Chaveiro - Aula 06

HW\XE MG HOBZGC\E - BWFB : ]CÊX MG @WCFOE]CKBX Zcdes kb fcàèe bktgrcer hede rgtcr rg tcrbr br es hc hcfck fckmre mress mg c` c`kcà kcàèe èe me mess mcjgrgktgs tcpes mg trbvbs mg mcrgàèe g hede mgsdektâ-fes. Gstum Gst umbrg brgde dess kg kgst stb b bu bufb fb es tcpes mg ùcfoetckbs g bs qubktcmbmgs utcfczbmbs utcfcz bmbs pgfbs mcvgr mcvgrsbs sbs dekt dektbmer bmerbs bs pbrb jerdbr e sg`rgme mes hcfckmres mg c`kcàèe g mbs pertbs mes butedøvgcs. E bf bfuk uke e iâ gs gstu tume meu u gd bu bufb fb bktg bk tgrc rcer er e sc scst stgd gdb b mg sg sg`r `rgm gme e gdprg`bkm gdpr g`bkme e ùcfoe ùcfoetckbs tckbs mes hcfckm hcfckmres res pbr brb b dø døvg vgcs cs he hedg dgrh rhcb cbcs cs,, he hed d b jckbfcmbmg mg mcdckucr e mcìdgtre mes hcfckmres. E sg`rgme mgstgs hcfckmres ã scdpfgs, gstâ sctubme kb pbrtg supgrcer me hbkoèe. Ke hbse mes hcfckmres utcfczbmes pgfbss ckmù pgfb ckmùstrcb strcbss bute butedel delcfäst cfästchbs chbs e sg`rg sg `rgme me ã mu mupfe pfe,, eu sgi sgib, b, pes pessu succ ùcfoetc ùcf oetckbs kbs sup supgrce grcergs rgs g ckjg ckjgrcer rcergs. gs. (Jcùrb 2).

êr sgr b qubktcmbmg mg ùcfoetck foetckbs bs lgd dbcer dbcer,, ehe eherrg rrg hgrtb hgrtb mcjchufmbmg ke dedgkte mg hekjghhcekbr b hobvg pbrb es es hcfckmres. hcfckmres. Bktgs Bktgs,, perãd, perãd, mg gktrbr kes mgtbfogs mb hekjghàèe mg hobvgs pbrb hcfckmres mg butedøvgcs, ã cdpert cdp ertbkt bktg g pb pbrb rb e bfu bfuke ke hek hekogh oghgr gr es sg`rgmes sg`rg mes g ùcfoe ùcfoetckbs tckbs bmetbmbs pgfbs mcvgrsbs mcvgrs bs dektb dektbmerbs merbs.. Blermbrgdes Blermbrg des e bssukte kb dgsdb dgs db sgq sgqöék öékhcb hcb bme bmetbm tbmb b kb buf bufb b bktgrcer e qug herrgspekmg b9 - Zefaswb`gk1 - @gkgr @gkgrbf bf Deters1 Deters1 - Jerm g1 - Jcbt. Ckch Ck chcb cbkm kme e he hed d b fcfcko kob b mb Zefaswb Ze faswb`gk, `gk, gstb dekt dektbmer bmerb b utcfcz utcfczb b qubt qu btre re ù ùcfcfoe oetctckb kbss mg bf bftu turb rbss ‖x ‖x—— mcjgrgkt mcjg rgktgs gs qug prep preperhc erhcekb ekb qub qubtre tre prejukmcmbmgs mg hbvbs pbmrekczbmbs.

^rejukmcmbmg mbs hbvbs9 K¹ 2 - ^rejukmcmbmg mb hbvb >,> dd. K¹ < - ^rejukmcmbm ^rejukmcmbmg g mb hbvb hbvb >,7 dd. K¹ 8 - ^rejukmcmbm ^rejukmcmbmg g mb hbvb hbvb 2,> dd. K¹ = - ^rejukmcmbm ^rejukmcmbmg g mb hbvb hbvb 2,? dd.

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8

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2

Btgkàèe Fgdlrg-sg qug bfturb ‖x— ã b qug jbz e sg`rgme. (Jcùrb <).

x

Jcùrb < - Bfturb x ã qug hektb pbrb jbzgr e sg`rgme.

@ucfoetckb Xupgrcer

Hcfckmre

@ucfoetckb Ckjgrcer

Jcùrb 2 - @ucfoetckbs supgrcergs g ckjgrcergs.

HW\XE MG HOBZGC\E ‘ BWFB :

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Bs ù ùcfcfoe oetctckbs kbs rg rghg hglg lgd d kù kùdg dgre ress mg ud b qu qubt btre re qu qug g bs cm cmgk gktctcjcjchbd. hbd. ]eme emess es but butedø edøvgc vgcs mb fckob fckob mb dektbmerb dekt bmerb Zefaswb`gk Zefaswb`gk utcfczb mgz (2>) ùcfoetckb foetckbss ke sg` sg`rgm rgme e me hcfckmre kmre mg c`kcàè c`k càèe e g sgt sgtg g (0) (0)ùc ùcfoetck foetckbs bs kes keshcfc hcfckmres kmres mbs per pertbs tbs.. êrtbkte, e herrgte ã hekjghhcekbr b hobvg pgfe hcfckmre mb c`kcàèe, hektume sg jer hekjghhcekbr b hobvg hobv g pgfb pertb mgvgrâ mgvgrâ bhrgshgkt bhrgshgktbr br bs hbvbs jbftbktgs, qug sgrâ gksckbme dbcs bmcbktg. Ke hbse mes butedøv butedøvgcs gcs @efj, Bumc,c, êf Bum êfe e g ^bs ^bssbt sbt,, qug pes pessug sugd d hobvgs hobv gs pbkt pbkte`râj e`râjchbs, chbs, bs ùcfoe ùcfoetckbs tckbs CKX]C]W]E WKCZG\XBF L\BXCFGC\E

kudgrbmbs mg 2 b = tbdl kudgrbmbs tbdlãd ãd prepc prepchcbd hcbd qubtre qub tre pre prejuk jukmcm mcmbmg bmgss mg hbv hbvbs bs b sbl sblgr gr.. (Jcùrb
2 < 8 =

4 4 4 4

Elsgrvbàèe Bfãd mg kudgrbmbs mg 2 b = gssbs ùcfoe ùc foetckb tckbs s pem pemgd gd sgr hefe hefercmb rcmbs. s.

(Jcùrb =).

>,> > ,> dd >,: dd >,: 2,< dd 2,< 2,? dd 2,?

Ke Ke Ke Ke

2 2

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8

2 < 8 =

4 ( Zgrdgfo Zgrdgfob) b) >,> >,> dd 4 (^rgtb) (^rgtb) >,: >,: dd 4 (^rbtb) (^rbtb) 2,< 2,< dd 4 (Bdbrgfb) (Bdbrgfb) 2,? 2,? dd

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8

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Jcùrb <-B - Hobvg pbkte`râjchb tgd hbvbs fb-tgrbcs

E kù kùdg dgre re mg sg sg`r `rgm gmes es me hcfckmre mg c`kcàèe g me sg`rgme mbs pert pe rtbs bs ã e dg dgsd sde, e, eu sgib, sgib, bdles bdles utcfczbd utcf czbd qub qubtre tre ùc ùcfoet foetckb ckbss kb pbr pbrtg tg supgrcer supgr cer g qubtre ùcfoetckb ùcfoetckbss kb pbrtg ckjgrcer me hbkoèe. ^brb dgfoer hedprggksèe, bs ùcfoetckbs qug sèe utcfczbmbs kb jerdbàèe me sg`rgme sèe bs qug gstèe rgprgsgktbmbs kb jcùrb 8.

Jcùrb 8 - @ucfoetckbs me scstgdb pbkte`râjche.

Mb fckob @D (@gkgrbf Deters) es hb hbrr rres es He Hers rsb, b, De Dekz kzb, b, Ab Abmg mgt, t, Bstrb, Bstr b, Hgf Hgftb tb g bck bckmb mb eut eutres res but butedø edøvgc vgcss qug sg utcfczbd me dgsde hcfckmre, e sg`rgme ã jgcte hed qubtre ùcfoetckbs mg bft ftu urb ‖x— mc mcjjgrg rgk ktg tgss g qug preperhcekbd preper hcekbd qubtre prejuk prejukmcmbmg mcmbmgss pbmrekczbmbs mg hbvbs b sblgr. Es bute ted døvg vgcs cs mb fcfck kob @gkgrb @gk grbff Det Deters ers pe pessu ssugd gd mgz (2> (2>)) ùcfoetc ùcf oetckbs kbs jerd jerdbkm bkme e e sg` sg`rgm rgme e mb c`kcàè c`k càèe e g sg sgtg tg (0) ù ùcfo cfoet etckb ckbss ke kess hcfcfckm hc kmre ress mb mbss pe pert rtbs bs.. ê êrt rtbk bkte te,, ã bheksgfoâv bheks gfoâvgf gf hekjg hekjghhcek hhcekbr br b hobv hobvg g pgfe hcfckmre mb c`kcàèe. HW\XE MG HOBZGC\E ‘ BWFB :

Jcùrb = - Demgfe mbs qubtre ùcfoetckbs mes Jcùrb hbrres mb @gkgrbf Deters.

Es bu bute tedø døvg vgcs cs Ed Edg` g`b b g Zghtrb pessugd hobvgs pbkte`râjchbs qug qu g utc utcfcz fczbd bd hck hckhe he ùc ùcfoe foetck tckbs bs mg bfturbs ‖x— mcjgrgktgs kudgrbmbs mg 2 b 7. (Jcùrb 7). Gstb ã udb hobvg cdpessävgf mg sgr gxghutbmb b dèe. Ã kghgssârce pessucr pess ucr ud hemcjchbmer pbrb qug b hobvg hob vg pes pessb sb sgr hek hekjgh jghhce hcekbm kbmb b kb dâquckb pbkte`râjchb. E hemcjchbmer ã ud mcspesctcve, qug kes pgr pgrdct dctg g trb trbàbr àbr,, btr btrbvã bvãss mg pgqugk pgq ugkbs bs gk` gk`rgk rgkb`g b`gks, ks, e pgr pgrjcf jcf mb hobvg, pgfes kùdgres mbs ùcfoetckbs. êrr gx ê gxgd gdpf pfe, e, vb vbde dess su supe perr qu qug g e sg`rgme mb hobvg sgib jerdbme pgfbs sgùcktgs ùcfoetckbs 2, 8, <, = g 7.

Bsscd, devcdgkt devcdgktbkme-sg bkme-sg bs gk`rgkb`g gk`rg kb`gks ks me hemcj hemcjchbme chbmerr qug sèe kudg ku dgrb rbmb mbs, s, pbr brb b bf bfck ckob obrr gs gssb sb kudgrbàèe 2, 8, <, = g 7, vbdes eltgr e pgrjcf mb hobvg. Fgvbme Fgv bme gss gssg g hem hemcjchb cjchbmer mer ke derm rmg gktg mcr crg gct cte e mb dâ dâq quck ckb b pbkte`râjchb (fbme me ùcb) gfg sgrvcrâ mg de demg mgfe fe pb pbrb rb b hø høpc pcb b mb ho hobv bvg. g. (jcùrb :). Kb fcfcko kob b Je Jerm rm,, es vg vgäh ähuf ufes es Herhgf Her hgf CC, Mgf Mgf-\g -\gyy, Lgf Lgfckb ckb,, ^bd ^bdpb pb g Hbdc Hb dcko koèe èe sè sèe e es ùk ùkch ches es hu huie iess sg`rgm sg` rgmes es mes hcfc hcfckmr kmres es mb c`k c`kcàèe càèe,, pertbs g mgdbcs sèe me scstgdb Sbfg hekvgk hek vgkhce hcekbf kbf,, eu sgi sgib, b, e scs scstgd tgdb b mg sg`rgm sg` rgme e ã jer jerdbm dbme e per pck pckes es sg` sg`rgm rgmes, es, hektrb pckes (tcpe hepckoe) g defckobs hekjerdg iâ gxpfchbme bktgrcerdgktg. B qubktcm qubktcmbmg bmg mg pckes mes hcfckmres mg c`kcàèe g mbs pertbs ã e dgsde dg sde,, pe pertb rtbkte kte,, b he hekjg kjghà hàèe èe mb hobvg pemg sgr jgctb per qubfqugr ud mes hcfckmres. Es butedøvgcs9 Gshert, Zgrekb g Zgr grsb sbfg fgss ut utcfc cfczb zbd d qu qubt btre re bf bftu turb rbss ‖x ‖x—— mg ùcfoetckbs, b sblgr9 K¹ K¹ K¹ K¹

2 < 8 =

4 4 4 4

>,> > ,> dd >,7 dd >,7 2,> dd 2,> 2,? dd 2,?

Dbcs mgtbfogs selrg b hekj he kjgh ghàè àèe e mb ho hobv bvg g pb pbrb rb gs gssg sgss butedøvgcs sgrèe mbmes dbcs bmcbktg, qubk qu bkme me bl bler ermb mbrd rdes es e bs bssu sukt kte9 e9 butedøvgcs mb Bute Fbtckb (Wkcèe mb dektbmerb Jerm g Zefaswb`gk) bpøs e bke mg 233< btã bprexcdbmbdgktg e bke mg 233:.

Jcùrb 7 - @ucfoetckbs me Edg`b g Zghtrb.

8

CKX]C]W]E WKCZG\XBF L\BXCFGC\E

HEKJGHÀÈE HEKJGHÀÈ E MB HOB HOBZG ZG ^B\B BW]EDØZ BW]EDØZGCX GCX

Jcùrb : - Hemcjchbmer mb pbkte`râjchb mb @gkgrbf Deters.

Kb fckob Jcbt, hede iâ jec mcte kb fcàèe selrg bs trbvbs mg mcrgàèe, e hbkoèe pessuc bs ùcfoetckbs trbvbmbs e qu qug g ke kess cd cdpg pgmg mg mg uk ukcj cjch chbr br e sg`rgme. êrtb êr tbkte kte,, b sul sulstc stctuc tucàèe àèe mes hcfckmr hcfc kmres es mb c`k c`kcàè càèe, e, per pertbs tbs g per pertb tb-dbfb db fbs, s, ã rg rghe hedg dgkm kmbm bme e pbr brb b es butedøvgcs Wke, ^rédce g Gflb. E qug pemg sgr jg jgct cte e ã b hekjgh hek jghàèe àèe mb hob hobvg vg pgfe sg` sg`rgm rgme e hede vgrgdes b sgùcr. Ke hbse mes butedøvgcs ^bfce, ]cpe, ]gdprb, Xcgkb, Dbrgb g Lrbvb, qug tbdlãd pessugd bs ùcfoetckbs mes hcfckmres trbvbmbs, hede ke hbse me Wke Wke,, per perãd, ãd, mg jer jerdb db mcjg mcjgrgk rgktg. tg. Wdb vgz qug kèe pgrdctgd tbdlãd qug sg jbàb b ukcjchbàèe me sg`rgme. ]bkte cste ã vgrmbmg, qug be hedprbr e Act mg hcfckmre kbs hbsbs mg butepgàbs, ke hbse me Wke, e dgsde pessuc qubtr tre e pgàbs gkqu gk qubk bkte te qu qug g es mg mgdbc dbcss hb hbrre rress pessugd hckhe pgàbs. (Jcùrb 0). HW\XE MG HOBZGC\E ‘ BWFB :

Es hbrr rre es mb fcfck kob Jc Jcb bt utcfc ut cfczb zbd d tré tréss bf bftu turb rbss ‖x ‖x—— pb pbrb rb bs ùcfoetckbs, b sblgr9 Ke 2 4 >,> >,> dd e K < 4 2,> 2,> dd Ke 8 4 < <,> ,> dd

Bsscd, b dgfoer sefuàèe ã hekjgh hek jghhce hcekbr kbr b hob hobvg vg pgf pgfe e sg` sg`rgm rgme e hede vgrgdes feè dbcs.

Xèe me Xèe mecs cs es tctcpe pess mg ho hobv bvgs gs utcfczbmes, pgfb ckmùstrcb butedelcfästchb. ^rcdgcre, b hobvg qug gktrb ke hcfcfckm hc kmre re gd ud udb b ùkchb ùkchb pesc pescàèe àèe, g sgùkme b hobvg qug gktrb ke hcfckmre qubfqugr pesc pescàèe àèe. Ke pr gd qubfqugr prcd cdgc gcre re hbse gxcstgd mecs sg`rgmes mcjgrgktgs gkqubk gkq ubkte te ke sg` sgùkm ukme, e, es sg` sg`rgm rgmes es sèe cùbcs. (Jcùrb ?). B hekjghàè hekjghàèe e mg bdlbs, bs hobv ho bvgs gs tb tbdl dlãd ãd ã mc mcjg jgrg rgkt ktg. g. Ke prcdgcr prc dgcre e hbs hbse e pb pbrb rb hek hekjghh jghhcek cekbr br b hobvg sgùg-sg e dgsde prehgsse mg udb hobvg Sbfg mupfb, eu sgib, jbz-sg ud fbme, vcrb-sg b hobvg g jbz-sg e eutre fbme. (Jcùrb 3). Ke sg sgù ùkm kme e hb hbse se,, ã pr prgh ghcs cse e jbzgr b hobvg gd mubs gtbpbs mg hbmb fbme mb hobvg. Bsscd, jbz-sg ud fbme kcvgfbkm kcvg fbkme e bs ùcf ùcfoet oetckbs ckbs sup supgrce grcergs rgs.. Dbktgk tgkme me-sg -sg b ho hobvg bvg (Jcùrb (Jc` urb 2>). Dbk prgs pr gsb b kb de ders rsb, b, `c `crb rb-s -sg g e hb hbko koèe èe,, cktremu cktr emuzck zckmeme-e e kb hob hobvg. vg. Hed css csse, e, pemgdes ketbr qug bs ùcfoetckbs mes sg`rgm sg` rgmes es `éd `édges ges,, kèe jbz jbzgd gd ‖fck ‖fckob ob zgre—. êrtbkte, mgvgdes bfbr`br bs hbv hbvbs bs pb pbrb rb gss gssgs gs sg` sg`rgm rgmes es `édges. (Jcùrb 22) .

Jcùrb 0 - Ieè hedpfgte mg hcfckmres me ^bfce.

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2¹ XG@\GM XG@\GME E

XG@\GMEX C@WBCX

<¹ XG@\GME

XG@\GMEX C@WBCX

Jcùrb ? - Hobvg hed sg`rgmes mcjgrgktgs g hobvg hed e dgsde sg`rgme.

2¹ FBME MB HOBZG ^\EK]E

Jcùrb 3 - Hekjghàèe mg hobvg hed sg`rgmes mcjgrgktgs.

Hekjghhc Hekjg hhcek ekbm bme e ud fbm fbme e mb hobv ho bvg g tg tgde dess mu mubs bs ep epà÷ à÷gs gs pb pbrb rb hekhfuä-fe. B prc prcdgc dgcrb rb epà epàèe èe ã rgp rgpgtc gtcrr bs mubs mu bs ep epgr grbà bà÷g ÷gss pb pbrb rb jb jbzg zgrr e eu eutre tre fbme, eu, e qug ã dbcs hekvgkcgktg, usbr gssg fbme mb hobvg hede demgfe fgvb fg vbkm kmee-b b b he hepc pcbm bmer erb b g bs bssc scd d hekjgh hek jghhce hcekbr kbr gd eut eutrb rb hob hobvg vg vcr vcr`gd `gd es mecs fbmes. E qug bhektghg sg kèe jczgrd jcz grdes es gst gstb b hob hobvg vg he hed d bs mub mubss epgrbà÷gs pbrb hbmb fbme5 Hbse sg sgib ib jgc gcttb he hed de kb prcdgcrb sctubàèe, jbz-sg ud fbme, vcrbsg e hbkoèe hed b hobvg g jbz-sg e eutre eut re fbm fbme. e. B hob hobvg vg crâ juk jukhce hcekbr kbr kb pescàèe ckchcbf. Xg vcrbr b hobvg g hefehâ-fb ke hbkoèe vgrcjchbrâ qug bs ùcfoetckbs jchbd fgvbktbmbs trbvbkme e hbkoèe, pertbkte pert bkte b hobv hobvg g kèe crâ jukh jukhcekb cekbr. r. Bfcâs,, gssg preh Bfcâs prehgsse gsse sgrâ vcste kb hekjghàèe ^bsse b ^bsse mb hobvg. (Jcùrb 2<).

^B\]CHWFB\CMBMG

@ucfoetckbs mes sg`rgmes `édges Jcùrb 2> - Hekjghàèe mg hobvg hed sg`rgmes cùbcs.

E s b ut ut e dø dø vg vg c s m b B ut ut e Fbtckb, tbcs hede9 Feùs, Gshert, Zgrekb, Zgrsbffgs, Xbktbkb, @efj g bc bckm kmb b eu eutr tres es he hede de De Dekz kzb b g A bm bm gt gt t b pø pø s e b ke ke m g 2 33 33 <, <, utcfczbd kes hcfckmres mbs pertbs ud hbk hbkoèe oèe lcp lcpbrt brtcme cme,, eu sgi sgib, b, mcvcmcme gd mubs pbrtgs.

Bfbr`br bs hbvbs mbs ùcfoetckbs `édgbs. hbvbs dbcs fbr`bs

Jcùrb 22 - Hbvbs pbrb ùcfoetckbs `édgbs.


7


Hobvg jukhcekb kerdbfdgktg

Hobvg vcrbmb jbz bfckobdgkte mbs ùcfoetckbs mes sg`rgmes `édges

Jcùrb 2< - Hobvg jukhcekb kerdbfdgktg/ Hobvg kèe jukhcekb.

Gssb pbrtchufbrcmbmg, sgùkme sgus cmgbfczbmergs, sgrcb bktc-dchob. Dbs cste rgbfdgktg kèe eherrg. E dbcer prelfgdb qug bhektghg kgstg hcfck hc fckmr mre e ã b qu qugl glrb rb mb ho hobv bvg g kb fc` fc`bà bàèe èe gktrg es mecs pgmbàes, jchbkme b pektb mb hob hobvg vg ke ckt cktgr grcer cer me sg sgù ùkme kme gstâ`ce me hbkoèe kèe pgrdctckme sub rgde rg deàè àèe, e, sg sgd d b mg mgsd sdek ektb tb`g `gd d me hcfckmre. (Jcùrb 28). Kes but butedø edøvgc vgcss qug utc utcfczb fczbd d gstg gs tg tctcpe pe mg hc hcfcfckm kmre re kb kbss pe pert rtbs bs,, bheksg bhe ksgfob fobdes des jbz jbzgr gr b hob hobvg vg pgf pgfe e hcfckmre mg c`kcàèe.

Dbs qubkme pessucr b hobvg quglrb qug lrbmb, mb, kèe rgs rgstb tb eut eutrb rb bft bftgrk grkbtcv btcvb bb kèe sgr mgs mgsdek dektbr tbr e hcf hcfckm ckmre re pb pb-rb -rb rgtcr rg tcrbr br e pg pgmb mbàe àe qu qug g jcjche heu u ke ck cktg tgrc rcer er me sgùkme gstâ`ce me hbkoèe. Cdpertbktg B hobvg qubkme quglrb, ã perqug es mecs mgktgs qug fc`bd bs mubs pbrtgs pbr tgs,, qug quglre lreu u ter terkb kbkme kme-es -es ckmgpgkmgktgs. Feè kèe jukh jukhcek cekb b hed hede e udb kevb hobvg, perqug gstb kèe vbc bt ã e j ck ck bf bf m e hb ko ko èe èe g k gd gd rgbf c zb b u k cèe m e s m e cs pgmbàes mb hobvg.

Be sg mgs mgsdek dektbr tbr gst gstg g hcf hcfckm ckmre re pbrb pb rb rg rgde devg vgrr e pg pgmb mbàe àe mb ho hobv bvg g bheksgfob-sg b sulstctucàèe me hbkoèe perr ud ck pe cktg tgcr crcà càe e qu qug g ã jb jblr lrch chbm bme e pb pbrb rb es mcvgrses butedøvgcs. (Jcùrb 2=). B mgs mgsdek dektb` tb`gd gd mgs mgstg tg hcf hcfckm ckmre re kèe kè e ã jâ jâhc hcff mg sg sgrr rg rgbf bfcz czbm bmb, b, pe pecs cs gkqu gk qubk bkte te b db dbce cerr pb pbrt rtg g me mess hc hcfck fckmr mres es mg butedø but edøvgcs vgcs sèe trbv trbvbme bmess per pck pcke e trbvb, bkgf gfâstche, defb mg prgssèe g bckm bc kmb b eu eutr tres es dg dghb hbkc kcsd sdes es qu qug g pgrdc pg rdctgd tgd su sub b rgd rgdeà eàèe èe he hed d hgr hgrtb tb jbhcf jb hcfcm cmbm bmg, g, kg kgst stg g tcp tcpe e mg hc hcfck fckmr mre, e, pe perr sg sgr r e hbk hbkoèe oèe lcp lcpbrt brtcme cme,, b trb trbvb vb sct sctubub-sg sg cktgrk ckt grkbdg bdgktg ktg î hb hblgà lgàb b pfâ pfâstc stchb hb me hcfckmre. (Jcùrb 27). ^brb ^b rb rg rgde devg vgrr e hb hbko koèe èe,, gd vcstb vcs tb mgs mgstb tb trb trbvb, vb, mgv mgvgde gdess bqu bqughg ghgr r gssb hblgàb pfâstchb pbrb jbhcfctbr sub sbämb, jeràbkme-e gd udb dersb.(Jcùrb 2:). êrãd, sg hbse kèe jer rgbfczbme e prehgsse mg bqughcdgkte mb hblgàb pfâstchb, e hbkoèe tgrâ sub sbämb jeràbkme-e. Hede gssb trbvb jchbrâ ckutcfczbmb, pecs hed b sulstctucàèe me hbkoè hb koèe e per eut eutre re ckt cktgcr gcrcàe càe,, b trb trbvb vb pbssb b sgr e bkgf gfâstche qug prgkmg tbdlãd b bfbvbkhb mg bhcekbdgkte.

Bfbvbkhb cdpufserb

Hbkoèe mcvcmcme

<ª dgtbmg

2ª dgtbmg

Jcùrb 28 - Hcfckmre hed hbkoèe lcpbrtcme.


:


Jcùrb 2= - ]cpes mg hbko÷gs pbrb sulstctucr es lc-pbrtcmes.

Hcfckmre mb pertb

Ke cktgrc cktgrcer er tgd udb trbvb trb vb pfâ pfâst stchb chb qu qugg kèe pgrdctg pgrdctg b sbämb sbämb me hbkoèe.

êmg eherrgr pgqug-kes mbkes ke cktgrcer me herpe me hcfckmre, e qug kèe sgrâ prgiumchcbf pbrb b dektb`gd. êrtbkte, e dgfoer ã gvctbr mg hekjghhcek hekjg hhcekbr br b hobvg pgfes hcfckm hcfckmres res mbs pertbs g pertb-dbfbs, perãd sg jer ckgvct ckg vctâv âvgf gf tbf pre prehg hgsse sse e dgf dgfoer oer ã sgù sg ùcr cr e pre prehg hgmcd mcdgk gkte te mb sg sgù ùckt cktg g dbkgcrb9

Jcùrb 27 - Hcfckmre hed hbkoèe lc-pbrtcme.

Ã prghcse gstbr hed b hobvg ke hcfckmre

Zcstb mg fbme

Jcùrb 2: - Hede prgksbr e hcfckmre pbrb rgdevgr e hbkoèe.


0


2ª Dbrq Dbrqug ug b pe pesc scàè àèe e mb mbss

Hekjerdg iâ gksckbme, cste mgvg sgr jgcte jgct e tbd tbdlãd lãd pb pbrb rb bs hbv hbvbs bs mup mupfbs fbs (sg`rgmes `édges). êmgdes tbdlãd hekjghhcekbr b ho hobv bvg g pg pgfb fb tã tãhk hkch chb b gk gksc sckb kbmb mb ke Bk Bkgx gxe e Gspghcbf. Hekhfu Hek hfuämb ämbss tem tembs bs bs hbv hbvbs bs gstâ prektb b hobvg mb pertb, qug hed hgrtgz hgr tgzb b crâ juk jukhce hcekb kbrr kb kbss mgd mgdbcs bcs jghobmurbs me hbrre, hed gxhgàèe me hcfckmre mg pbrtcmb. (Jcùrb <>). Ke hcfckmre mg pbrtcmb b qubktcmbmg mg ùcfoetckbs ã dbcer, pecs pess pe ssuc uc kb pb pbrt rtg g ck ckjg jgrce rcerr e dg dgsd sde e kù kùdg dgre re mg ùcfoetckbs herrgspekmgktgs î pbrtg supgrcer.

ùcfoetckbs supgrcergs mes hcfckmres 2, <, 8 , = g 7. Bpøs b dbrhbàèe dbrhbàèe,, elsgrvg qug bs hbvbs <,= g 7 vèe sgr mupfbs, pecs pe cs he herrg rrgspe spekm kmgd gd be bess sg` sg`rg rgmes mes `édges. (Jcùrb 20).

<ª Gd sgùcm sgùcmb b db dbrqu rqug g bs hbvbs mbs ùcfoetckbs ckjgrcergs, (mubs ke hbse) : g 0. (Jcùrb 2?).

8ª ]rbkspertg gssb dbrhbàèe pbrb b pbrtg supgrcer mb hobvg :B g 0B. (Jcùrb 23). =ª Jg Jgctctb b b db dbrh rhbà bàèe èe he hefe fequ qug g bs ùcfoetckbs udb b udb, vâ fcdbkme bs hbvbs, btã qug jcqugd tembs rgktgs î supgrj sup grjähc ähcg g me hbk hbkoèe oèe (‖fc (‖fckob kob zgr zgre—) e—)..

2

<

8

=

7

Jcùrb Jcùr b 20 - Dbrhbs mbs hbvbs supgrcergs.

<

2

8

=

7

:

Kgstg hbse ã prghcse rgpgtcr bs hbvb hb vbss mb mbss ù ùcfo cfoetc etckbs kbs su supgr pgrcer cergs gs tbdlãd pbrb bs hbvbs mbs ùcfoetckbs ckjgrcergs. Gstb epgrbàèe, ke gktbkte, pemgrâ sgr jgctb kb hepcbmerb, hede sgrâ bprgsgktbme ke ^bsse b ^bsse Gspghcbf. (Jcùrb <2). Hed He d cs cstte hekhfu fuäd äde es es gstumes selrg es mcjgrgktgs hcfckmres utcfczbmes pgfbs dektbmerbs gd sgus butedøvgcs buted øvgcs.. Bktgs mg gxpfc gxpfchbrde hbrdess b hekjghàèe mbs hobvgs mg butedøvgcs ã cdpertbktg e bfuke tgr hekoghcdgkte mâ gxcstékhcb mg udb jgrrbdgktb qug pgrdctg jbzgr b hobvg pgfe hcfckmre mb pertb gd qubfqugr fehbf. Dgsde hed bs per pertb tbss me but butedø edøvgf vgf trb trbkhb khbmbs mbs,, kèe ã kghgssârce, blrc-fbs kgd rgtcrbr es hcfckm hcf ckmres res,, mcs mcspg pgksb ksbkm kme, e, pe pert rtbkt bkte, e, jgrr jg rrbd bdgk gktb tbss mg bl blgr grtu turb rb.. Gs Gstb tb jgrr jg rrbd bdgk gktb tb ã hobdb hobdbmb mb mg Hobvg ^bquädgtre. Hed He d b ho hobv bvg g pb pbqu quäd ädgt gtre re pemg pe mgde dess mg mgtgr tgrdck dckbr br bs dg dgmcm mcmbs bs gxbtbs mb bft ftu urb ‖x ‖x—— bs qubcs mgtgrdckbd b prejukmcmbmg mbs hbvbs mbs hobvgs pbmrekczbmbs hekjerdg iâ gstumbme. B hobvg pbquädgtre tgd b jerdb mg udb hobvg, sgkme e pgrjcf mb obstg gxbtbdgktg cùbf be mb hobvg erc`ckbf. (Jcùrb <<). 2 - Hurser < - Bùfob mg bhcekbdgkte (bpbfpbmer) 8 - Fckob mg dgmcàèe me hurser = - Gshbfb 7 - ]rbàes mg rgjgrékhcb

0

Jcùrb Jcùr b 2? - Dbrhbs mbs hbvbs ckjgrcergs.

E hurser devg b bùfob mg 2

<

8

= :B

7

0B

bhcekbdgkte (bpbfpbmer) qug gstâ b gf g

j c xbmb

pbrb

f gvbktbr

bs

ùcfcfoe ù oetc tckb kbss g bs bssc scd d je jerk rkgh ghgr gr b prejukmcmbmg mbs hbvbs btrbvãs mb fckob mg dgmcàèe me hurser, ckmchbmb kb gshbfb. (Jcùrb <8).

Jcùrb 23 - ^bssbkme b dbrhb mbs ckjgrcergs prb iukte mbs supgrcergs.


?


2

<

8

=

:B 7

0B

0

:

Jcùrb <> - Hobvg prektb pbrb jukhcekbr gd tembs bs jghobmurbs me hbrre, dgkes kb c`kcàèe.

Jcùrb <2 - Hobvg jukhcekb gd tembs bs jghobmurbs g kb c`kcàèe.

Fckob mg dgm Fckob dgmcàè càèe e ckm ckmchb chbkme kme e zgre zg re mb gs gshb hbfb fb b b` bùf ufob ob bv bvbk bkàb àb.. Kb prâtchb qubkme gssb bùfob vbc tedbkme bfturb bft urb mb ùcfoetckb foetckb,, ekm ekmg g gfb pbr pbrbr br,, b gshbfb ckmchbrâ e vbfer mb prejukmcmbmg mb hb hbvb vb dg dgmc mcmb mb.. Es trbàes mg rgjgrékhcb ckmchbd qug qu g b pe pescà scàèe èe mb ho hobv bvg g pb pbqu quäd ädgt gtre re mg mgvg vg jchbrr kb gkt jchb gktrbm rbmb b me hcfckmre kmre pb pbrb rb dgm dgmcr cr mgtgrdckbmb mgtgr dckbmbùcfoe ùcfoetckb. tckb. êr gxgdpfe, hefehbkme b hobvg pbquäd pbq uädgtre gtre pes peschce chcekbm kbmb b ke trbà trbàe e mg rgjgrékhcb B, b bùfob crâ dgmcr b ùftcdb ùcfoetckb B. Ke hbse mgstg gxgdpfe b ùcfo ù cfoet etck ckb b dg dgmc mcmb mb ã b kù kùdg dgre re = qu qug g herrgspekmg b udb hbvb mg 2,?dd mg prejukmcmbmg. K b J c ` u r b < = gstbdes mgdekstrbkme e prehgmcdgkte mb fckob mg dgm dgmcàè càèe e rgb rgbfczb fczbkme kmegss gssb b epg epgrbà rbàèe èe kb gshbfb. 2 - Hurser

= - Gshbfb

E

< - Bùfob mg bhcekbdgkte

8 - Fckob mg dgmcàèe

7 - ]rbàes mg rgjgrékhcb

Jcùrb << - Hobvg pbquädgtre.

Bùfob mg bhcekbdgkte

Fckob mg dgmcàèe

Jcùrb <8 - Bùfob qug dgmg bs ùcfoetckbs.


3


Fcdctg me ]bdle ]bdlerr @ucfoetckbs B

L

H

M

G

=

2

8

<

8

G

J Bùfob mg bhcekbdgkte mbs ùcfoetckbs

M

H

L

B

@

]rbàes mg rgjgrékhcb

Jcùrb <= - Hobvg pbquädgtre dgmckme b qubrtb ùcfoetckb.

Xg pes peschc chcek ekbrd brdes es b ho hobvg bvg pbquädgtre ke trbàe mg rgjgrékhcb L , gfb crâ dgmcr b ùcfoetckb L, g bsscd suhgsscvbd suhgs scvbdgktg gktg btã b ùcfo ùcfoetckb etckb M. Bhedpb Bhe dpbkob kob b hob hobvg vg pbq pbquäd uädgtr gtre, e, ud `blbrcte hed e pbsse mbs ùcfoetckbs. Hed gfg dbrhbdes b pescàèe mbs mcvgrsbs mcvgrsbs hbv hbvbs bs qug mgvgd sgr jgctb jgc tbss kb hob hobvg vg.. (Jcùrb (Jcùrb <7). Xèe vârc rce es es demgfe fess mg hobvgs pbquädgtre, pbrb es mcvgrses demgfes mg hbrres g dektbmerbs. Be bmq bmqucr ucrcrcr qub qubfqu fqugr gr dem demgfe gfe vehé rghglgrâ ud dbkubf hed tembs bs ckjerdbà÷gs g jerdb mg dbkusgbr hbmb udb. Es mb mbme mess bq bquc uc je jerk rkgh ghcm cmes es lg lgd d hede bs cfustrbà÷gs jerbd utcfczbmbs tgkm tg kme e he hede de lb lbsg sg e db dbku kubf bf me jblrchbktg @efm.

BLG\]W\BX Bfãd mbs jgr Bfãd jgrrbd rbdgkt gktbs bs ker kerdbc dbcs, s, bs fìdckbs hed hbvbs mupfbs jcùrb <:, sè sèe e du ducte cte ut utcfc cfczb zbmb mbss kb bl blgr grtu turb rb mg butedøvgcs qug btubd mcrgtbdgktg ke dghbkcsde cktgrke mbs pertbs. Gstbs jgrr jg rrbd bdgk gktb tbss bp bpgk gkbs bs pe pemg mgd d sg sgr r bmq bm qucr crcm cmb bs per prejc jcsssc sce ekbcs oblcfct obl cfctbme bmes, s, hed jcrd jcrdb b rg` rg`cstr cstrbmb bmb g buterc but erczbm zbmb b b juk jukhce hcekbr kbr ke rbd rbde e mg hob ho bvgcr cre e. Bhe hed dpbkob gss ssb bs jgrrbdgktbs dbkubcs mg hede utcfczâfbs. (Jcùrb <0).

2¹ Hbmb Hbmb mcs mcshe he pes pessuc suc udb ud b hb hbvb vb pe perr ek ekmg mg mg mgvg vg pbs bssb sbrr es mgktgs mgk tgs mb obs obstg1 tg1

Jcùrb <: - Fìdckb mupfb pbrb blgrturb mg jghobmurb mg butedøvgcs.

HBMGBMEX HED XG@\GMEX

Jcùrb <7 - @blbrcte.


prehgmcdgkte qug pemg sgr sefchctbme be hobv ho bvgc gcre re,, ã su sub b bl blgr grtu turb rb qu qubk bkme me mgshekogh mgsh ekoghcme cme e sg`rg sg`rgme. me. Hede mcssgdes, es hbmgbmes hed he d sg sg`rg `rgme me kè kèe e utc utcfcz fczbd bd ho hobv bvg, g, pertbk per tbkte, te, kèe pes pessug sugd d hek hekiuk iukte te mg pcke pc kess sg sg`r `rgm gmes es,, he hekt ktrb rb pc pcke kess g defckobs. E hbmgbme ã hedpeste9 ^gfe herpe, obstg, hekiukte mg mcshes, pckes g defbs hefehbmes gd hbkbcs ke herpe, qug jukhcekbd hede jrgce mes mcshes pbrb qug kèe `crgd hed he d jb jbhc hcfcfcmb mbmg mg pr prgi gium umch chbk bkme me b hekjghàèe me sg`rgme g bkgf trbvb mb obstg. (Jcùrb
Gdlerb Gdle rb kè kèe e sg sgib ib ud mc mcsp spes esctc ctcve ve mgsgùr mg sgùrbkàb bkàbcktgrg cktgrgssbk ssbktg tg be beprejcss prejcsscekbf cekbf hobv ho bvgc gcre re,, iâ qu qug g kè kèe e pe pess ssug ugd d ho hobv bvgs gs,, g scd ud dghbkcsde ducte scdpfgs qug mcjchcfdgkt hcfdgktg g kgh kghgss gssctb ctbmg mgrgp rgpbre bres. s. E ùkche he 2>

<¹ ^brb csse ã prghcse bfckoâ-fbs1

sg`rgm rgme e bhe bhektg ktghg hg 8¹ E sg` qubkme qub kme pes peschce chcekbd kbdes es es mcs mcshes hes (Jcùr ùrbb <3). kb mcr mcrgà gàèe èe mb sg sgtb tb.. (Jc


OB >> >>2= 2=

OB >>23

@cre Fcvrg pbrb tbdpb mg hed-lustävgf

Brbdg Jehus

Abkèe

]eyetb Hbrdy/ \bv-= Kcssbk Dbxcdb

Acb Xgpocb/ Xu-zcac/ Oekmb/ Csuzu/ Dgrhgmgs/ Dgrh gmgs/ Jerm cdp./ ]eyetb Ghoe/

OB >>< >>
OB >><7

@efj/ ^bssbt bfgdèe/ Fckob @ef `gr.fff

OB >>< >><3 3

OB >>8> Dgrhgmgs =<>/LDP sãrcg 7,0 g ?/ZP Lg-gtfg/ @efj 3?/ ZP Lu`/ ^bssbt 3>->>

]eyetb Hbrdy 30->>

LDP

OB >>27

OB >>< >><= =

OB >> >><8 <8

OB >>8< Dgrhgmgs 8>>/ Bumc/ Bhurb/ LDP/ Mbcobtsu/ Oekmb Bhherm, Hcvch/ Oyukmbc/ Xekbtb/ Dbzmb/ ^retg`g/ Dctsulcsoc/ @bfbkt/ Dcrb`g/ Kcssbk/ Dbxcdb/ Xgk-trb/ ]eyetb Hereffb/ Zefve/ ZP/ Lggtfg/ @efj/ Bhurb/ Oekmb ^bssbpert/ Csuzuf/ D^Z/ Kbvbie/ Kcssbk ^btocjckmgr g eutres

OB >>8 >>80 0

abmgtt/ Hogvgtg keve/ Dbzmb

OB >>< >><< <

OB >>2:

OB >>8=

Kcssbk ^btockmgr 37->>/ ]eyetb \bv- =3:->>
OB >> >>83 83

OB >>8 >>8? ?

Jcgstb/ Gshert keve/ Ab/ Feùs

Iggp Hogreagg/ @rbkm Hogreagg/ Fudckb g eutres

OB >>= >>=< <

Lerb/ @efj/ ^øfe

Hbrre tcpe- temes

OB >> >><0 <0

OB >><:

Oyukmbc/ Dctsulcscoc/ Kcssbk/ Jerm.cdp/ Hbrbvbk Horysfgr/ Dgrhgmgs 8>>

^bfce temes

OB >>82

]eyetb Hereffb 3?->>

OB >>87

Hurses ]emes

OB >> >>=> =>

]gdprb g ]cpe

OB >> >>88 88

J <7>/J87>

OB >>8:

@ef HFC

OB >>= >>=2 2

^bfce, Xcgkb, Xtrbmb

OB >> >>=8 =8

Hersb g Bstrb btã 3?/ Zghtrb g Edg`b btã 30

êrtb Dbfb Zghtrb/ Edg`b/ Feùs/

Jcùrb <0 - ]cpes mg jgrrbdgktbs pbrb blgrturb mg butedøvgcs.


22


Obstg

Mgktgs

Mcshes

Herpe

Defbs ^ckes Jrgces Bkgf ]rbvb Jcùrb Jcùr b
Kb rg rgbf bfcm cmbm bmg g e ‖s ‖sg` g`rg rgme me—— mgss mg ssgs gs hb hbmg mgbm bmes es ã bp bpgk gkbs bs ud kùdgre mgshekoghcme, qug pemg sgr mgtgrdckbme. Zehé pemg gstbr sg pgr` pg rùk uktb tbkm kme. e. G cs cste te kè kèe e ã sg sg`r `rgm gme5 e5 Xg hedpbrbme bes hejrgs,. kèe1 es hejrgs Hbvbs mg pbssb`gd mb obstg

hedlckbd hedlck bd tré tréss eu qub qubtre tre kùd kùdgre gres, s, qug sø pemgd sgr mgtgrdckbmes hed tãhkchbs g prehgmcdgkte fø`ches. Iâ kes hbm hbmgbm gbmes es pb pbrb rb mgt mgtgrgrdckbr dck br e ‖s ‖sg` g`rg rgme me—— ã sø sg sgù ùcr cr ud udb b sgqöékhcb kudãrchb qug vbc mg zgre b kevghgktes g kevgktb g kevg1 ke hbse mg hb hbmg mgbm bmes es he hed d tr trés és mc mcsh shes es ã mg zg zgre re b kevg dcf, kevghgktes g kevgktb g kevg, kev g, pb pbrb rb hbm hbmgbm gbmes es mg qub qubtre tre mcs mcshes hes.. Dbss se Db selr lrg g cs csse se jb jbfb fb-r -rgd gdes es db dbcs cs bmcbktg. R ub ubk me me s g b mq mq uc uc rg rg u d hbmgbm hbm gbme e bhe bhedp dpbko bkob b e dgs dgsde de udb ho hobp bpcko ckob b dg dgtâf tâfchb chb he hed d ud kùdgre `rbvbme, gstg ã e sg`rgme. (Jcùrb 8>) . Gstg ã e sg`rgme.

Jcùrb 8> - H o b p c k o b h e d k ù d g r e m e sg`rgme.

Jcùrb <3 - Hekiukte mes mcshes.


Bsscd sg peschc peschcekbrd ekbrdes es es mcshe mc shess je jerdb rdbkm kme e gs gssg sg kù kùdg dgre re kb mcrgàèe mb sgtb, bs hbvbs per ekmg mgvg mg vgrâ râ pb pbss ssbr br es mg mgkt ktgs gs mb ob obst stg g sgrèe bfckobmes, fclgrbkme b blgrturb. (Jcùrb 82).

2<


2 4 Mcshe mbs ukcmbmgs (> b 3) < 4 Mcshe mbs mgzgkbs (2> b 3) 8 4 Mcshe mbs hgktgkbs (2>> b 333)

8 < 2

Jcùrb 82 - Hede jbzgr e sg`rgme hed trés mcshes.

Ã pe pess ssäv ävgf gf du dumb mbrr e sg sg`r `rgm gme, e, eu dgfo dg foer er,, e kù kùdg dgre re gd qu qug g sg bl blrg rg gs gssg sg hbmgbme5 Xcd. G b jerdb mg rgbfczbr gstb gst b dum dumbkà bkàb b vgd ckm ckmchb chbmb mb kb prø prøprc prcb b gdlbfb`gd me hbmgbme. Rubk Ru bkte te b su sub b bl blgr grtu turb rb sg sgd d hekogh hek oghcdg cdgkte kte me sg` sg`rgm rgme, e, qug kes rgjgrcdes rgjgrc des bktgr bktgrcerdg cerdgktg, ktg, e ‖sg`r ‖sg`rgme— gme— gstâ gst â gkt gktrg rg udb sgq sgqöék öékhcb hcb kud kudãrc ãrchb hb qug e bfuke iâ mgvg tgr pgrhglcme qug kèe ã pessävgf mgtbfobr, pecs, trbtb-sg mg sg`rgme ckmustrcbf. Ã ud kùdgre qug gstâ gktrg e ‖zgre— g kevghgktes g kevgktb g kevg, eu kevg dcf, kevghgktes g kevgktb g kevg, jâhcf mg sgr mgshelgrte sgùckme b kudgrbàèe 2 2,, <, 8, =, ...2 ...2>, >, 22, 22, 2<, 28, ... 3>, ... 2>>, ...23>, ...<>>, g bsscd suhgsscvbdgktg btã bhgrtbr e kùdgre gd qug e hbmgbme blrg. Hedgàbdes per zgrbr es mcshes kb mcrgàèe mb sgtb. Mg lbcxe pbrb hcdb tgdes e mcshe mbs ukcmbmgs g mbs mgzgkbs, g tgrgdes e mcshe mbs hgktgkb hgktgkbss sg jer hbmgbme hbmgbme mg trés mcshes g mbs dcfobrgs sg jer mg qubtre qubtr e mcshes. mcshes. . ^brb gxgdpfcjchbr, vbdes super ud hb hbmg mgbm bme e mg tré tréss mc mcsh shes es hu huie ie e sg`rgme ã mgshekoghcme. HW\XE MG HOBZGC\E ‘ BWFB :

Hedgàbdes per zgrbr es trés mcshes. B sgùcr puxbkme b obstg ke sgktcme mb blgrturb `crbdes es mcshes mbss uk mb ukcm cmbm bmgs gs.. Hb Hbse se e sg sg`r `rgm gme e gstcvgssg gktrg zgre (>) g kevg (3) gfg iâ blrcrcb. Kèe blrcu. Zb Zbdes des devcd de vcdgkt gktbr br e mcs mcshe he mb mbss mg mgzg zgkbs kbs,, iuktbdgktg iuktbdg ktg hed e mbs ukcmbmgs ukcmbmgs..

Hedgàbdes Hedgàb des hed ekz ekzg, g, mez mezg, g, trg trgzg zg btã kevg ke vgkt ktb b g ke kevg vg.. Hb Hbse se je jess ssg g ud kùdg kù dgre re gk gktr trg g ek ekzg zg g ke kevg vgkt ktb b g ke kevg vg,, e hbmgbme blrcrcb. Kèe Kè e bl blrc rcu. u. He Hedg dgàb àbde dess b devc de vcdg dgkt ktbr br b` bèr erb b e mc mcsh she e mb mbss hgktgkbs, iuktbdgktg hed e mcshe mbs mgzg mg zgkbs kbs g mb mbss ukc ukcmb mbmg mgs. s. Xgd Xgdprg prg dbktgkme b obstg puxbmb ke sgktcme mg blrcr. Hedgàbdes hed e hgkte g ud, hgkte g mecs, hgkte g trés, hgkte g qubt qu btre re,, hg hgkt kte e g hc hckh khe, e, bt btã ã hgkte hgkte g hckqög hck qögktb ktb g sgc sgcss qub qubkme kme gfg blr blrcrâ crâ,, pecs gstg ã e kùdgre me sg`rgme me kesse gxgdpfe. (Jcùrb 88). Gstg Gst g pre prehg hgmcd mcdgkt gkte e pb pbrgh rghg g mgderbme, mgde rbme, dbs kèe ã. Bpøs ud peuhe mg trgckbdgkte, e bfuke vgrâ qug ke hbse hb se mg tré tréss mc mcsh shes es,, kè kèe e fg fgvb vbrâ râ db dbcs cs me qug 27 dckutes, sg e sg`rgme jer e ùftcde ùft cde kùd kùdgre gre,, kev kevghg ghgkte ktess g kev kevgkt gktb bg kevg1 g fgvbrâ 298>o (udb oerb g trcktb dckutes) sg jer e ùftcde kùdgre, kevg dcf, kevghgktes g kevgktb g kevg me hbmgbme mg qubtre mcshes.

Xg`rgme K¹ <.70:

Dcfobr 2.>>> b 3333 3333

(<)

Hgktgkbs 2>> b 333

(7)

Mgzgkbs 2> b 33

(0)

Wkcmbmgs > b 23

(:)

Jcùrb 8<- Hede jbzgr e sg`rgme hed qubtre mcshes.

28


Jcùrb 88 - Hede mgshelrcr e sg`rgme.

Gstg pre Gstg prehgm hgmcdg cdgkte kte vbf vbfg g pb pbrb rb bs pb pbstb stbss gxg gxghut hutcvb cvb,, her herrgk rgktgs tgs mg det dete e g mg lchchfgtbs, gth. Hede He de e bf bfuk uke e iâ mg mgvg vg tg tgr r pgrhg pg rhglcm lcme, e, gst gstg g hbm hbmgb gbme me gd kb kbmb mb bhrgshgktb ke jbturbdgkte mb ejchckb. êr gxgdpfe, sg e hfcgktg hog`br hed ud hb hbmg mgbm bme e mg qu qubt btre re mc mcsh shes es b mgderb mgd erb pgfe pgfe sgrvcàe sgrvcàe sgr sgrâ â `rbkmg, `rbkmg, e qug qu g cdp cdpfch fchb b ku kudb db he helrb lrbkàb kàb pg pgfb fb blgrturb mg ud vbfer ghekýdche bfte, mg trés eu qubtre vgzgs e vbfer me hbmgbme. HW\XE MG HOBZGC\E ‘ BWFB :

êr csse, bs vgzgs ã prgjgrävgf ercg er cgkt ktbr br e pr prep eprc rcgt gtâr ârce ce b bl blrc rcrr eu quglrbr b obstg g sulstctucr e dgsde per eutre hbmgbme.

HEJ\GX Es hejrgs `brbktgd b sgùrbkàb btrbvãs mbs trbvbs, sg`rgme g jghobmurbs. Hed csse, sgd mùvcmb bfùd bf` udb b g ckm ckmgp gpgk gkmgk mgktgd tgdgk gktg tg sg hedgrh hed grhcbf cbf,, ckm ckmust ustrcb rcbff (hb (hbse se mes mesdbc dbcerg ergs) s) eu rgscmgkhcbf (hbse mes mg gdlutcr) e hobv ho bvgcr gcre e ã se sefch fchctctbme bme he hed d bf` bfùdb udb 2=

jrgqöé jrgq öékh khcb cb b pr prgs gstb tbrr bf` bfùd ud tcp tcpe e mg sgrvcàe sgr vcàe,, prc prckhc khcpbf pbfdgk dgktg tg ke qug mcz rgspgcte î dumbkàb mg sg`rgme. Bktgs Bkt gs perãd mg ble blermb rmbrde rdess b pbrtg pb rtg tã tãhk hkch chb, b, ã cdp cdper ertb tbkt ktg g qu qug g es bfukes g jutures prejcsscekbcs tgkobd hekoghcdgkte mg qug kèe sg rgbfczb qubfqugr sgrvcàe gd hejrgs sgd qug e preprcgtârce eu rgspeksâvgf mgvc mg vcmb mbdg dgkt ktg g cm cmgk gktctcjcjchb hbme me gs gstg tgib ib prgsgk prg sgktg. tg. êrtbkt êrtbkte, e, kukhb kukhb gxg gxghut hutg g qubfqugr sgrvcàe gd hejrgs, sgd tgr b hgrtgzb hgrtg zb mb cmekg cmekgcmbmg cmbmg me sefchc sefchctbktg tbktg.. CKX]C]W]E WKCZG\XBF L\BXCFGC\E

Gd hb hbse se mg mù mùvc vcmb mb,, kè kèe e gx gxgh ghut utg g e sgrvcàe, eu, sg e gxghutbr gstg mgvgrâ eherrg ehe rrgrr kb prg prgsgk sgkàb àb eu hed pgr pgrdcs dcssèe sèe mg udb butercmbmg pefchcbf. Es hejrgs dbcs db cs he hedu duks ks gk gkhe hekt ktrb rbme mess ke kess gstb gs tblg lgfg fghc hcdg dgkt ktes es hedg he dgrh rhcb cbcs cs,, ckmustrcbcs g rgscmgkhcbcs ckmgpgkmgktg me tb tbdb dbko koe, e, pe pess ssug ugd d e dg dgsd sde e dghb dg hbkc kcsd sde e g b dg dgsd sdb b je jerd rdb b mg gxghut gxg hutbr br es dev devcdg cdgkte ktess me sgfg sgfgter ter pbrb jbzgr e sg`rgme qug pgrdctg b blgrturb me dgsde. E qug pemg vbrcbr kes hejrgs, ã b jg jgho hobm bmur urb. b. Ke Kess db dbcs cs bk bktctcè èss b jgho jg hobm bmur urb b us usbm bmb b gr grb b me sc scst stgd gdb b @er`g. Es btubc btubcss utcfczb utcfczbd d jghob jghobmurbs murbs tgtrbs, tgtr bs, g btã dgs dgsde de scs scstgd tgdb b mc` mc`ctb ctbf,f, qug je`g mb bfàbmb me hobvgcre. Rubk Ru bkme me b jg jgho hobm bmur urb b ã me scstgdb @er`g, `grbfdgktg pessuc sgcs (:)) è (: èr` r`gs gs pbr brb b b bl blgr grtu turb rb mb dg dgsd sdb bg kb hekjghàèe mb hobvg gdprg`b-sg e scstgdb scst gdb mg cdpr cdprgss gssèe èe iâ gks gksckb ckbme. me. Xgkme me scstgdb Sbfg, gd `grbf, bs jghobmurbs utcfczbmbs sèe bs dgsdbs gd døvgcs hedgrhcbcs g qug iâ jerbd gstumbmbs gd bufb bktgrcer. Ckmgpg Ckm gpgkmg kmgktg ktg me scs scstgd tgdb b mg jgho jg hobm bmur urb, b, es he hejr jrgs gs tg tgd d e dg dgsd sde e dghbkc dgh bkcsde sde g prc prckhä khäpce pce mg juk jukhce hcekbkbdgkt dg kte. e. Gd `grb `grbff es hejr hejrgs gs sèe sèe jghobm jgh obmes es per mec mecss sg` sg`rgm rgmes. es. E sg` sg`rgm rgme e mb ho hobv bvg g g e sg sg`r `rgm gme e me mess mc mcsh shes es qu qug gã hekscmgrbme e prckhcpbf. Gxcs Gx cstg tgd d he hejr jrgs gs bk bktc tcè èss g `rbkmg `rb kmgss qug pem pemgd gd pes pessuc sucrr btã tré tréss (8) sg`rgmes mg mcshes, pertbkte, hed trés sgfgtergs. Xèe rbres, dbs pemgd bpbrghgr.

Xgfgter

Jghobmurb

Zefbktg eu Dbàbkgtb Jcùrb 8= - Zcste mg jrgktg b pertb me hejrg.

ZGIBDEX E JWKHCEKBDGK]E MGX]GX MGX] GX DGHB DGHBKCXD KCXDEX EX

^brtg cktgrkb

Jgrrefoe, pgàb ekmg b tcrb me vefbktg vef bktg eu dbà dbàbkg bkgtb, tb, hek hekiukt iukte e me sg`rgm sg` rgme, e, hed hedpes peste te per tré tréss mcs mcshes hes,, bhcekbmes pgfe sgfgter g b jghobmurb. (Jcùrb 87).

E sg`rgm jgcte cte sg`rgme e me hej hejrg rg ã jg pgfes mcshes, qug gstèe dektbmes ke gcxe me sgfgter.

Jgrrefoe Hekiukte Hekiukt e mg sg`rg sg`rgme me @ucb supgrcer e o f e r r g J

Fckùgtb me Jgrrefoe Jghobmurb

DGHBKCXDE DGHBKCX DE MEX HEJ\GX

Bfbvbkhb me vefbktg g eu @ucb Ckjgrcer vefbkt dbàbkgtb

^brtg gxtgrkb

e m s b h c r m k ä f c h s b t g u ` k c F

Kb pertb es hejrgs pessugd e vefb ve fbkt ktg, g, eu sg sgib ib,, db dbàb àbkg kgtb tb,, sg sgfg fgte terr g e hcfckmre mb jghobmurb. (Jcùrb 8=). Jcùrb Jcùr b 87 - Zcstb cktgrkb mb pertb me hejrg.


27


(Jcùrb 80). E hbvb vgrm vgrmbmgcr bmgcrb. b. (Jcùrb

suhg su hgss sscv cvbd bdgk gktg tg

mcshe prckhcpbf, qug qug he hedb dbkm kmb b es mgdbcs mcshes, gstâ jcxbme be gcxe

‖sg`rgme—. (Jcùrb 8?).

E he heki kiuk ukte te mg sg sg`r `rgm gme, e,

me sgfgter, pgfb pgàb hedbkme. Gstg

rgspeksâ rgsp eksâvgf vgf pgfe bhcek bhcekbdgk bdgkte te mes

bprgsgktbme kb jcùrb 8:, ã e dbcs

mcshe ã e mg kùdgre 2 g qug gstâ

mcshes pemg sgr ud pbrbjuse, pcke

hedpfgte.

rgprgsgkt rgprg sgktbme bme kb jcùr jcùrb b 8:.

sc dc f br

Kerdbfdgktg sèe trés mcshes g

pgàb pg àbss

hedp he dpfg fgdg dgkt ktbr brgs gs qu qug g

jerdbd e hekiukte. (Jcùrb 8:).

Gxcst Gxc stgd gd eu eutre tress he hekiu kiukt ktes es

Gstg Gs tg mc mcsh she e pe pess ssuc uc ud pc pcke ke

dbcs scdpfgs, perãd e prckhäpce mg

trbt tr bter er eu cd cdpu pufs fser er qu qug g bh bhce cekb kb e

jukhcekbdgkte ã e dgsde.

sgùkme mcshe.

btã bt ã

jerd je rdbr br

e

E pcke trbter eu cdpufser ,

be

r glc tg

eu

hobpb,

rghertbmb me prøprce dbtgrcbf me mcshe. (Jcùrb 83) . Hekogh Hek oghcme cme es hed hedpek pekgkt gktgs gs me

Es mcsh mcshes es me sg sg`r `rgm gme e

Gstg sgùkme mcshe per sub

dghbkcsde me hejrg, vbdes pbssbr b

mgpgkmgk mgpg kmgkme me me jblrch jblrchbktg bktg pemg pemgd d

vgz, tgd eutre pcke trbter qug bhcekb

hekogh hek oghgr gr e prc prckhä khäpce pce mg juk jukhce hcekbd kbdgkt gkte e

sgr mg =, 7 eu : hbvbs jbfsbs dbcs b

e

mes dgsdes.

t grhgc r e

mc she

g

bssc d

Mcshe k¹ 2 Mcshe k¹ < Mcshe k¹ 8

Hupcfob

Brrugfb

Gcxe me mcshe Defb

Xgfgter Gcxe me sgfgter

Hedbkme me mcshe

Jcùrb 8: - Hedpekgktgs me sg`rgme.

: HBZBX JBFXBX

7 HBZBX

= HBZBX

Jcùrb 80- Hbvbs jbfsbs mes mcshes.


2:


Xg`rgme

E sg`rgme gd `grbf ã jerdbme per trés kùdgres g tgd per eligtcve bfckobr bs hbvbs vgrmbmgcrbs mes trés mcsh mc shes es kb mc mcrg rgàè àèe e mb fcfck` k`ög ögtb tb me jgrrefoe, qubkme gssgs kùdgres jergd jgctes `crbkme-sg e sgfgter ke sgktcme î mcrgctb, gsqugrmb g mcrgctb, hede sgrâ gxpfchbme, feè dbcs. (Jcùrb =>). Bktgs, Bkt gs, per perãd, ãd, vgi vgibde bdess hed hede e gjgtubr b fgcturb me sgfgter . E sgfgter pessuc ud mcshe kudgrbme mg > b 33. (Jcùrb =2). Jcùrb 8? - Hekiukte dektbme me sg`rgme.

Hobpb

^cke eu rglctg

^brbjuse

Jcùrb 83 - ]cpes mg pckes cdpufsergs.

Jcùrb => - Bfckobdgkte mbs hbvbs vgrmbmgcrbs.


20


Bktc-oerârce hrgshgktg

Oerârce mghrgshgktg

Elsgrvbàèe9 Kb sg sgù ùkm kmb b ve veft ftb, b, ek ekmg mg tgdes tgd es qug hed hed-pf -pfgtb gtbrr udb vef veftb tb hedpfg hed pfgtb tb mg 8:> 8:>¹¹ `rb `rbus, us, hede e bf uk uke

c râ râ

dbkusgbr

pgrhglgr ud

qubkme

heki ukte

mg

sg`rgme, ã e `cre kghgssârce pbrb qug e pcke trbter me sgùkme mcshe bfhbkhg e pcke trbter me sgùkme pbrb pemgr `crâ-fe.

Jcùrb =2 - Xgfgter.

Rubkme Rubk me `c `crb rbme me ke sg sgkt ktcm cme e oerârce oerâr ce b kudg kudgrbàèe rbàèe ã mghrg mghrgshgk shgktg, tg, eu sgib, vbc me kùdgre dbcer pbrb e kùdgre kùd gre dgk dgker er,, g ke sgk sgktcm tcme e bk bktctcoerârce b kudgrbàèe ã hrgshgktg, eu sg-ib sg -ib,, vb vbcc me kù kùdg dgre re dg dgke kerr pb pbrb rb e kùdgre dbcer. ^brb heksgùcrdes bfckobr bs hbvb hb vbss vg vgrm rmbm bmgc gcrb rbss me mess mc mcsh shes es ã prghcse jbzgr e sg`rgme, hekjerdg iâ jecc mc je mcte te11 g pbr brb b cs csse se sg sgù ùgg-sg sg b sgùcktg ermgd9

K¹ gd qug e sgfgter sg gkhektrb 8?

• B prcdgcrb veftb me sgfgter ã ke sgktcme mb mcrgctb pbrb b gsqugrmb, (sgktcme oerârce)1 • B sgùkmb veftb ã ke sgktcme mb gsq gsqugr ugrmb mb pb pbrb rb b mcr mcrgct gctb b (sg (sgktc ktcme me bkt bktc-coerârce), sgkme kghgssârce udb veftb hedpfgtb mg 8:>¹ (`rbus) ckchcbfdgktg1 • B tgrhgcrb veftb ã kevbdgktg mb mcrgctb mcrgctb pbrb pbrb b gsqugrm gsqugrmb b (sgktcme (sgktcme oerârce). Zeftbkme gktèe pbrb e sg`rgme vgibdes hede gjgtubr b blgrturb me

Fgvbr e sgfgter b ‖>—

2¹ `cre hedpfgte g pbrbmb ke ‖>—

hejrg, pgfe sg`rgme. Xgib b tätufe mg gxgdpfe es sg`rgmes 7>, <8 g 7:. E pr prcd cdgc gcre re pb pbss sse e ã zg zgrb rbrr e sgfg sg fgte terr. G cs cste te ã jg jgcte cte mb sg sgù ùck cktg tg dbkgcrb9 `crg e sgfgter pbrb b mcrgctb, kèe cdpertbkme e kùdgre gd qug gfg sg gkhektrg (8? ke kesse gxgdpfe) g pbrg ke zgre. Mgstg Mgs tg pe pekte kte,, `cr `crg g e sgf sgfgt gter er (sgd (s gdpr prg g pb pbrb rb b mc mcrg rgctctb) b) ud udb b ve veftftb b hedpfgtb g pbrg ke zgre. Gstâ mbmb b prcdgcrb veftb. \gpctb \gp ctb gs gstb tb epg epgrb rbàèe àèe db dbcs cs mubs vgzgs pbrb hedpfgtbr b sgùkmb g b tgrhgcrb tgrhgcrb veftb g bsscd bsscd zgrbr e scsscstgdb mg sg`rgme. (Jcùrb =<). Wdb vg vgzz zgr zgrbm bme e e sgf sgfgt gter er,, pemg pe mgde dess trb trbkqu kqucfb cfbdg dgktg ktg,, jbz jbzgr gr e sg`rgme, pbrb blgrturb me hejrg. Zeftb Ze ftbkme kme be kes kesse se gxg gxgdpf dpfe e huie hui e e sg`rgme sg`rgme ã 7>, <8 g 7:, vbdes vbdes jbzgr e prcdgcre kùdgre me sg`rgme.

<¹ `cre g pbrbmb ke ‖>—

8¹ `cre g pbrbm pbrbmb b ke ‖>—

Jcùrb =< - Ygrbkme e sgfgter.


2?


^brb cs ^brb csse se `c `crb rbde dess e sg sgfg fgte terr qu qug g sg gk gkhe hekt ktrb rb pb pbrb rbme me ke zg zgre re,, bt btã ã e kùdgre 7>, g pbrbdes. (Jcùrb =8). Kgst Kg stb b pbr brbm bmb b me sg sgfg fgte ter r bfck bf ckob obde dess b hb hbvb vb vg vgrm rmbm bmgc gcrb rb me tgrhgc tgr hgcre re mcs mcshe he me sg` sg`rgm rgme. e. @cr @crbde bdess bèr b` erb b e sg sgfg fgte terr pb pbrb rb b gs gsqu qugr grmb mb (sgktcme bktc-oerârce), rgbfczbkme udb veftb ve ftb he hedp dpfgt fgtb b mg 8: 8:>¹ >¹ (`r (`rbu bus) s) g pbrbdes ke kùdgre <8. Zgib lgd, pbrb mbr udb veftb hedp he dpfg fgtb tb,, ã pr prgh ghcs cse e pb pbss ssbr br pg pgfe fe prcd pr cdgc gcre re kù kùdg dgre re,, qu qug g ke hb hbse se ã e kùdg kù dgre re 7> 7>,, pb pbrb rb mg mgpe pecs cs pb pbrb rbrr ke (Jcùrb rb ==). Kg kùdgre kùd gre <8. (Jcù Kgst stg g kù kùdg dgre re e sgfgter bfckoeu b hbvb vgrmbmgcrb me sgùkme mcshe. @crb @c rbkm kme e e sg sgfg fgte terr, pb pbrb rb b mc mcrg rgctctb b pbrbdes ke tgrhgcre kùdgre qug ã 7:. Be rgb rgbfcz fczbr br gst gstb b pb pbrbm rbmb b bfck bfckobd obdes es b hbvb hbv b me prc prcdgc dgcre re mcs mcshe. he. (Jcù (Jcùrb rb =7). Xg b jgh jghobm obmurb urb gst gstcvg cvgrr bhc bhcek ekbm bmb b pb pbrb rb trbvbr e jgrrefoe, e hejrg gstbrâ blgrte. ^brb ^br b tbk tbkte te `cr `crbde bdess b dbà dbàbkg bkgtb tb eu vefb ve fbkt ktg g ke sg sgkt ktcm cme e mg bl blgr grtu turb rb,, g puxbdes b pertb pbrb qug e hejrg sg blrb. (Jcùrb =:). Zbdes vgr e qug bhektghgu hed e dghbkcsde cktgrke mb pertb, pbrb pb rb qu qug g gs gssb sb bl blgr grtu turb rb je jess ssg g pess pe ssäv ävgf gf5 5 Be sg he hedp dpfg fgtb tbrr e sg`r sg `rgm gme, e, ke sg sgfg fgte terr es mc mcsh shes es tcvgrbd tcvg rbd sub subss hbv hbvbs bs vgr vgrmbm mbmgcrb gcrbss bfckobmbs kb mcrgàèe mb fck`ögtb me jgrrefoe be bhcekbr b dbàbkgtb eu vefbktg, ke sgktcme mb blgrturb, b fck`ögt fck` ögtb b pgk pgkgtre gtreu u kbs hbv hbvbs bs mes mcshes, mcshe s, pgrd pgrdctckme ctckme e bjbs bjbstbdg tbdgkte, kte, me jgr jgrref refoe, oe, rgh rghefo efogkm gkme e bss bsscd cd bs fck`ögt fck` ögtbs bs hcfä hcfäkmr kmrchb chbss qug trb trbvbd vbd b pertb. (Jcùrb =0).

Jcùrb =8 - Jbzgkme e prcdgcre kùdgre me sg`rgme.

Jcùrb == - Jbzgkme e sgùkme kùdgre me sg`rgme.

DWMBKÀB MG XG@\GME B dumbkàb me sg`rgme mg ud he hejr jrg, g, ã lb lbst stbk bktg tg sc scdp dpfg fgs, s, rgspgctbkm rgspg ctbkme e bs epà÷ epà÷gs gs ejgrg ejgrghcmbs hcmbs pgfe jblrchbktg. HW\XE MG HOBZGC\E ‘ BWFB :

Jcùrb =7 - Jbzgkme e tgrhgcre kùdgre me sg`rgme.

23


@ucb supgrcer Jgrrefoe Hekiukte mg sg`rgme

s b h c r m k ä f c h

Jghobmurb

s b t g u ` k c F

Jcùrb =: - Blrckme e hejrg.

E qug qugrgdes mczgr, ã qug kèe ã pessävgf, e hfcgktg sefchctbr es kùdgres qug mgsgib, pbrb e keve sg`r sg `rgm gme, e, es kù kùdg dgre ress me ke keve ve sg`rgme sgrâ e qug rgsuftbr mb dumbkàb mg pescàèe mb pgàb hedbkme. Zbdes gxgdp gxgdpfcjchb fcjchbr, r, b pgàb hedb he dbkm kme, e, he hede de iâ jec gx gxpfc pfchb hbme me bktgrcerdgktg ã jcxbmb be gcxe me sgfgter qug bhcekb e prcdgcre mcshe qug per sub vgz bhcekb es mgdbcs mcshes mcs hes.. Hbs Hbse e gss gssb b pgà pgàb b hed hedbkm bkme e sgib pbrbjusbmb hekjerdg destrb kb jcùrb 3, eu sgib mg gkhbcxg hede jcùrb =?, gfb sg destrbdes destrb des kb jcùrb peschcekb gd mgtgrdckbme jure me prcdgcre mcshe.

Jcùrb Jcùr b =0 - Jgrrefoe rghubme pbrb blrcr b pertb.

Be sg dum dumbr br gss gssb b pgà pgàb b hed hedbkm bkme e pbrb qubfqugr eutre jure me prcdgcre mcshe, gstâ butedbtchbdgktg bftgrbme e sg`rgme. Xupekme qug b pgàb hedbkm hed bkme e kb pes pescàè càèe e des destrb trbmb mb kb jerk rkgà gàb b e sg sgù ùck cktg tg sg sg`r `rgm gme e jcùrb jc` urb =3, je 8?, 73 g ?:. Dumb Du mbkm kme, e, gs gssb sb pg pgàb àb he he-dbkme pbrb e jure kùdgre qubtre, e sg`rgm sg` rgme e crâ bft bftgrb grbrr pb pbrb rb e sg` sgùck ucktg tg sg`rgme :8, ?= g 22 jcùrb 7>. Hede e bf bfuk uke e pe pemg mg vg vgrr b du dumb mbkà kàb b mg sg`rgme ã lbstbktg scdpfgs lbstbkme dumbr mg pescàèe mb pgàb hedbkme. E qug mgvg jchbr hfbre ã qug be dumbr b pgàb hedbkme mg jure me prcdgcre mcshe, es kùdgres iâ gstèe gstbl gst blgfg gfghcm hcmes es mg jbl jblrch rchb b sg sgkm kme e pessävgf gshefogr es dgsde.

BLG\]W\B MG HEJ\GX

Jcùrb =?- ^gàb hedbkme me mcshe.


Ke hb hbse se mb mbss jg jgho hobm bmur urbs bs,, e prehgs pre hgsse se mg blg blgrtu rturb rb mbs dgs dgsdbs dbs sèe es dgsdes gksckbmes pbrb bs jghobmurbs jghob murbs Sbfgs Sbfgs hedu heduks. ks. Ke hbse mg jghob jghobmurbs murbs @er`g @er`gs, s, rghe rghedgkmb dgkmb-sg -sg e scstgdb mg hobvg per cdprgssèe, iâ gksck gk sckbm bme. e. êr êrtb tbkte kte be sg jb jbzg zgrr e sg`rgme mes mcshes pbrbs bfckobr bs hbvbs vgrmbmgcrbs ã prghcse tbdlãd <>

blrcr bs jg blrcr jgho hobm bmur urbs bs pb pbrb rb qu qug g e jg jgrr rref efoe oe pessb herrgr. Ke hbse mg pgrmb me sg` g`rrgme me,, sgkme kghhgssârc kg rce e, rgmgshelrcr e dgsde, e scstgdb mgvg sgrr pe sg perr ju jurb rbàè àèe, e, iâ qu qug g e sc scst stgd gdb b bumc bu mctctcve ve,, jch jcheu eu du ductcte e mc mcjä jähc hcf,f, he hed d b ckhfusèe mbs hbvbs jbfsbs, bes mcshes. Xgib Xg ib pe perr gx gxgd gdpf pfe e rg rgmg mgsh shel elrc rcrr e sg`r sg `rgm gme e me he hejr jrg. g. Ck Ckch chcb cbfd fdgk gktg tg fgvbdes e sgfgter pbrb ‖E— kb mcrgàèe mb sgtb g kb mcrgàèe me kùdgre 07, jbzgde jbz gdess udb db dbrhb rhb,, bjb bjbst stbm bmb b 2,7 dcfädgt dcfä dgtres res me gsp gspgfo gfoe, e, mgt mgtbfo bfog g mb jcùrb 72. Hed ud pukàèe, rgjeràbdes b dbrhb dbr hb ke hru hruzbd zbdgkt gkte e mbs mub mubss fck fckobs obs.. B sgùcr hed udb lrehb mg 8 dcfädgtres dcfädg tres mg mcìdg mcìdgtre, tre, gxgh gxghutbd utbdes es ud jure hekjerdg jcùrbs 7<, 7<-B G 7<-L. Xg pg pgrh rhgl glgr gr qu qug g fe feè è qu qug g b lrehb trbkspbsseu b hobpb mb pertb per bprexcdbmbdgktg < dcfädgtres, g bmgktreu e hejrg, udb hgrtb mcstìkhcb, bktgs mg lbtgr, gd bfùdb hecsb, ã led sckbf, iâ qug cste kèe eherrgkme g b lrehb feè qug uftrbpbssbr b hobpb mb pertb tehbr gd bfè, ã per qug es jblrchbktgs hestudbvbd hefehbr udb hobpb mg bàe tgdpgrbme, pbrb gvctbr b jurbàèe. CKX]C]W]E WKCZG\XBF L\BXCFGC\E

HEDBKME

2

2

<

=

8

< 8

=

Jcùrb 7>- Dumbkme b pgàb hedbkme pbrb e jure ke = e sg`rgme.

Jcùrb =3 - Hed b pgàb hedbkme e jure k e 2e sg`rgme ã 8?, 73 g ?=.

Kgstg Kgst g hb hbse se ã pr prgh ghcs cse e us usbr br eu eutrb trb lre rehhb, prøpr prcb cb pbrb jurb rbrr bàe tgdpgrbme. tgdpg rbme. (Jcùrbs (Jcùrbs 7<-B g L). E jure jgcte kgstb pescàèe crâ sbcr sb cr pg pgfe fe fb fbme me ck cktg tgrk rke e mb pe pert rtb b gxbtbdgktg kb mcrgàèe mb fck`ögtb me jgrr jg rref efoe oe,, ek ekmg mg mg mgvg vg sg sgrr jg jgct cte e e bfckobd bfck obdgkte gkte mbs hbvb hbvbss vgrm vgrmbmg bmgcrbs crbs mes mcsh mcshes. es. (Jcùrb Wdb b vg vgzz (Jcùrb 78). Wd jurbm ju rbmb b b pe pert rtb, b, pe pemg mgde dess ckc ckchc hcbr br b ‖hbàb— ‖hb àb— bes mcs mcshes hes mb sg` sgùck ucktg tg dbk dbkgcrb gcrb.. Bhedpb Bhe dpbkog kog b sgqöé sgqöékhc khcb9 b9

GX^GFOE

07

Jcùrb 72 - Dbrhbkme pbrb jurbr.

Xgfgter

Hobpb mb pertb

7< B Jgrrefoe

8dd

7< L

Hobpb mg bàe tgdpgrbme Gspgfoe Jcùrb 7< - Jurbkme b pertb.


<2

B) Cktremu Cktremuzb zb pgf pgfe e jur jure e udb obstg mg dgtbf, pemg sgr bre mg remb mg lchchfgtb, eu brbdg mg bprexc bpr excdbm dbmbdg bdgktg ktg <,7 dcf dcfädg ädgtre tress mg mcìdgt mcì dgtre re btã sgktcr sgktcr qug gfg teh tehb b ke tgrhgcre mcshe. ^brb ^br b tgr hgrtgzb hgrtgzb qug e mcs mcshe he `crb e sgfgter sgfgter pbrb pbrb b mcrgctb, mcrgctb, sgktc sgktcrâ râ e dgsd dg sde e rbs rbspb pbrr kb pe pekt ktb b mb ob obst stg. g. (Jcùrb 7=). Dbktgkme b obstg L) Db prgssce prg sscekbm kbmb b fgvg fgvgdgk dgktg tg be tgrh tgrhgcre gcre mcshe, vbdes `crbkme e sgfgter pbrb b mcrgctb, btã qug sg pgrhglb qug b obstg bvbkàb ‖hbàbkme— b hbvb vgrmbmgcrb. (Jc` (J cùr urbb 77 77)). Kgstg dedgkte mgvgdes bketbr e kùdgre ckmchbme ke sgfgter 4 <7. CKX]C]W]E WKCZG\XBF L\BXCFGC\E

B]GKÀÈE9 pemg bhektghgr mb obstg ‖hbàbr— udb hbvb jbfsb eu ud jure ju re.. ^b ^brb rb tg tgrr hg hgrt rtgz gzb b sg e qu qug g je jecc ‖hbà ‖h bàbm bme— e— ã b hb hbvb vb vg vgrm rmbm bmgc gcrb rb,, devcdgktg b obstg, pbrb b mcrgctb g pbr brb b b gs gsqu qugr grmb mb.. Xg b hb hbvb vb je jerr b vgrmbm vgr mbmgcr gcrb, b, e pgr pgrhur hurse se mb obs obstg tg kb dgsd dg sdb b dg dgsd sdb b ã db dbce cerr me qu qug g ke hbse mb jbfsb eu me jure. (Jcùrb 7:).

Jure

Jef`b

Jcùrb 78 - Ekmg sbc e jure cktgrkbdgktg mb pertb.

H) ‖Hbàbmb— b hbvb vgrmbmgcrb me tgrhgcre mcshe, g bketbme e kùdgre dbktg db ktgde dess b ob obstg stg prg prgss sscek cekbk bkme me e sgùkm sg` ukme e mcs mcshe, he, g `cr `crbde bdess e sgf sgfgte gter r pbrb b gsqugrmb. Kèe gsq gsqug ughgr hgr qug kgs kgstg tg de vc d gkt e e sg f gt e r mg vg hedp he dpfg fgtb tbrr ud udb b ve veft ftb b mg 8: 8:>¹ >¹ (`rbus), bktgs qug sg scktb e mcshe rbspbrr kb pektb mb obstg. rbspb

Jcùrb 7= - Ckchcbkme b ‖hbàb— bes mcshes.

Jcùrb 77 - Hbàbkme e tgrhgcre mcshe.


<<


Jcùrb 7: - Hede cmgktcjchbr hbvb jbfsb g vgrmbmgcrb.

Bpøs hed Bpøs hedpfg pfgdgk dgktb tbrr b veftb mg 8:>¹¹ (`r 8:> (`rbus bus), ), hek hektck tckubd ubdes es b `cr `crbr br e sgfg sg fgte terr pb pbrb rb b gs gsqu qugr grmb mb bt btã ã qu qug g b obstg bvbkhg ckmchbkme tgr ‖hbàbme— b hbvb hbv b vgr vgrmbm mbmgcr gcrb b me sg` sgùkm ukme e mcs mcshe. he. Wdb vgz ‖hbàbme— e sgùkme mcshe, bketg e kùdgre ckmchbme ke sgfgter ke hbse 7<. (Jcùrb 70).

M) Bke Bketb tbme me e sgùkme sgùkme kùdgr kùdgre e me sg`rgme, `crbdes e sgfgter pbrb î mcrgctb dbktgkme b obstg prgsscekbmb be pr prcd cdgc gcre re mc mcsh she, e, bt btã ã b dg dgsd sdb b bvbk bv bkàb àbrr ck ckmc mchb hbkm kme e b ‖h ‖hbà bàb— b— mb hb hbvb vb me

prcdgcre mcsh prcdgcre mcshe. e. (Jcùrb .Hed ed b (Jcùrb 7?).H hgrtgzb mg qug ã b hbvb vgrmbmgcrb, bket bk etg g e kù kùdg dgre re ck ckmc mchb hbme me ke sg sgfg fgte terr, ke hbse 88. Bketbm Bke tbme e e kùdgre kùdgre,, rgtcrbd rgtcrbdes es b obstg, g sg b jghobmurb kèe gstcvgr btcv bt cvbm bmb, b, `c `crb rb-s -sg g e ve vefb fbkt ktg g eu b dbàbkgtb ke sgktcme mg blgrturb, qug gstbrâ blgrte e hejrg. Hbse Hb se b jg jgho hobm bmur urb b gs gstg tgib ib bhce bh cekb kbmb mb ã pr prgh ghcs cse e pr preh ehgm gmgr gr b blgrturb mb dgsdb. Es trés kùdgres bketbm bke tbmes es ke hbse <7, <7, 7< g 88, gstâ rgmgshelgrte e sg`rgme.

HEDE CKCHCB\ KB ^\EJCXXÈE B pr prej ejcs cssè sèe e mg ho hobv bvgc gcre re bc bckm kmb b kèe ã rghekoghcmb per udb Fgc Jgmgrbf. Gdlerb iâ gxcstb preigte mg fgc, vcsbkme gssg gss g rgh rgheko ekoghc ghcdgkte dgkte eu pgfe dgk dgkes es rgùfbdgkt rgùfb dgktbkme bkme sgu gxgrh gxgrhähce. ähce. Iâ gxcstg gd bfùks Gstbmes tbdl tb dlãd ãd Fg Fgcs cs qu qug g rg rghe heko kogh ghgd gd b prej pr ejcs cssè sèe, e, db dbss kè kèe e gx gxcs cstg tg ud udb b rgùfbdgkt rgùf bdgktbàèe bàèe pbrb e gxgr gxgrhähce hähce mb prejcssèe. Ã e hb hbse se pe perr gx gxgd gdpf pfe e me Gstb Gs tbme me mg Xè Xèe e ^b ^buf ufe, e, qu qug g pe pess ssuc uc b Fg Fgcc

Jcùrb 70 - Hbàbkme e sgùkme mcshe.

Jcùrb 7? - Hbàbkme e prcdgcre mcshe.


<8


22>:: 2>::/<>>< /<>><,, huib rgù rgùfbdgk fbdgktbàè tbàèe e jec

>2 ieè mg hobvg ôcfcps >2 ieè mg hobvg hobvg Bffgk >2 ieè mg hobvg mg lehb jcxb >2 bfchbtg ukcvgrsbf >2 bfchbtg mg lche >2 bfchbtg mg hertg >2 pukàèe >2 dbrtgfe mg lefb >2 tbfobmgcrb pgqugkb >2 sbhb-pcke >2 tgseurb hedud >2 pckàb >2gshe >2gs hevbmg vbmg bà bàe e pbrbfcd rbfcdp pbr fcfcd dbs >2 fcdb hobtb mg ?— / dursb (bprexcdbmbdgktg <> hd) >2 fcdb jefob mg efcvgcrb >2 fcd fcdb b qu qubm bmrb rbmb mb mg ke dä däkc kcde de :— (bprexcdbmbdgktg 27 hd) / dursb >2 fcdb `ressb rgmekmb

hobvgcres qug gstèe gstblgfghcmes gd

MCZG\XBX JG\\BDGK]BX MG BLG BLG\]W \]W\B \B

ejch ej chck ckb, b, sg pr prøx øxcd cdb b mg he hedã dãrh rhce ce g gshefbs g eutres. Kgstg hbse eptbkme

g he hed d

>2 Jurbmgcrb >2 ieè mg lrehbs >8 lr lreh ehbs bs mg <, <,= = dc dcfäfädg dgtr tres es mg mcìdgtre >2 Brh Brhe e mg sgrrb >2 ^bquädgtre >2 Hedpbsse mg dgmcr >2 Dersb mg lbkhbmb kùdgre zgre (>) eu ud (2) >2 De Ders rsb b pe pert rtât âtcfcf pg pgqu qugk gkb b pb pbrb rb hbrrg`br kb hbcxb mg jgrrbdgktbs >2 Dâquckb hepcbmerb

hgrtg hg rtgzb zb gs gstb tbrâ râ ke hb hbdc dcko koe e hg hgrt rte e g

JG\\BDGK]BX JG\\BDGK] BX E^HCEKBCX

sgùre sg` ure pb pbrb rb gxg gxgrhg rhgrr b pre prejcss jcssèe. èe. B

Jurbmgcrb mg lbkhbmb Dete gsdgr gsdgrcf cf

btrcluämb btrclu ämb î Xghrg Xghrgtbrcb tbrcb mg Xgùr Xgùrbkàb bkàb ^ùlfchb, qug bckmb kèe b jgz. êrtbkte, êrtb kte, rghed rghedgkmb gkmbdes des bes kess sse es

bfu fuk kes

pbrb

eltg tgrrgd

ckjerdbà÷gs selrg es prehgmcdgktes kghgss kgh gssârc ârces es pb pbrb rb blg blgrtu rturb rb mg jcrd jcrdb, b, sgib sgi b hed hede e prg prgstb stbmer mer mg sgr sgrvcà vcàes es eu dgsde hede butýkede, iukte b Iuktb Hedg He dgrh rhcb cbff eu ^r ^rgj gjgc gctu turb rb me sg sgu u Gs Gstb tbme me eu Dukchäpce. êcs, qubkme eherrg mg pgqugkes pgqu gkes kg`ø kg`øhces hces sgrgd jcshb jcshbfczbme fczbmess g kèe gstbrgd rgùfbrczbmes, bhblbd per sgr duftbmes g btã cktgrmctbmes. E cd cdpe pert rtbk bktg tg ã sb sblg lgrr qu qug g ã prgh pr ghcs cse e gs gstb tbrr gs gstb tblg lgfg fghc hcme me pb pbrb rb gxgrh gxg rhgr gr sg sgd d pre prelfg lfgdbs dbs iuk iukte te bs butercmbmgs b prejcssèe mg hobvgcre, prckhcpbfd prckhc pbfdgktg gktg gd sgrvcà sgrvcàes es gxtgr gxtgrkes kes hede blgrturbs. B tgk tgkmék mékhcb hcb,, qub qubkme kme mg sub rgùfbdgktbàèe ã tcrbr udb - Ermgd mg Xg Xgrv rvcà càe e - pb pbrb rb qu qubf bfqu qugr gr tctcpe pe mg sgrvcàe gxghutbme, mgsmg udb høpcb mg hobvg scdpfgs btã udb blgrturb, ekmg mgvgrâ hekstbr b cmgktcjchbàèe me hfcgktg, sgrvcàe gxghutbme, mcb g oerb. êrr gssb ê gssb rbzèe rbzèe,, be blrcr blrcr b jcrdb jcrdb g ckch ck chcb cbrr e sg sgu u tr trbl blbf bfoe oe,, e bf bfuk uke e iâ mg mgvg vgrâ râ tedb te dbrr gs gssb sbss pr prev evcm cmék ékhc hcbs bs

cdpe cd perrtì tìk khc hcb b mg sg tg tgrr b jc jcrrdb rg`cstrbmb, sgib hede butýkede, sgib

Gstbs jgrrbdgktbs hekstctugd-

hede prgstbmer mg sgrvcàes, ã perqug,

sg ke dbtgrcbf lâsche pbrb b

bsscd bss cd e ‖ju ‖jutur ture e ho hobv bvgcr gcre— e— pe pemg mgrâ râ

dektb` dek tb`gd gd mg udb ejchckb ejchckb dãm dãmcb cb g

hedprbr g jbzgr use mbs jgrrb-dgktbs

pbrb

mg blg blgrtu rturb, rb, hui huib b vgk vgkmb mb ã pre preclcm clcmb b pb pbrb rb

herrcqugcres me mcb b mcb me hobvgcre.

e pùlfche mg ud deme `grbf.

es

sgrvcàes

kerdbcs

g

Hbse Hb se sg mg mgsg sgib ibrr trb trblb lbfo fobr br he hed d

`rbkmgs hgktres mg `rbkmgs hbpctbcs, eutrbss jgrrbd eutrb jgrrbdgktb gktbss g gqucp gqucpbdgkt bdgktes es sgrèe kghgssârces, dbs qug pemgrèe sgrr bm sg bmqu qucr crcm cmes es db dbcs cs pb pbrb rb b jr jrgk gktg tg mgpgkmgkme mb gvefuàèe mb ejchckb. ^brb ^br b dg dgfoe foerg rgss mgt mgtbfo bfogs gs mg hede utcfczbr bs jgrrb jgrrbdgktb dgktbss fcstb fcstbmbs mbs bhcdb heksuftg heksuftg b Bufb 2. Ã bhe bheksg ksgfoâ foâvgf vgf be hob hobvgc vgcre re gd sub su b

ejch ej chck ckb b

btcv bt cvcm cmbm bmgs gs

mgsg mg sgkv kvef efvg vgrr

hede he de,,

perr pe

eutr eu trbs bs

gxgd gx gdpf pfe, e,

hekjgh hek jghàèe àèe mg hbr hbrcdl cdles, es, bjcb bjcbàèe àèe mg jgrrbjgr rb-dg dgkt ktbs bs (bf (bfchb chbtg tg mg uk ukob, ob, mg hutäh hu tähufb ufbs, s, tgs tgseu eurbs rbs,, gth gth.), .), _gr _grex ex,, gkhb gk hbmg mgrkb rkbàèe àèe,, gt gth. h. Cst Cste e mg mgvg vg sgr bvbfcbme gd jukàèe mb fehbfczbàèe mb ckmùstrcb ckmù strcb,, hblg hblgfgcrg fgcrgcrbs crbs g lbrl lbrlgcre gcres, s, per udb eu dbcs mgstbs btcvcmbmgs ã kghgssâ kgh gssârce rce bmqu bmqucrcr crcr jgrr jgrrbdgk bdgktbs tbs g gqucpbgquc pb-dgkt dgktes es gspg gspghäjch häjches es pbr pbrb b bs dgsdbs. E fehbf pbrb dektb`gd mb ejchckb pemg vbrcbr ducte. êmg sgr ud quces qu cesqu qug, g, ud pgq pgqugk ugke e cdø cdøvg vgf,f, eu dgsd dg sde e ud udb b pb pbrg rgmg mg fb fbtg tgrb rbff mg ud cdøvgf. cdøv gf. Ckmg Ckmgpgk pgkmgkt mgktg g me tbd tbdbko bkoe e mgssg mgs sg gsp gspbàe bàesgr sgrâ â kgh kghgss gssârc ârce e pes pessuc sucr9 r9 - Fe Fehb hbff pb pbrb rb jg jgrr rrbd bdgk gktb tbs. s. Rubkme e gspbàe ã jghobme g kèe oâ hcrhufbàèe mg eutrbs pgssebs pemg-sg eptb ep tbrr pe perr mc mcsp spýý-fb fbss gd ud pb pbck ckgf gf pgkmurbme kb pbrgmg, hede cfustrbme kb jcùrb 73. Me hektrârce, ã dgfoer dbkté-fbs, dbkté -fbs, mg jerdb er`bkczbmb, er`bkczbmb, gd `bvgtbs qug pessbd sgr trbkhbmbs. - Lb Lbkh khbm bmb, b, qu qug g hb hbcl clb b ke däkcde udb hepcbmerb g b dersb mg

Jgrrbdgktbs Kghgssârcbs

mg bu bute tedø døvg vgcs cs,, db dbss qu qug g bc bckm kmb b

>2 ieè mg hobvg mg jgkmb

rgprgs rgp rgsgkt gktbd bd duc ducte te peu peuhe he pb pbrb rb es

lbkhbmb. (Jcùrb :>). - ^b ^bck ckgf gf mg ho hobv bvgs gs pb pbrb rb pb pbrg rgmg mg (Jcùrbs :2) eu `bvgtgcre (gstg ùftcde ehupb ehu pb dbc dbcer er gsp gspbàe bàesel selrg rg b lbk lbkhbm hbmb). b).

<=


DEK]B@GD MB EJCHCKB


jghobmurbs jghob murbs gspg gspghcbcs, hcbcs, prckhc prckhcpbfd pbfdgktg gktg

Jcùrb 73- ^bckgf mg jgrrbdgktbs.

Zbrcâvgf => hd

d h > 3

@bvgtbs pbrb jgrrbdgktbs

Jcùrb :> - ^bkhbmb hed `bvgtbs.


<7


^rgè ckhfckbme

^bckgf mg hobvg jgcte mg hobpb mg dbmgcrb hedpgksbmb

- Lbfhèe mg btgkmcdgkte btgkmcdgkte,, qug pemg sgr tbdlãd gxpescter. (Jcùrb :<). Gstg lbfhèe ã b fcdctbàèe gktrg b ârgb mg trblbfoe g e btgkmg-dgkte. Kb cdpessclcfcmbmg mg sub hefehbàèe, bfè bf` e mg mgvg vg sul sulstc stctuä tuä-fe -fe,, he hede de per gxgdpfe, udb pertckoefb mg vbc g vgd eu mg herrgr, eu dgsde udb mcvcsørcb lbcxb gth.

FBSEW] FB SEW] MB EJCHCKB ^bckgf mg pfâstche hed `bkhoes gd bàe, vgkmcmes gd vârces tbdbkoes

Jcùrb :2- ^bckgf mg hobvgs

B bhe bhedem dembàè bàèe e mgs mgssgs sgs døv døvgcs gcs,, lgd hede sgus jerdbtes, pemg vbrcbr mg bh bher erme me he hed d e fe fehb hbff b sg sgrg rgd d ckstbfbmes. Kbs jcù jcùrb rbss :8 g := destrbdes mubs su`gst÷gs mg hede sg pe pemg mg rg rgbfc bfczb zbrr b mc mcsp spes escàè càèe e me mess gfgdgktes gfgdg ktes qubkme mb dekt dektb`gd b`gd mg sub ejchckb.

LBKHBMB Wdb lbk lbkhbm hbmb b duc ducte te prâ prâtchb tchb,, hed pgq pgqugk ugke e pb pbckg ckgff per pertb tb jgr jgrrbd rbdgkt gktbs bs g pertb hobvgs, qug e bfuke dgsde pemgrâ pem grâ dek dektbr tbr sgr sgrâ â des destrb trbmb mb b sg` sgùcr ucr.. Gfb sgrâ dektbmb hed 2.<>d mg hedprcdgkte, perãd gssb dgmcmb pemg pe mg sg sgrr qu qubf bfqu qugr gr ud udb b pb pbrb rb sg bmgqubr be fehbf. Btã 2.7 2.7>d >d ã pes pessäv sävgf gf dbk dbktgr tgr mubs mu bs he hefuk fukbs bs mg bp bpec ece, e, pb pbrb rb ud udb b dgmcmb dgm cmb sup supgrc grcer er bhr bhrgsh gshgkt gktbr br dbc dbcss udb hefukb hefuk b hgktr hgktrbf. bf. ^rcdgc ^rcdgcrbdgk rbdgktg tg hertg hertg,, eu gkhedgkmg bs sgùcktgs pgàbs mg dbmgcrb. Hertg mecs sbrrbjes mg 7x7 kb dgmcmb dgm cmb mg 2.? 2.?>d >d mg hed hedprc prcdgk dgkte. te. Hertg mecs sbrrbjes mg 7x7 hed >,3>d mg hedprcdgkte. (Jcùrb :7). Gssbs pgàbs sgrvcrèe mg pãs pbrb b hefukb mg bp bpec ece e mb lb lbkh khbm bmb. b. He Hed d sb sbrr rrbj bjes es mg : x < hd, hertg = pgàbs mg >,7>dd mg hedprcdgkte. (Jcùrbs ::).

Lbfhèe hedud teme Lbfhèe jgcte mg dbmgcrb

Lbfhèe gxpescter hed dbmgcrb g vcmres

Jcùrb :< - Lbfh÷gs.


<:


^bckgf mg hobvgs

^bckgf mg hobvgs

Lbkhbmb

Lbkhbmb

Lbfhèe \ghgpàèe

\ghgpàèe

Jcùrb :8 - Lbfhèe hedud mg dbmgcrb.

s g v b o h g m f g k c b ^

^bssb`gd

Lbkhbmb e è h f b L

e d è g à ` p b g s h s g b \ ^

\ghgpàèe

Lbkhbmb Lbfhèe

Lbkhbmb ^bckgf mg hobvgs

Lbfhèe

Lbfhèe \ghgpàèe Jcùrb :=- Fbyeut mg ckstbfbà÷gs mg ejchckbs.


<0


7 hd

) d h > ? 2 ( d > ? , 2

DEK]B@GD MB LBKHBMB

7 hd

7 hd ^gàb k¹ 2

) d h > 3 (

7 hd

^gàb k¹ <

d > 3 , >

Jcùrb :7 - Xbrrbjes mg 7 x 7 hd per 2,?> d / >,3> d mg bfturb.

< hd

: hd

) d h > 7 ( d > 7 , >

^gàb k¹ 8

Jcùrb :: - Xbrrbje mg : x < hd per >,7> d mg hedprcdgkte.

Gfbs sg Gfbs sgrè rèe e tr trbv bvgs gssb sbss mb hefukb pbrb bpece me tbdpe g mb prbtgf prb tgfgcr gcrb b ckj ckjgrc grcer er mb lbk lbkhb hbmb. mb. B sgùcr hertg me dgsde sbrrbje mg : x < hd hd,, udb pgà gàb b mg 2,> ,>7 7d mg hedprcdgkte. (Jcùrb :0). Hed sbrrbjes mg 2> x <,7 hd, hertg udb pgàb mg 2.>7 d g mubs mg >.7>d. (Jcùrb :?). Gssb Gs sbss pg pgàb àbss sg sgrv rvcr crèe èe mg fbtgrbcs pbrb b prbtgfgcrb tcpe lbkmgib, qug qu g jcjchb hb fe feè è bl blbc bcxe xe me tb tbdp dpe e mb lbkhbmb. Mg udb udbhob hobpb pb mg hed hedpgk pgksbm sbme e mg <.7 hd mg gspgssurb, hertbdes bs sgùcktgs pgàbs. HW\XE MG HOBZGC\E ‘ BWFB :

^brb b prb ^brb prbtgf tgfgcr gcrb b ckj ckjgrc grcer er g lbsg lbs g mb prb prbtgf tgfgcr gcrb b lbk lbkmgi mgib, b, mub mubss pgàb pg àbss mg >.7 >.7>d >d mg fb fbrù rùrb rb pe per r 2.2>d mg hedprcdgkte. (Jcùrb :3). ^brb b tbdpb, hertg b dgmcmb mg >, =7d per mg 2. <>d mg hedprcdgkte. Btgkàèe, pbrb ud lbkhbmb mg btã 2.7>d mg fbrùrb e tbdpe hed <.7d mg gspgssurb ã sujchcgktg. ^ br b e tbdpe dbc er usg e hedpgksbme mg 8 hd mg gspgssurb. (Jcùrb 0>). ^brb jckbfczbr hertg e pbckgf hed he d >. >.3> 3> mg bf bftu turb rb pe perr 2. 2.<> <>d d mg fbrùrb. (Jcùrb 02).
Hed bs pg pgàbs k¹ 2, 2, < g 8 dektg bs hefukbs mg sustgktbàèe mb lbkhbmb. (Jcùrb 0<). Elsgrvg qug bs mubs pgàbs k¹ 8 su supg pgrc rcer ergs gs,, sè sèe e pr prg` g`bm bmbs bs eu pbrbjusbmbs me fbme gxtgrcer g bs k¹ 8 ckjgrcergs pgfe fbme cktgrke mb hefukb mg sustgktbàèe. Dektg hed bs pgàbs k¹ =, 7, : g 0 b prbtgfgcrb tcpe lbkmgib. Dekt ktbm bmb b b prb prbtg tgfgc fgcrb rb (Jcùr (Jc ùrbb 08). De lbkmgib. Zbdes dektbr b lbkhbmb. Wkb Wk b bs mubs hefu fuk kbs mg sustgktbàèe, prg`bkme eu pbrbj pb rbjusb usbkme kme b prb prbtgf tgfgcr gcrb b ckj ckjgrc grcer er g b sgùcr b prbtgfgcrb lbkmgib. ^rgkmb hed bfùks prgès g pbrbj pb rbjuse uses. s. Mgp Mgpecs ecs mg hek hekhfu hfuämb ämb b dektb`gd dekt b`gd,, rgjer rgjeràbde àbdess b jcxbà jcxbàèe èe hed he d db dbcs cs pr prg` gès es eu pb pbrb rbjus juses es.. Elsgrvbà rvbàèe9 èe9 Bdlb Bdlbss (Jcùrb (Jc` urb 0=). Elsg sèe sè e jc jcxb xbmb mbss gk gktr trg g he hefu fukb kbss mg sust su stgk gktb tbàè àèe. e. ^b ^brb rb he hekh khfu fucr cr b dektb`gd jcxg b tbdpb mb lbkhbmb (pgàb ?) g e pbckgf (pgàb 3). (Jcùrb 07). ^brb jckbfczbr bhcdb mb bfturb mb hepcbm hep cbmerb erb,, dbc dbcss eu dgk dgkes es 8>h 8>hd, d, jcxg jcx g es prg prgès ès,, eu sup supert ertgs gs pb pbrb rb bpecbr bs prckhcpbcs jgrrbdgktbs me mcb b mcb, tbcs hede fcdbs, hobvgs mg jgkmb jgk mb g po pocff cffcp cps, s, bfc bfchb hbtg, tg, pu pukà kàèe èe,, dbrtgfe, gth. G b pbrtcr mg ² 87 mg hd mg fbrùrb me pbckgf, hefequg prgès sgd hblgàb g f c `gc rbdgkt g ckhf ck hfck ckbm bmes es,, pb pbrb rb hcdb hcdb mg 8 b = hgktädg hgk tädgtres tres ke sgk sgktcme tcme oer oerczek czektbf tbf gd hbrrgcrbs mg 7 hd udb mb eutrb ke sgktcme vgrtchbf. (Jcùrb 0:). E bf bfuk uke e mg mgvg vg gk gktg tgkm kmgr gr qu qug g gstb gst b ã udb epà epàèe èe lâschb, lâschb, dgmcmb dgmcmbs, s, pemgd sgr bftgrbmbs mg bherme hed b mcspekclcfcmbmg me dbtgrcbf mcspekävgf, lgd lg d he hede de mb mbss mc mcdg dgks ks÷g ÷gs, s, mb mbss ckst ck stbf bfbà bà÷g ÷gs. s. G sg sgd d mu muvc vcmb mb udb lbkhbmb scdpfgs dbs qug rgùkg kud pgqugke gspbàe, tu tum me qu qug g e prejcsscekbf hobvgcre prghcsb. CKX]C]W]E WKCZG\XBF L\BXCFGC\E

< hd

^gàb k¹ =

: hd

d 7 > , 2

Jcùrb :0 - Xbrrb Xbrrbje je : x < hd per 2,>7 d mg hedprcdgkt hedprcdgkte. e.

<,7 hd

2> hd

^gàbs k¹ : ^gàb k¹ 7

<,7 hd

2> hd

d 7 > , 2 d > 7 , >

Jcùrb :? - Xbrrbje mg 2> x <,7 hd g per 2,>7 mg hedprcdgkte.

^gàb k¹ 0 d 2 > 2, 2

> ,7 >

d

Jcùrb :3 - Hobpb mg hedpgksbme mg <,7 hd per 2,2> x >,7> d.


<3


^gàb k¹ ?

< > 2, <

d

> ,= 7 d

< ,7 h d

Jcùrb 0> - Hobpb mg hedpgksbme mg <,7 hd per 2,<> x >,=7 d.

<,7 hd ^gàb k¹ 3

d > 3 , >

d 2, < >

Jcùrb 02 - ^rb jckbfczbr e hertg e pbckgf hed >,3> d mg bfturb per 2,<> d mg fbrùrb.


8>


2

8

8 8

< Jcùrb 0< - Hefukbs mg sustgktbàèe mb lbkhbmb.

7

:

:

0

= :

7

Ephcekbf 0 :

=

Jcùrb08 - ^rbtgfgcrb tcpe lbkmgib.


82


^rbtgfgcrb lbkmgib

B prbtgfg prbtgfgcrb crb,, tcp tcpe e lbkmgib lbkmgib pemg sgr sulstctuämb per `bvgtbs, ‖mubs eu dbcss mgp dbc mgpgkm gkmgkm gkme e mg hed hedprcd prcdgkt gkte, e, perãd bhobdes qug b prbtgfgcrb tcpe lbkm lb kmgib gib ã db dbcs cs pr prâtc âtchb hb,, pg pgrd rdctg ctg b mcvcsèe pbrb bs jgrrbdgktbs dbcergs hede brhe mg sgrrb, jurbmgcrb gth, g pbrb bs dbcs mgfchbmbs hede, pertb pckes pck es,, ù ùbrm brmb b pck pckes es g de defck fckob obs, s, mcsp mc spes esctctcv cve e yb ybfg fg g tg tgtr trb, b, gt gth, h, qu qug g tbdlãd tbdl ãd pemg pemgrèe rèe sgr mcstrcl mcstrcluämes uämes mg jerdb b prepchcbr jâhcf dbkusgce, sgd tgr qug blrcr g jghobr bs `bvgtbs. Hed gstb lbkhbmb jckbfczbdes kesse kes se hur hurse se mg hob hobvgc vgcre. re. ]gde gdess b vgrtgzb mg qug vehé, hekhfucktg mgstg hurse,, gstbrâ bpte hurse bpte sg terkbr terkbr ud keve prejcsscekbf, sgib pbrb trblbfobr hede gdprg`bme gdprg `bme,, hede hedcs hedcsscekb scekbme me eu per hektb prøpcb.

Leb Xertg g

^rbtgfgcrb ckjgrcer

Hektg Hekeshe!

0

Jcùrb 0= - \gjeràg b lbkhbmb hed prgès.

3 ?

Jcùrb Jcùr b 0: - Zgib b lbkhbmb prektb.

Jcùrb 07 - Jcxbkme b tbdpb mb lbkhbmb.


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Chaveiro - Aula 06

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