuh Enhl qe te~kt`~kuh ]k~kek" Tčnhkȗl ]mfekh( <;15( b~" ><> e}te }m~k}č qe t~ek ~îbdu~k( țk m`bȗkbe ` âb~eck}t~l~e buie~kmč âb }k}teiuh
































]k}tei de buie~lȗke qebt~u ič}u~l~el me~elheh`~&]E+ ]m~ke~el & ]E+ 3;:

>Ó=11':Ó=1'=Ó5'<Ó< Qebt~u ič}u~l~el mlqlmktčȗkh`~( âb }qemklh l me~elheh`~ e~l j`h`}kt ub }k}tei âb ml~e jlmt`~kk de iuhtkqhkmktlte e~lu 5( :( <1( Ők =( l}tjeh âbmît( ubktltel mel ilk il~e lzel zlh`l~el de 5 Ó : Ó <1 Ó = Ó<19 ;111 ubktčŭk de nlč( kl~ ubktltel de nlč e~l de lq~`vkiltkz 5 h " < > = 4 T`tlh < Mlbtktčȗk de `~

T`tlh cebe~lh T`tlh >

Mlbtktlte ilhȗ

de
































lie}tem( `~ țk ilhȗ( lțelte qe dùč hkbkk( kl~ âb m`h`lbehe t~ek țk qlt~u lzei mlbtktčȗkhe de `~ țk ilhȗ" ê}qemtîbd ~ecuhkhe de mlhmuh lhe }k}teiuhuk de buie~lȗke( qutei ze~kjkml i`duh âb ml~e }uie~kebkk lu `nȗkbut mlbtktltel t`tlhč de 53> ubktčȗk ič}u~lnkhe" De eveiqhu( t`tlhuh < e}te `nȗkbut dlmč }e ldubč mlbtktčȗkhe dkb m`h`lbl =( 3Ó=1'4Ó5'49>=4u" `~ mu >Ó=1'49:4u" ilhȗ ldkmč >;6 ubktčȗk de lie}tem( kl~ t`tlhuh > e}te `nȗkbut dlmč }e ldubč mlbtktčȗkhe dkb m`h`lbl 4 3Ó=1'49><4u" `~ mu >Ó=1'49:4u" ilhȗ ldkmč >34 &>36+ ubktčȗk de lie}tem" ]e `n}e~zč e~`l~el de mlhmuh hl t`tlhuh >" Âb}uiîbd t`tlhuh < mu t`tlhuh > }e `nȗkbe t`tlhuh cebe~lh" Qebt~u ič}u~l~el tkiquhuk }uie~kebkk lu j`h`}kt ub }k}tei nllt qe âiqč~ȗk~el lbuhuk âb <> hubk țk l hubkk âb =1 de khe" ]kin`hu~khe j`h`}kte }ubt u~ičt`l~ehe? hubk

<1 hubk

461 Ubktltel de ič}u~č

4 3 1 <

<1khe

< k
































mlbtktlte m`b}uiltč qe tkiq de t~ek lbk( țk lbuie 5;4u"( kl~ qe }qltehe qhčmuȗek lzei t`tlhuh( <134u" Qebt~u ič}u~l~el }uq~ljeȗeh`~ te~ebu~kh`~( }uie~kebkk utkhklu u~ičt`l~ehe ubktčȗk de ič}u~č? unu >

kgu :

ëŬe =

nÿ~ <1

nÿ~‛u :

Ŭì~ <1

Ŭì~‛u

Ubde < kgu 9=:11 i>" Hl }jî~țktuh ikhebkuhuk lh KKK)hel })l kbt~`du} }k}teiuh de buie~lŭke }evlce}kilh q`kŭk`blh" Nlnkh`bkebkk lu q~ehult }k}teiuh }evlce}kilh de hl }uie~kebk( qe nll mč~ukl lu âiqč~ȗkt me~muh âb =:1 de c~lde( c~lduh âb :1 de ikbute țk ikbutuh âb :1 de }emubde" Qebt~u l }m~ke mehe :1 de eheiebte lhe }k}teiuhuk }evlce}kilh ek j`h`}elu âb }m~ke~el mubekj`~ič dùč }eibe" Lzelu Lzelu ub }eib }eib qebt~u qebt~u ubu & + &de~kzlt &de~kzlt dkb dkb m`buh m`buh ikm+( ikm+( ml~e ~eqetlt dčdel d`k ( t~ek Ők lŐl ilk deql~te( qîbč hl eme( qebt~u qebt~u ml~e ml~e evk}tl ub lht }eib }eib & + &de~kzlt &de~kzlt dkb me~muh me~muh ikm+" ikm+" Qebt~u Őlkemk }e j`h`}el lmehlŐk }eib ml qebt~u ubu( dl~ zlh`l~el }l e~l dltč de m`h`lbl âb ml~e }e cč}el" <

>

=

4

5

:

3

6

;

<1 << <>
































j`h`}k zk~cuhl § ( · kl~ qebt~u l de}qč~ȗk ql~te âbt~elcč de ql~tel emkilhč zì j`h`}k qubmt j`h`}k qubmt țk zk~cuhč § 7 · " Buič~uh <>(=:(4< q`lte jk t~lb}j`~ilt âb nll eme l}tjeh? > < <>(=:(4< 9<>Ó:1 '=:Ó:1 '4<9>5;4>1<" Dlmč }m~kei <>7=:(4<( ltubmk buič~uh t~lb}j`~ilt âb nll eme e}te? <> 

=5 :1



4< :1

>

Qebt~u j~lmȗkkhe uulhe

9 <>(1<<51;>5;…… < < > ( ( > = =

nlnkh`bkebkk j`h`}elu

}kin`hu~khe ( ( " Lme}t }k}tei lzel țk kbm`bzebkebte7 de eveiqhu( }kin`huh q`lte ~eq~eebtl <( :1 &: ³ <1+( =":11 &:1 ³ :1+( <

(

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:1 :1

>

etm" zlh`l~el }l deqkbîbd de q`kŭkl qe ml~e `

`muqč" Ub lht eveiqhu ? dlt`~ktč j lqtuhuk lqtuhuk mč bu evk}tl ub }eib qebt~u `~dkbehe ln}ebte &hkq}l mkj~ek 1+( buič~uh q`lte jk mktkt <=Ó:1': }lu <=Ó:1>': }lu <='

: :1

" De ~ecuhč(

ltubmk mîbd âb mlhmuhe lqč~el lmel}tč mkj~č( ie}`q`tlikebkk hč}lu ub h`m hkne~" Dl~ bu âbt`tdelubl7 l}tjeh( bu e}te mhl~ dlmč âb}elibč >( :<( =:1< }lu =::1" Uhte~k`~ l j`}t ehkikblt ehkikblt lme}t lme}t kbm`bzebkebt kbm`bzebkebt q~kb


































}evlce}kilhktlte" Âb jubmȗke de etlqehe dez`htč~kk }`mketčȗkk ie}`q`tlikebe âbtîhbki ikmk dkje~ebȗe âb q~kzkbȗl ~lq`l~teh`~ dkbt~e iuhtkqhkk țk }uniuhtkqhkk ubktčȗkh`~ de ič}u~č" êil~mči mîtezl ubktčȗk de ič}u~č jubdliebtlhe? qebt~u hubckie ) g uŬ uŬ &m`tuh+( qebt~u }uq~ljlȗč ) }l~ &hkzldl+( qebt~u mlqlmktlte ) }khl( qebt~u c~eutčȗk ” ikbl" Âb tlnehehe de ilk o`} }ubt q~eebtlte ubktčȗkhe de ič}u~č j`h`}kte de zemfkk nlnkh`bkebk( mu iuhtkqhkk țk }uniuhtkqhkk q~kbmkqlhk" Ubktčȗkhe de ič}u~č qebt~u hubckie ? ]û)Ŭk &decetuh+

Zlh`l~e lq~`vkiltkzč <(3 mi

guŬ &m`tuh+

Ubktltel

]kin`h

Ui" <=1

Ó=1

51 mi =1 decete

<

Ó<>

bkbdl

: i 9<> m`ȗk

<>

Ó:

uŬ

=:1 i 9 :1 bkbdl

3>

Ó=1


































Ubktčȗkhe de ič}u~č qebt~u mlqlmktlte? ckb

Zlh`l~e lq~`vkiltkzč <3 ih

]khl&|û+

Ubktltel

]kin`h

Ui" <:1

Ó:1

< h :1 ckb

<

Ó<1

nlb

<1h 9 <1 }khl

<1

Ó:

nl)~k)cl

:1h 9 :nlb

:1

Ó5

cu~

=11h 9 5nl~kcl

=11



Ubktčȗkhe de ič}u~č qebt~u il}č? Ubktltel Ŭe ckb &}fegeh+ il)bl &ikbl+ cu

]kin`h

Zlh`l~e lq~`vkiltkzč 45ic 6c <61 Ŭe 

511c 9 :1 ckb =1gc

Ui" <<1611 Ó<61 Ó:1 <:1 <

Ó:1
































I] =6:; ( t~lb}j`~ič~k me lu ml ubktlte de nlč }evlce}kilhč( bkbdl" Âb ql~tel }tîbcč l jkemč~ek m`h`lbe }ubt t~emute ubktčȗkhe de ič}u~č qebt~u hubckie âbmeqîbd mu < decet qîbč hl ; decete7 <1 decete }ubt }m~k}e ml ⅝ m`t ( lq`k <5 decete ml ¹ m`t țk >1 decete ml ⅔ m`t " Tlnehuh m`btkbuč mu =1 decete&
T~ldume~e Bkbdl

< decet > decete = decete 4 decete 5 decete : decete

1711(<1 1711(>1 1711(=1 1711(41 1711(51 171<(11

]kin`h

T~ldume~e Bkbdl ¹ m`t 171>(=1 ⅔ m`t < m`t <⅝ m`t <¹ m`t <⅔ m`t

171=(>1 1715(11 171:(41 1713(=1 1716(>1
































t~lb}j`~ič~k me lu ml nlč }evlce}kilhč ubktltel de ič}u~č ckb" Ubktlte de ič}u~č

<}e <¹ }e >}e >¹ =}e :}e <>}e <=}e <5}e >1}e

]m~ke~e }evlce}kilhč

1711(>1 1711(=1 1711(41 }e 1711(51 171<(11 171>(11 1714(11 1714(>1 1715(11 171:(41

Ubktlte de ič}u~č

>5}e >3}e >6}e =1}e ⅝ckb ¹ ⅔ckb 5:
]m~ke~e }evlce}kilhč

1716(>1 171;(11 171;(>1 >;}e 171;(41 17<1(11 17>1(11 ckb 17=1(11 1741(11 ckb 1751(11 <711(11

>"= @qe~lȗkk l~ktietkme Ldubl~el țk }mčde~el Qebt~u ejemtul~el `qe~lȗkkh`~ l~ktietkme eheiebtl~e(
































>`=4‛>5‛‛'< `4>‛<5‛‛9 4 `<3‛41‛‛ <

`

> ` =4‛ >5#‛ ' < ` 4>‛ <5‛‛ 4 ` <:‛ 41‛‛

Ldubl~el = `=4‛>5‛‛ ) < `4>‛<5‛‛9 < `5>‛<‛‛ / :1‛ = ` =4‛ >5‛‛ ) < ` 4>‛ <5‛‛ < ` 5>‛ <1‛‛

=4‛'4>‛93:‛9 :1‛'<:‛ :1‛'=4‛9;4‛ 9< `'<:‛ ;4‛) 4>‛95>‛ Qebt~u l }kin`hkl }mčde~el ie}`q`tlikebkk utkhklu de}e`~k }eibuh ( de eveiqhu buič~uh =3 âh }m~klu ml ` dkje~ebȗč( țk lbuie 41)=( ldkmč "

Âbiuhȗk~el țk ~kdkml~el hl qute~e Hl jeh ml ldubl~el( âbiuhȗk~el ` ejemtulu dk~emt(

]mčde~el


































Dlmč }e d`~el ejemtul~el q~`du}uhuk 45Ó=5( }e }m~kl =5 ml =1'5( lq`k }e ldublu zlh`~khe dkb tlneh qebt~u 45Ó=1 țk qebt~u 45Ó5( `nȗkbîbd ~euhtltuh >:(<5" Ltubmk mîbd e~lu j`h`}kte buie~e ilk il~k }e q~`medl hl jeh( de eveiqhu? >5Ó<3(=1 9 >5Ó<3(11 ' >5 Ó=1 9 3(15(11 ' <>(=1 9 3(<3(=1 Âb kilckbel de ilk o`} q`lte jk `n}e~zltč tčnhkȗl ljhltč hl iueuh de lbtkmfktčȗk lh ubkze~}ktčȗkk dkb Oebl( Ce~ilbkl( qe ml~e e}te }m~k}č tlnhl âbiuhȗk~kk mu ;"


































ml >1)<( q~`nlnkh dkb m`b}kde~ebte q~lmtkme }m~knuh l lhe} }č j`h`}el}mč ` l}tjeh de b`tlȗke" Dlmč buie~ehe j`h`}kte bu qutelu jk ~ecč}kte âb tlnehe( âbiuhȗk~el e~l ejemtultč `~dkb mu `~dkb" 3

=5

3

=5

5Ó5

>5

5Ó=1

>

5Ó3

=5

=1Ó5

>

=1Ó=1

<5

=1Ó3

=

=1

3(=5

=1

3(=5

=1

53(=1(>5


































Tčnhkȗl I]" >3>6

Tčnhkȗl I]" =;::


































l n 

l  n>  &l  n+> 4

" Ubehe tlnehe m`bȗkb q~`du}e de

j`~il b b &b'<+( &b'<+( ubde b kl zlh`~k de hl < hl <>( }lu q~`du}e l t~ek buie~e m`b}emutkze de j`~il b &b'<+ &b'<+ &b'>+( &b'>+( ubde b kl zlh`~k de hl < hl =1" J~lciebtuh dkb tlnehuh I] =146 m`bȗkbe qe m`h`lbl b buie~e de hl < hl ; kl~ qe m`h`lbl b&b'<+&b'>+ q~`du}ehe? < > =7 =7 > = 47 47 = 4 57 57 4 5 :7 :7 5 : : 37 37 : 3 3 67 67 3 6 ;7 ;7 6 ; <1" <1" Qebt~u ejemtul~el mlhmuheh`~( âb ljl~l `qe~lȗkek de ~kdkml~e hl qčt~lt țk mun( âbtîhbki ~kdkmč~k hl qute~k de `~dkb }uqe~k`~" Qe tčnhkȗl I] >>4> }e `n}e~zč mlhmuhe mu qute~k( 





























 

 

 

 




































Âiqč~ȗk~el( kbze~}uh ubuk buič~ @qe~lȗkl de âiqč~ȗk~e l dùč buie~e e~l ejemtultč ml ` âbiuhȗk~e dkbt~e ub buič~ țk kbze~}uh mehukhlht buič~" Âb cebe~lh( q~kb kbze~}uh ubuk buič~ bltu~lh l dkje~kt de 1( }e âbȗehece buič~uh

<

l

( âb}č t~enuke }č ȗkbei m`bt de jlqtuh mč

ie}`q`tlikebkk j`h`}elu ilk ~l~ b`ȗkubel de j~lmȗke `~dkbl~č" Ek lzelu mîtezl }kin`hu~k qebt~u l khu}t~l j~lmȗkkhe `~dkbl~e uulhe( âb}č ilo`~ktltel j~lmȗkkh`~ e~lu }m~k}e }un j`~ič emkilhč"




































< hl 5;" De`l~eme buie~`l}e }eibe lu j`}t dete~k`~lte( }qemklhkțtkk ~e}tlu~lt`~k lu ldu} hl j`~il kbkȗklhč }kin`hu~khe( q~eebtîbdu)he âb tlnehuh de ilk o`}" B~

jlȗč( m`h`lbl K

B~

jlȗč( m`h`lbl KK




































`n}e~zlt mč kbze~}uh buič~uhuk 3 âb nll :1( bu e~l buič~ jkbkt( eh jkkbd de j`~il 176(=4(<3(6(=4(<3(……"( de lmeel bu l j`}t t~emut âb tlneh" Âb tčnhkȗehe nlnkh`bkebkh`~ âbtîhbki mlhmuhe ubde l j`}t j`h`}kt kbze~}uh buič~uhuk 3 ( zlh`l~el lt~knuktč jkkbd 176(=4(<3(6(=4(<3 ldkmč?




































Tčnhkȗl NI<1:444 m`bȗkbe qe linehe jeȗe ` }e~ke de âiqč~ȗk~k }umme}kze lhe buič~uhuk :1 âb qč~ȗk muq~kb}e âbt~e > țk 54" Qe jlȗl3)l ql~te l huk :1" Ȗlkemk? l >)l ql~te e}te =1




































de}m~k} âb }em" K de mčt~e ilteiltkmklbuh c~em Fe~`b dkb Lhevlbd~kl &<1)31d"F~"+" Bu lzei me~tktudkbel mč nlnkh`bkebkk lu lqhkmlt lme}t lhc`~kti( de`l~eme âb mlhmuhe ek bu `je~elu `je~elu evqhkmlȗkk de}q~e zlh`~khe ~ldkmlhkh`~( qu~ țk }kiqhu he âbh`muklu âb eve~mkȗkk jč~č l jlme bkmk ub jeh de mìebtl~kk(




































l=



= >

> >   < = >

<3 l



<>





<3 <>



<(4<::""" (țk

> <> 

< <3



533



< 4<4><5:6:

(

`

lq~`vkil~e















































































































Lqhkmlȗkk ilteiltkme
































































































































































































































































































































































































































































































































































































































































































































































































































































































ldkmč ub }k}tei de dùč emulȗkk mu dùč bemub`}mute" L}tčk mub`lțtei buie~`l}e iet`de de ~e`hzl~e l lme}tuk }k}tei( kbte~e}lbt e}te i`duh mui ie}`q`tlikebkk lu dete~ikblt }`huȗkkhe" Ek lu ldublt ilk âbtîk emulȗkkhe( `nȗkbîbd l}tjeh hkbkl &<+ dkb t~ldume~e( v'{'v){'v{9=(=1 }lu v&>'{+9=(=1" Hkbkl &>+ ` qutei t~lb}qube l}tjeh >'v'{9>;" Dlmč âb uhtkiehe dùč ~ehlȗkk jlmei }un}tktuȗkl 9{'>( `nȗkbei  vz  =(=1 }k}teiuh emfkzlhebt?   v  z  >;

Lțl mui li `n}e~zlt âb eveiqhehe lbte~k`l~e( qebt~u ~e`hzl~el }k}teiuhuk( ie}`q`tlikebkk evq~kilu bemub`}mutehe âb jubmȗke de }eik}uil țk }eikdkje~ebȗl h`~" Dlmč l 

v  z >

țk <47=1 

v  z >

&hkbkl = dkb t~ldume~e+( ltubmk

v9<47=1'l țk 9<47=1)l de ubde( v9=(=19 &<47=1+>) l>" l>9&<47=1+>)=(=1 l>917<5&hkbkkhe 4 țk 5 dkb t~ldume~e+ l9 17<5 ( l917=1 &hkbkl :+ v9 <47=1'17=1( v9<5 &hkbkl 3+ 9<47=1)17=1( 9<4&hkbkl 6+ {9)>9<4)>( {9<> &hkbkl ;+































Lbeve

LBEVE































Lbeve

Tčnhkȗehe dkb lbeve lql~ȗkb? M`hemȗkek ]mfö{eb( H`bd~l M`hemȗkek Ubkze~}ktlȗkk [lhe M`hemȗkek C L Qhkiqt`b( Ubkze~}ktltel M`huinkl































Lbeve

Âb~eck}t~l~e buie~kmč l ubek mlbtktčȗk de me~elhe































Lbeve

Oet`lbe mìqheve

Tčnhkȗl I]Z@ ="5< ) âb~eck}t~l~e ldikbk}t~ltkzč

































Lbeve

Tčnhkȗl I] <644 ) mlhmuhuh }uiek te~iebkh`~ q~`c~e}kek ceìet~kme































Lbeve

Tčnhkȗl Qhkiqt`b ) buie~e qktlc`~ekme































Lbeve

Tčnhkȗl [NM 3>6; ) mlhmuhuh dklc`blhek ubuk qčt~lt































Lbeve

Tčnhkȗl I]><13) mlhmuhuh l~kek ubuk t~lqe































Lbeve

































Lbeve































Nknhk`c~ljke

NKNHK@C^LJKE ]EHEMTKZĎ

WY Oú~lb J~kne~c( ]ù~me} lbd ]tudke} kb tfe Fk}t`~{ `j Iltfeiltkm} lbd Qf{}kmlh ]mkebme} ( Deql~tiebh `j Iltfeiltkmlh ]mkebme} Mflhie~} Ubkze~}kt{ `j Temfb`h`c{ C`tfebnu~c( ]sedeb( Fl}}hef`hi( ]sedeb( Oube <=( >114 &jkblh ~ezk}k`b Demeine~ =<( >11:+" W=Y Oú~lb J~kne~c( Ube}qemted hkbg} netseeb Ec{qtklb lbd Nln{h`bklb Iltfeiltkm}( S`~hd ]mkebtkjkm Qunhk}fkbc( ]kbclq`~e( >115" W4Y Oú~lb J~kne~c( Lilkbc T~lme} `j l Nln{h`bklb @~kckb kb C~eeg Iltfeiltkm}( S`~hd ]mkebtkjkm Qunhk}fkbc( ]kbclq`~e( >11:"































Nknhk`c~ljke

W<1Y Qete~ Dlie~`s( Tfe @~kckb} `j S~ktkbc l} l Q~`nhei `j Fk}t`~kmlh Eqk}tei`h`c{ ( Ilv Qhlbmg Kb}tktute j`~ tfe Fk}t`~{ `j ]mkebme(<;;;" W<" W<>Y Zkmt`~ O" Glt( Lbbette Kiflu}eb( Ehe`b`~ ^`n}`b Tfe iltfeiltkm} `j Ec{qt( Ie}`q`tlikl( Mfkbl( Kbdkl( lbd K}hli( Q~kbmet`b Ubkze~}kt{ Q~e}}" W<=Y ]teqfeb D" Fù}t`b( Tfe jk~}t s~ktkbc" ]m~kqt Kbzebtk`b l} Fk}t`~{ lbd Q~`me}}( Mlin~kdce Ubkze~}kt{ Q~e}}" W<4Y E" M`hilb( K}t`~kl ilteiltkmkk âb lbtkmfktlte ( Edktu~l Őtkkbŭkjkmč( Numu~eŐtk( <;:=" W<5Y @zkdku D~âinč ( K}t`~kl muhtu~kk Ők mkzkhklŭkek( Edktu~l Ȗtkkbȗkjkmč țk Ebmkmh`qedkmč( Numu~ețtk(<;65" W<:Y B" Ikfčkhe}mu( K}t`~kl Ilteiltkmkk ( Edktu~l ebmkmh`qedkmč ~ìîbč( Numu~eŐtk( <;34" W<3Y L" Zl~tkm( Q`~tlmuh huk N`~klm( Dlzl Kbte~bltk`blh( >11>" W<6Y Ehkl ^ìlb( L~kbl âb ȟl~l buie~eh`~( Edktu~l





























































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