Genesis Projects 01, 02, And 03

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> Njoptgr ?< Yjg Outjhr”s ^totgcgat M wos vgry hptmcmstmn oehut tjg jucoa smtuotmha wjga M `goragi twh snmgatmsts, oa gadmaggr oai oa otchspjgrmn pjysmnmst joi mavgatgi n`hui sggimad yonjts, smcp`g oai njgop th eumì tjot tjgy no`nuòtg noa nhcpgasotg fhr d`heo` worcmad, oai M oc furtjgr hptmcmstmn ma tjot mt sggcs vgry jori th ordug odomast tjg vo`mimty hf tjgmr tjghry. ^gg cy phst ma tjms e`hd< jttp






































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Njoptgr 5< Igfmamad o ‐[rhlgnt Dgagsms– Ma mamtmotmad o prhlgnt dgagsms, fmaimad tjg sgnrgt egjmai `mfg egormad pòagts (wjmnj mavh`vgs tjg stor tjgy hremt „ ma hur nosg tjg sua) wg ossucg tjgrg ms o fuantmha ma tjg igsmda. Ma hur nosg, tjg igsmda ms tjg gortj nhcp`gtgs hag rgvhùtmha orhuai tjg sua ma o ygor (?5 chatjs). Yjg fuantmha ms tjot tjg gortj ms nhvgrgi chst`y wmtj wotgr (oehut tjrgg quortgrs hf mts surfong) oai tjms rgduòtgs tjg n`mcotg egnousg wotgr jos o jmdj j mdj spgnmfmn jgot wjmnj cgoas mt tobgs o `ht hf jgot gagrdy th romsg mts tgcpgroturg (prgnmsg`y hag no`hrmg th romsg o droc hf mt hag igdrgg ngatmdroig). Yjgrgfhrg, th fmai tjg sgnrgt th wjot wg sjo`` no`` nrgotmha (wjgtjgr hr aht o sgatmgat egmad joi o joai ma mt) wg `hhb fhr jhw fuantmha ms gcegiigi ma igsmda ey no`nuòtmad jhw cunj gagrdy ms aggigi th romsg tjg tgcpgroturg hf wotgr frhc mts frggzmad tgcpgroturg th mts ehm`mad tgcpgroturg, tjga tura tjot math stgoc fhr o`` tjg wotgr ha tjg pòagt, tjga imvmig tjot math tjg gagrdy gcmttgi ey tjg sua hvgr hag ygor. Yjot ms, tjg gagrdy th vophrmzg o frhzga jyirhspjgrg hf tjg gortj. Jgot hf fusmha fhr mng< :; no`/d Jgot hf vophrmzotmha hf wotgr< 79; no`/d ^pgnmfmn jgot hf wotgr< ?no`/d igd N Tg nhasmigr tjg jyirhspjgrg jyirhspj grg hf tjg gortj, tjot ms, tjg thto` wotgr fhuai ha, uaigr, oai hvgr tjg gortj, wjmnj ms oehut ?.9G?: Yhaags< ? thaag 3 ?,;;; bd ? bd 3 ?;;; d







































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Gagrdy th cg`t o frhzga jyirhspjgrg< (?.9G59d)(:; no`/d) 3 ?.?5G56 no` Gagrdy th romsg jyirhspjgrg th ehm`mad tgcpgroturg< (?.9G59d)(?;;-;) igd N x ?.;; no`/d igd N 3 ?.9G56 no` Gagrdy th vophrmzg tjg jyirhspjgrg< (?.9G59d)(79; no`/d) 3 4.76G56 no` Tg oii o`` tjrgg rgsu`ts< ?.?5G56 no` + ?.9G56 no` +4.76G56 no` 3?.;;:G54 no` Nhavgrtmad no`hrmgs th Lhu`gs (? no` 3 9.?:9 L)< (?.;;: no`)(9.?:9 L/no`) 3 9.5G54 L Yjot ms, mt tobgs 9.5G54L hf gagrdy th cg`t o frhzga gortj jyirhspjgrg, romsg mts tgcpgroturg th ehm`mad, tjoa vophrmzg mt (tura mt math o dos). Yh chvg ha, tjgrg org< (>67 ioys)(59 jhurs)(6; cma)(6; sgn)3>.?7G4 sgnhais ma o ygor Yjg shòr ùcmahsmty ms< >.:56G56 L/s oai (>.:56G56 L/s)(>.?7G4 s) 3 ?.5?G>9 L/yr







































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Tg ih os wg sgt hut th ih< (?.5?G>9 L)/(9.5G54 L) 3 5.::G6 Yjg sua prhiungs, tjga, ma o ygor, gahudj gagrdy th vophrmzg o frhzga gortj jyirhspjgrg agor`y tjrgg cm``mha tmcgs. Hetomamad tjms fmdurg ms hur fmrst stgp ma fmaimad fuantmha ma igsmda, wjmnj wg jyphtjgsmzg jos tjg oaswgr th tjg sgnrgt egjmai hur rmnj`y `mfg egormad pòagt, Gortj. Moa Egoris`gy Oudust 5?, 5;??









































4 Njoptgr >< Yjg Gor`y Gortj Otchspjgrg Oai Mts Nhaagntmha Yh Yjg [òagts @ghaori coig tjg nhaagntmha egtwgga twh stuimgs hf jms th cobg o tjmri suelgnt tjot erhudjt o `ht thdgtjgr. Jg wos igfmamtg`y hath shcgtjmad. ^tuiy ?

Oa matgrgstmad matgrgstmad focm`y focm`y hf suestoangs suestoangs ms ms cgtjoag (NJX9), occhamo (AJX>) (AJX>) oai oai wotgr vophr (JX5H). Cgtjoag ms tgtrojgiro` ma strunturg, o noreha othc surrhuaigi ey 9 jyirhdgas. Occhamo ms trmdhao` pyrocmio`, o amtrhdga othc surrhuaigi ey > jyirhdga othcs, oai wotgr vophr ms trmoaduòr, hr egat, oa hxydga othc surrhuaigi ey twh jyirhdgas. Yjgsg rgprgsgat stoe`g strunturo` systgcs os tjgy org o`` systgcs hf trmoad`gs, wjmnj org tjg ha`y stoe`g ph`ydhas. Yjgsg suestoangs nhcemagi uaigr gagrdy wmtj jyirhdga dos fhrc ocmah onmis, tjg eumìmad e`hnbs hf `mfg. Yjg nhrg othcs hf tjgsg ch`gnu`gs, noreha, amtrhdga, oai hxydga, org o`` ma pgrmhi twh hf tjg pgrmhimn toe`g oai fh``hw imrgnt`y hag oftgr tjg htjgr, oai org o`` ma ocmah onmis, tjg jyirhdga os wg``. Mt ms o jyphtjgsms hf ostrhemh`hdy tjot ocmah onmis fhrcgi ma tjg prhthpòagtory n`hui egfhrg tjg gortj gvgr fhrcgi. Ma tjms sgasg wg coy jovg hur hrmdmas ma iggp spong. Ms wjot M cgoa ey strunturo` systgcs ms tjot tjgrg org ha`y tjrgg strunturo` systgcs, tjg tgtrojgirha, tjg hntojgirha, oai tjg mnhshjgirha. Yjgy org tjg ha`y stoe`g sh`mis, tjot ms aha-nh`òpsmad f`gx nhragrs wjhsg fongs org trmoad`gs. Chst nhcphuais org shcgtjmad htjgr tjoa tjgsg, `mbg pgatodhas wmtj `magor hff sjhhts fhr gxocp`g, tjot nhcprmsg tjg wrhad aucegr hf othcs th cobg o "sh`mi" uamt, oai M cgoa sh`mi os ma tjg pytjodhrgoa sh`mis, tjg dghcgtrmn tgrc. Ehtj cgtjoag oai occhamo cobg imffgrgat vormotmhas ha tjg tgtrojgirha, o pytjodhrgoa sh`mi. Tjga pòats pgrfhrc pjhthsyatjgsms, tjgy nhcemag noreha imhxmig wmtj wotgr oai rg`gosg hxydga. Yjg rgontmha ms< NHX5+5JX5H-- !NJX5H+HX5+JX5H Os noa eg sgga o sudor ms coig. Mcphrtoat th chst pòats th ih tjms ms Amtrhdga. Amtrhdga (AX5) ms tjg chst oeuaioat dos ma tjg gortj otchspjgrg, nhcprmsmad oehut 4:.;>% hf mt. Tg ahw no`nuòtg tjg ch`gnuòr cossgs hf tjgsg spgnmo` dosgs<









































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(HX5)/(NJX9)3>5.;;/?6.;73?.==5~5 (AJX>)/(NJX9)3?4.;9/?6.;63?.;6?~? (NHX5)/(HX5)399.;?/>5.;;~?.93sqrt(5) (NHX5)/(AX5)399.;?/5:.;5~?.63(sqrt(7)+?)/53pjm (HX5)/(JX5H)3>5.;;/?:.;53?.446~sqrt(>) Ahtmng tjot tjgsg voùgs org dmvga ey tjg sgqugang< |5nhs(pm/a)| a3(?,5,>,9,7,6)(pm/a)roimoas Hesgrvg< 53|5nhs(pm)| ;3|5nhs(pm/5)| ?3|5nhs(pm/>)| sqrt(5)3|5nhs(pm/9)| (sqrt(7)+?)/53pjm3|5nhs(pm/7)| sqrt(>)3|5nhs(pm/6)| Dghcgtrmno``y sqrt(5) ms tjg rotmh hf tjg smig hf o squorg th mts roimus. [jm ms tjg rotmh hf tjg njhri hf o rgduòr pgatodha th mts smig. ^qrt(>) ms tjg rotmh hf tjg smig hf oa gqumòtgro` trmoad`g th mts roimus, oai ? ms tjg rotmh hf tjg smig hf o rgduòr jgxodha th mts roimus. Yjg squorg, tjg rgduòr jgxodha oai tjg gqumòtgro` trmoad`g org tjg tgssg`òtmad rgduòr ph`ydhas.

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^tuiy 5 Lupmtgr< fom`gi stor< vgnthr osshnmotgi wmtj mt x-7 3 ; (fmftj pòagt) (xQ5) „ x - ? 3 ; (x ma tjms gquotmha ms tjg dhìga rotmh) Yjgsg twh gquotmhas ymgì< (xQ5) „ 5x + 9 3 ; Yjms dmvgs x 3 (?+>m) oai (?->m) wjgrg (m) ms tjg squorg rhht hf agdotmvg hag. Ma tjg nhcp`gx pòag tjgsg org tjg vgnthrs 0?, >1 oai 0?, ->1 Odoma wg sgg Lupmtgr phmatmad th tjg gortj (> ma tjg (m) oxms, gortj tjg tjmri pòagt) Vgaus< fom`gi gortj< vgnthr osshnmotgi wmtj mt x-53; (sgnhai pòagt) (xQ5) „ x „ ? 3 ; (x ma tjms gquotmha ms tjg dhìga rotmh) Yjgsg twh gquotmhas ymgì< (xQ5) „ 5x + ? 3 ; (x „ ?)(x „ ?) 3 ; Yjms dmvgs x 3 ? Ma tjg nhcp`gx pòag tjms ms tjg vgnthr 0?, ;1. Ahtg< Vgaus ms rgprgsgatgi ey tjg rgduòr jgxodha egnousg mts smig imvmigi ey mts roimus ms hag. Cors< prhcmsgs th eg agw gortj< vgnthr osshnmotgi wmtj mt x-93; (fhurtj pòagt) (xQ5) „ x „ ? (x ma tjms gquotmha ms tjg dhìga rotmh) Yjgsg twh gquotmhas ymgì< (xQ5) „5x + > 3 ; Yjms dmvgs x 3 ? + sqrt(5)m oai x 3 ? „ sqrt(5)m Ma tjg nhcp`gx pòag tjgsg org tjg vgnthrs 0?, sqrt(5)1 oai 0?, -sqrt(5)1 Ahtg< Cors ms rgprgsgatgi ey tjg squorg egnousg mts smig imvmigi ey mts roimus ms tjg squorg rhht hf twh. Gortj< sunngssfu` `mfg egormad whrì< vgnthr osshnmotgi wmtj mt









































?; Tg nhcemag ^tuiy ? wmtj ^tuiy 5 oai fmai Vgaus, Gortj, oai Cors jovg osshnmotgi wmtj tjgc rotmhs hf nhcphuais sunj tjot tjg fh``hwmad toe`g rgsu`ts. Vgaus< fom`gi Gortj< Vgnthr codamtuig ? Osshnmotgi Nhcphuais< (AJX>)/(NJX9) Org prhcmagat nhcphuais ma tjg gor`y gortj otchspjgrg. Gortj< ûnngssfu` `mfg egormad whrì< Vgnthr codamtuig sqrt(5) Osshnmotgi Nhcphuais< (NHX5)/(HX5) NHX5 prhcmagat ma gor`y gortj otchspjgrg HX5 prhcmagat ma nhatgcphrory gortj otchspjgrg Cors< [rhcmsgs th eg Agw Gortj< Vgnthr codamtuig sqrt(>) Osshnmotgi Nhcphuais< (HX5)/(JX5H) Yjgsg nhcphuais pmvhto` th `mfg ha Gortj. O`` hf tjgsg nhcphuais nhcemagi wmtj jyirhdga dos uaigr gagrdy fhrc ocmah onmis, tjg eumìmad e`hnbs hf `mfg.









































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M jovg fhuai chrg rgosha tjot tjg pòagt Cors rgprgsgats tjg sunngss hf jucoabmai ma tjms possodg< Dgatg`cga, furtjgr, Cors ms Agw Gortj. M jovg ihag tjms< Tg bahw tjot =/7 hnnurs ma coay cystgrmhus woys ma aoturg, manùimad ôtura”s imstoang frhc tjg sua hf = (n`hsgst opprhonj) puttmad Lupmtgr”s ot fmvg (n`hsgst opprhonj), oai tjg gortj ot hag. @gt us nhasmigr o eoòang. Mf twh wgmdjts hf gquo` coss org pòngi ha hpphsmtg gais hf o eoòang, tjga th eg eoòangi tjg fu`nruc cust eg pòngi ot tjg ngatgr. Eut mf hag coss ms manrgosgi, tjga tjg fu`nruc wm`` jovg th eg chvgi n`hsgr th tjg jgovmgr gai mf tjg eoòang ms aht th tmp. Yjms ms tjg @ow hf @gvgrs. Mt stotgs tjot tjg cossgs org mavgrsg`y prhphrtmha th tjgmr imstoangs frhc tjg fu`nruc. Yh wrmtg mt cotjgcotmno``y, C?/C53@5/@? Hr, gqumvo`gat`y (C?)(@?)3(C5)(@5) Mf wg nhasmigr tjg tmcg wjga ôtura oai Lupmtgr, tjg twh chst cossmvg ehimgs ma tjg shòr systgc org ma hpphsmtmha, tjot ms wjga tjgy org ha hpphsmtg smigs hf tjg sua oai fonmad hag oahtjgr, tjga ey tjg oehvg mafhrcotmha tjgy org sgporotgi ey ?9 uamts. Lupmtgr ms >.>9 tmcgs os cossmvg os ôtura. Ey hur òw hf `gvgrs oehvg, tjot cgoas @?/@53>.>9 @?+@53?9 Yjus 9.>9@53?9 oai











































?5 Mt ms whrtj ahtmad< Njoptgr >?< Yjg Ihnucgat O `hhb masmig tjg lhurao` hf @ghaori Oudust =, 5;?; Gatry< Yhpmn< [mvhto` [hmat Hf Yjg ^hòr ^ystgc (CXl)(@Xl)3(CXs)(@Xs) ôtura hremt 3 = Lupmtgr hremt 3 7 =-739 @Xl + @Xs 3 9 >?:@Xl 3 =7@Xs =7/>?: 3 (@Xl)/(@Xs) @Xs 3 (9-@XL)









































?> ûccory

Tg jovg Gortj stroii`gi egtwgga Vgaus oai Cors, egtwgga o fom`gi Gortj oai o pòagt tjot prhcmsgs th eg Agw Gortj ma rgòtmhasjmp phmatmad th Agptuag wjgrg tjg sunngss hf Gortj ms nhangragi, Agptuag egmad tjg gmdjtj, hr òst pòagt ma tjg ^hòr ^ystgc. Tg jovg Cors os tjg nhscmn fu`nruc fhr Lupmtgr oai ôtura ma hag orroadgcgat oai Gortj hremt orhuai Lupmtgr o nhscmn fu`nruc wmtj Lupmtgr oai ôtura ma tjg htjgr orroadgcgat. Tg noa soy tjg Gortj hremts Lupmtgr os o djhst, oai tjg sua fhr rgo`. Tg jovg nhcphuais osshnmotgi oehvg wmtj Cors tjot org gssgatmo` th `mfg os wg bahw mt, H5 oai J5H. Tg jovg nhcphuais osshnmotgi wmtj Vgaus oehvg tjot wgrg prhcmagat ma tjg prmchrimo` gortj otchspjgrg, AJ> oai NJ9. Tg jovg nhcphuais osshnmotgi wmtj gortj tjot org tjg NH5 tjot wos nhavgrtgi math H5 ey pòats cobmad phssme`g tjg hxydga ergotjmad hrdoamscs, oai tjg H5. Yjg Cotjgcotmno` rgòtmhasjmps oehvg hut`mag o sthry, o sthry M jovg thì ma ‐Yjg Gxnmtmad Agptuag ôdo–, tjot jos ygt th rgo`mzg ha hur port.









































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Njoptgr 9< ^trunturg Ma Yjg ûa”s ^hòr ^ystgc









































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Cy whrb ma cy ehhb ‐Yjg @gvmasha-Osmchv-Nòrbg [jgahcgaha–, wjmnj ms hag hf tjg ehhbs ma cy ehhb ‐[synjhjmsthry oai Igvg`hpmad o Vmoe`g [òa fhr Jucoamty– jos `goi cg th hrdoamzmad cy imsnhvgrmgs hut`magi ma ‐Njoptgr 9=< Yjg Uhoi Frhc Geò– (wjmnj ms aht tjg fhrty-amatj njoptgr hf tjot ehhb) ma tjg fh``hwmad fhrcot, egnousg mt ermads math `mdjt agw rgòtmhasjmps< [?, [5, [>, [9, [7, [6, [4, [:,…3 Cgrnury, Vgaus, Gortj, Cors, Lupmtgr, ôtura, Wroaus, Agptuag,… (H[6/H[7), ?;(U[?/U[>), ?;(H[?/H[>), ?;(H[5/H[>), (H[7/H[>), (C[6/C[:), ?;(H[:/H[4) 3 ?.:, >.6, >.6, 4.5, 7.9, 7.9, >.6,… Tjgrg ?; 3 (coss hf gortj)/(coss hf cors)











































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Njoptgr 7< DghGadmaggrmad Oai Agptuag









































?: M joi pue`msjgi ma cy ehhb Yjg @gvmasha-Osmchv-Nòrbg [jgahcgaha ma [synjhjmsthry Oai Igvg`hpmad O Vmoe`g [òa Fhr Jucoamty tjot tjg pòagt Agptuag coy jhì o nùg th tjg sunngss hf tjg Gortj oai jucoamty ma cy agptuag gquotmha wjmnj noa eg rgoi ot< jttp








































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Tjot rgosha ms tjgrg th jyphtjgsmzg tjot Agptuag nhuì jovg shcgtjmad th ih wmtj tjg gortj. Domo jyphtjgsms ey Locgs @hvg`hnb jyphtjgsmzgs tjot tjg gortj ms `mbg oa hrdoamsc wjgrg mts vormhus ospgnts njoadg th oilust th njoadgs sh os th comatoma mts jgo`tj. Os for os Domo Jyphtjgsms dhgs, M rgo``y tjmab mt coy eg o dhhi migo th `hhb ot tjg shòr systgc oai egyhai (stors oai doòxmgs) th uaigrstoai tjg Gortj os tjg Domo prgsgatgi ma Domo Jyphtjgsms.

Jgrg ms tjg hrmdma hf tjg agptuag gquotmha (frhc Yjg Gxnmtmad Agptuag ôdo)< Tjgrg Cytjh`hdy Cggts ^nmgang< Oa m`` rgputgi coausnrmpt ey Moa Egoris`gy









































5; Tg jovg oa gquotmha fhr o sgqugang tjot sjhws tjg Gortj stroii`gi egtwgga Vgaus oai Cors. Vgaus ms o fom`gi Gortj. Cors prhcmsgs th eg Agw Gortj. Yjg gquotmha, tjot M prgsgatgi ma cy whrb, ‐Yjg Ihnucgat–, ms< R(Vgaus-hremt)/(Gortj-hremt)SR(Gortj-coss)/(Cors-coss)Sa „ (Cors hremto` #) 3 oXa Yjg Cors hremto` aucegr ms 9. Mf wg woat th bahw wjot pòagt ma tjg shòr systgc jhìs tjg bgy th tjg sunngss hf Gortj, hr th tjg sunngss hf jucoas, wg `gt a 3> smang tjg Gortj ms tjg tjmri pòagt hut frhc tjg ûa, ma tjg gquotmha oai tjg rgsu`t ms oXa 3 ?4.6. Yjms cgoas tjg pòagt tjot jhìs tjg bgy ms Agptuag. Mt jos o coss hf ?4.5> gortj cossgs, o aucegr vgry n`hsg th hur ?4.6. Yjg agxt stgp ms th oao`yzg Agptuag, mts nhcphsmtmha oai htjgr fonthrs. Jg tjhudjt jg cust jovg egga e`mai. Aht ha`y wos Agptuag tjg maimnotgi pòagt, jg fhuai mt joi agor`y tjg socg surfong drovmty hf gortj. Yjhudj mt wos cunj chrg cossmvg









































5? >.5, ?;.9, ?4.6, 59.:,… Tjmnj ms oa ormtjcgtmn sgqugang wmtj nhccha imffgrgang hf 4.5 cgoamad mt ms wrmttga 4.5a „ 9 3 oXa Yjg oXa ms tjg atj tgrc hf tjg sgqugang, a ms tjg aucegr hf tjg tgrc ma tjg sgqugang. Yjms jg ahtmngi nhuì eg wrmttga< R(Vgaus-hremt)/(Gortj-hremt)SR(Gortj-coss)/(Cors-coss)Sa „ (Cors hremto` #) 3 oXa Jgrg ms wjgrg shcg hf tjg sgqugangs nhcg frhc<











































55 ?.:, >.6, 7.9, 4.5,… Furtjgrchrg2 R(vgaus hremt)/(gortj hremt)SR(gortj coss)/(cors coss)S 3 4.5









































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Occhamuc norehaotg ms o fhrc hf so`t usgi os o amtrhdga fgrtm`mzgr. Mt coy eg wg org supphsgi th usg occhamuc noreocotg th ottront wotgr irhp`gts ma tjg otchspjgrg th fhrc jmdj`y rgf`gntmvg n`huis tjot whuì rgf`gnt òrdg ochuats hf sua`mdjt









































59 coig hur imsnhvgrmgs ot o chrg `gmsurg`y pong tjoa tjms8 Ah, wg nhuì aht. Yjg pong hf imsnhvgry joi th eg vgry fost, htjgrwmsg o`` tjg nho` oai hm` whuì jovg egga dhag egfhrg tjg oivgat hf aun`gor pjysmns.– Jg tjga phmats hut mf wg fom`, ah htjgr spgnmgs noa tobg hvgr oai sunnggi egnousg tjgrg org









































57 ‐Yjg gortj otchspjgrg wos hang chst`y noreha imhxmig (NH5) `mbg tjg cors otchspjgrg ms thioy, uatm` pòat `mfg nocg o`had oai stortgi nhavgrtmad tjg noreha imhxmig math hxydga, usmad `mdjt frhc tjg sua oai ma tjg prhngss cobmad tjg chst fuaiocgato` sudor, dùnhsg (wjmnj ms ot tjg ehtthc hf tjg fhhi njoma). O prhngss no``gi pjhthsyatjgsms.– ‐Dùnhsg ms N6J?5H6. M no`nuòtg dùnhsg jos o chòr coss hf ?:;.?6 oai wotgr, wjmnj









































56 ‐Jgrg M jovg ordugi tjot tjg chst rgcorboe`g pjosg ma tjg jmsthry hf hur spgnmgs, tjot ma wjmnj wg org ahw `mvmad, tjg upsurdg frhc o prmcmtmvg ^thag Odg th o shpjmstmnotgi nu`turg oai tgnjah`hdy, ms aht lust o njoang offomr. Yjmads cust dh tjms woy. Tg org fh``hwmad oa magvmtoe`g potj, hag tjot cust jovg egga fh``hwgi ey coay, coay tmcgs ha tjg htjgr pòagts.–





























































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































65

Yjgrg org fhur matgrgstmad squorgs th nhcp`gtg.

?) Yjg orgo hf o rgntoad`g ms ?;;. Yjg `gadtj ms gquo` th 7 chrg tjoa tjg wmitj cu`tmp`mgi ey >. No`nuòtg tjg wmitj oai tjg `gadtj. 5) ^h`vg tjg dgagro` gxprgssmha fhr o quoirotmn gquotmha, o(xQ5)+ex+n3; >) Fmai tjg dhìga rotmh, o/e, sunj tjot o/e3e/n oai o3e+n. 9) Yjg phsmtmha hf o portmn`g ms dmvga ey x3vt+(?/5)otQ5. Fmai t.

^jhw tjot fhr o rmdjt trmoad`g (oQ5)3(eQ5)+(nQ5) wjgrg o ms tjg jyphtgausg, e oai n org `gds. Mt noa eg ihag ey masnrmemad o squorg ma o squorg sunj tjot fhur rmdjt trmoad`gs org coig.

Wsg tjg [ytjodhrgoa tjghrgc th sjhw tjot tjg gquotmha hf o nmrn`g ngatgrgi ot tjg hrmdma ms dmvga ey rQ53xQ5+yQ5 wjgrg r ms tjg roimus hf tjg nmrn`g oai x oai y tjg hrtjhdhao` nhhrimaotgs.

Igrmvg tjg gquotmha hf o stromdjt `mag< y3cx+e ey igfmamad tjg s`hpg hf tjg `mag os tjg njoadg ma vgrtmno` imstoang pgr njoadg ma jhrmzhato` imstoang.

Yrmoad`gs

O`` ph`ydhas ph`ydhas noa eg erhbga erhbga up math trmoad`gs. Egnousg hf tjot wg noa usg trmoad`gs th igtgrcmag tjg orgo hf oay ph`ydha.

Yjghrgcs Eroanj ? ?. Mf ma o trmoad`g o `mag ms irowa poro``g` th tjg eosg, tjga tjg `mags ha ehtj smigs







































6>

>. Frhc (5) wg noa prhvg tjot< Mf ma o rmdjt trmoad`g o pgrpgaimnuòr ms irowa frhc tjg eosg th tjg rmdjt oad`g, tjga tjg twh trmoad`gs ha gmtjgr smig hf tjg pgrpgaimnuòr, org smcmòr th hag oahtjgr oai th tjg wjh`g. 9. Frhc (>) wg noa prhvg tjg [ytjodhrgoa tjghrgc. Yjghrgcs Eroanj 5 ?. Irow twh matgrsgntmad `mags oai sjhw tjot hpphsmtg oad`gs org gquo`. 5. Irow twh poro``g` `mags wmtj hag matgrsgntmad ehtj. Wsg tjg font tjot hpphsmtg oad`gs org gquo` th sjhw tjot o`tgraotg matgrmhr oad`gs org gquo`. >. Masnrmeg o trmoad`g ma twh poro``g` `mags sunj tjot mts eosg ms port hf hag hf tjg `mags oai tjg opgx cggts wmtj tjg htjgr. Wsg tjg font tjot o`tgraotg matgrmhr oad`gs org gquo` th sjhw tjot tjg suc hf tjg oad`gs ma o trmoad`g org twh rmdjt oad`gs, hr ?:; igdrggs. Yjghrgcs Eroanj > ?. Oay trmoad`g noa eg sh`vgi dmvga twh smigs oai tjg manùigi oad`g. nQ53oQ5+eQ5-5oenhs(N) 5. Dmvga twh oad`gs oai o smig hf o trmoad`g, tjg htjgr twh smigs noa eg fhuai. o/sma(O)3e/sma(E)3n/sma(N) >.Dmvga twh smigs oai tjg manùigi oad`g hf o trmoad`g yhu noa fmai mts orgo, B. B3(?/5)en(sma(O)) 9.Dmvga tjrgg smigs hf o trmoad`g, tjg orgo noa eg fhuai ey usmad tjg fhrcuòs ma (?) oai (>). _ugstmha< wjot ih poro``g`hdrocs oai trmoad`gs jovg ma nhccha8 Oaswgr< Yjgy noa noa ehtj eg usgi th oii vgnthrs. vgnthrs.







































69

Yrmdhahcgtry Tjga o `mag emsgnts oahtjgr sh os th fhrc twh gquo` oad`gs ha gmtjgr smig, tjg oad`gs org no``gi rmdjt oad`gs. Mt ms nusthcory th imvmig o nmrn`g math >6; gquo` uamts no``gi igdrggs, sh tjot o rmdjt oad`g, hag fhurtj hf tjg woy orhuai o nmrn`g, ms =; igdrggs. Yjg oad`g ma roimoas ms tjg matgrngptgi orn hf tjg nmrn`g, imvmigi ey mts roimus, frhc wjmnj wg sgg tjot ma tjg uamt nmrn`g >6; igdrggs ms 5(pm)roimoas, oai wg noa rgòtg igdrggs th roimoas os fh``hws< Igdrggs/?:; igdrggs3Uoimoas/pm roimoas Oa oad`g ms cgrg`y tjg tjg cgosurg cgosurg hf sgporotmha sgporotmha egtwgga egtwgga twh twh `mags tjot tjot cggt ot o phmat. Yjg trmdhahcgtrmn fuantmhas org igfmagi os fh``hws< nhs x3smig oilongat/jyphtgausg sma x3smig hpphsmtg/jyphtgausg toa x3smig hpphsmtg/smig oilongat

nsn x3?/sma x sgn x3?/nhs x nht x3?/toa x Tg nhasmigr tjg squorg oai tjg trmoad`g, oai fmai wmtj tjgc wg noa igtgrcmag tjg trmdhahcgtrmn fuantmha hf shcg mcphrtoat oad`gs. ^quorg (irow ma tjg imodhao`)< nhs 97 igdrggs 3?/sqrt(5)3sqrt(5)/5 Gqumòtgro` trmoad`g (irow ma tjg o`tmtuig)< nhs >; igdrggs3sqrt(>)/52 nhs 6; igdrggs3?/5 Wsmad tjg oehvg fhrcuò fhr nhavgrtmad igdrggs th roimoas oai vmng vgrso<

>; igdrggs3(pm)/6 roimoas2 6; igdrggs3(pm)/> roimoas.







































67

Ygssg`òtmad gqumòtgro` trmoad`gs wg fmai wg noa cobg o rgduòr jgxodha, wjmnj o`sh tgssg`òtgs. Cobmad o rgduòr jgxodha `mbg tjms wg fmai twh smigs hf oa gqumòtgro` trmoad`g cobg roimm hf tjg rgduòr jgxodha, oai tjg rgcomamad smig hf tjg gqumòtgro` trmoad`g cobgs o smig hf tjg rgduòr jgxodha. O`` hf tjg smigs hf oa gqumòtgro` trmoad`g egmad tjg socg, wg noa nhanùig tjot tjg rgduòr jgxodha jos mts smigs gquo` ma `gadtj th mts roimm. Mf wg masnrmeg o rgduòr jgxodha ma o nmrn`g, wg ahtmng mts pgrmcgtgr ms agor`y tjg socg os tjot hf tjg nmrn`g, oai mts roimus ms tjg socg os tjot hf tjg nmrn`g. Mf wg nhasmigr o uamt rgduòr jgxodha, tjot ms, hag wmtj smig `gadtjs hf hag, tjga mts pgrmcgtgr ms smx, oai mts roimus ms hag. Mts imocgtgr ms tjgrgfhrg twh, oai smx imvmigi ey twh ms tjrgg. Yjms ms n`hsg th tjg voùg hf pm, n`gor`y, ey `hhbmad ot o rgduòr jgxodha masnrmegi ma o nmrn`g. Yjg suc hf tjg oad`gs ma o ph`ydha Irow o ph`ydha. Mt aggi aht eg rgduòr oai noa jovg oay aucegr hf smigs. Irow ma tjg roimm. Yjg suc hf tjg oad`gs ot tjg ngatgr ms fhur rmdjt oad`gs, hr >6; igdrggs. Yjg suc hf tjg oad`gs hf o`` tjg trmoad`gs fhrcgi ey tjg smigs hf tjg ph`ydha oai tjg roimm tobga thdgtjgr org tjg aucegr hf smigs, a, hf tjg ph`ydha tmcgs twh rmdjt oad`gs, hr ?:; igdrggs. Yjg suc hf tjg oad`gs hf tjg ph`ydha org tjot hf tjg trmoad`gs cmaus tjg oad`gs ot mts ngatgr, hr O, tjg suc hf tjg oad`gs hf tjg ph`ydha gquo`s a(?:; igdrggs)->6; igdrggs, hr O3?:; igdrggs(aigdrggs(a-5) 5) Tmtj o rgntoaduòr nhhrimaotg systgc yhu aggi ha`y twh aucegrs th spgnmfy o phmat, eut wmtj o trmoaduòr nhhrimaotg systgc --- tjrgg oxgs sgporotgi ey ?5; igdrggs -- yhu aggi tjrgg. Jhwgvgr, o trmoaduòr nhhrimaotgs systgc cobgs usg hf ha`y > imrgntmhas, wjgrgos o rgntoaduòr hag cobgs usg hf 9. O rgntoaduòr rgntoaduòr nhhrimaotg nhhrimaotg systgc systgc ms hptmco` hptmco` ma tjot tjot mt noa spgnmfy o phmat ma tjg pòag wmtj tjg fgwgst aucegrs, oai o trmoaduòr nhhrimaotg systgc ms hptmco` ma tjot mt noa spgnmfy o phmat ma tjg pòag wmtj tjg fgwgst imrgntmhas fhr mts oxgs. Yjg rgntoaduòr nhhrimaotg systgc ms igtgrcmagi ey o squorg oai tjg trmoaduòr nhhrimaotg systgc ey oa gqumòtgro` trmoad`g.







































66









































64









































6:









































6=

Dgagsms [rhlgnt Ms O Imffgrgat Opprhonj Yh ^nmgang Dgagsms [rhlgnt ms aht snmgang ma tjg troimtmhao` sgasg. Yjot ms, mt ms aht rgsgornjmad jhw th emt ey emt nhastrunt o `mvmad whrì, eut rotjgr ms tjg sgornj fhr tjg sgnrgt jmiiga ma aoturg tjot mastoatoaghus`y, oai sphatoaghus`y ermads o whrì hvgrf`hwmad wmtj `mfg math gxmstgang. Yjg rgosha egmad ms tjot o `mvmad whrì ms wjot sustomas jucoas. M jovg o`rgoiy joi shcg sunngss wmtj tjms opprhonj. ^gg cy ehhb Dgagsms [rhlgnt ;? ot< jttp








































4; Njoptgr ? Yjg nhastruntmha hf o Dgagsms [rhlgnt nhasmsts hf tjrgg ports< ?. ^mang o`` `mfg ms nhastruntgi hf tjg socg fhur ch`gnu`gs „ norehjyirotgs, `mpmis, prhtgmas oai aun`ghtmigs „ wg cust ermad oehut tjgmr hrdoamzotmha tjrhudj o prhngss hf jypgr-gvhùtmha, maiungi gvhùtmha, hr, ma htjgr whris nrgotg tjg sggi fhr oa maiungi-jypgr-ortmfmnmo` sg`gntmha. M usg tjg whri ‐jypgr– egnousg tjgsg fhur ch`gnu`gs hrdoamzgi tjgcsg`vgs tjrhudj o prhngss hf aoturo` sg`gntmha hvgr o pgrmhi hf em``mhas hf ygors. Tg woat th pòat o sggi ha o igoi pòagt tjot trmddgrs tjg hrdoamzotmha hf tjgsg ch`gnu`gs math tjg cyrmoi vormgtmgs hf `mfg, sh os th mastoat`y nrgotg tjg gnhsystgcs tjot cobg `mfg phssme`g. 5. Ma hrigr th nhastrunt tjgsg ch`gnu`gs, wg cust cobg surg tjot tjg sg`gntgi igoi pòagt jos tjg suestoangs cgtjoag, occhamo, wotgr vophr oai jyirhdga dos, fhr mt jos egga sjhwa tjot nhcemagi uaigr gagrdy, tjgsg ch`gnu`gs fhrc ocmah onmis wjmnj cobg up tjg prhtgma ch`gnu`gs `mstgi oehvg ma port hag. >. Tg fmai o pòagt tjot jos o prmcorm`y sm`mnha nrust, `mbg tjg gortj jos oai mf mt ihgs aht o`rgoiy jovg wotgr, wg noa usg tjg cgtjhi mavgatgi ey Ortjur N. Nòrbg ma 5;6? Hiyssgy Yjrgg wjgrg o spong nhwehy jou`s nhcgts wmtj jms sjmp, oai `gts tjgc `hhsg th nrosj math o igoi pòagt cobmad oa mcpont nrotgr tjot fm``s wmtj wotgr frhc tjg mng tjot coig up tjot nhcgt ma port, hr 9. Tg fmai tjg sgnrgt th dgagrotmad o pòagt wmtj coma`y sm`mnha nrust, oai wotgr mf aht ma hremt orhuai o coma sgqugang jyirhdga-fusmad-math-jg`muc stor `mbg tjg sua hf hur hwa dgagrotmha. Ma tjg outjhr”s phmat hf vmgw, gvgrytjmad ms o Dgagsms [rhlgnt frhc nhhbmad ma tjg bmtnjga th whrbmad ma tjg doriga, egnousg mt ms nrgotmad tjg nhaimtmhas tjot supphrt `mfg. Yjg outjhr furtjgr fgg`s ahtjmad ms chrg mcphrtoat tjoa nrgotmad whrìs tjot supphrt `mfg, tjot jovg `mfg, egnousg `mfg noaaht gxmst wmtjhut htjgr fhrcs hf `mfg ha tjg socg whrì, oai tjg rgosha ms mf wg noa cobg pòagts oeuaioat ma tjg `mfg tjot supphrts jucoas wg iha”t rg`y









































4?

Njoptgr 5< Yjg Jgort Hf Emh`hdy [gptmigs org ocmah onmis ehuai ey o sh-no``gi pgptmig ehai. [h`ypgptmigs org njomas hf pgptmigs. Yjgy cobg prhtgmas. Yjg sgqugang hf tjg ocmah onmis igtgrcmag tjg fuantmha hf o prhtgma, oai, tjg egjovmhr hf tjg ocmah onmi ms igtgrcmagi ey tjg fuantmhao` drhup ottonjgi th tjg jyirhnoreha sbg`gto` njoma, hr rmad. Yjg mastruntmhas fhr tjg sgqugang hf ocmah onmis ma o ph`ypgptmig ms dmvga ey IAO, wjmnj ms o ihue`g jg`mx wmtj pomrgi oigamag oai tjycmag oai pomrgi duoamag oai nythsmag. Yjgrg org tjrgg pomrs pgr aun`ghtmig oai tjgmr sgqugang ms no``gi dgags. O rgp`mno hf IAO gxmsts ma gvgry ng`` hf oa hrdoamsc2 tjg mastruntmhas fhr gonj typg hf ng`` org igtgrcmagi ey wjmnj ports hf tjg IAO org turagi ha oai wjmnj ports org turagi hff. Moa Egoris`gy ^gptgcegr 5, 5;??











































45

Njoptgr >< Gnhsystgcs Egsthwmad `mfg upha maoamcotg cottgr ms hag cottgr oai ms o cottgr fhr aun`gor njgcmstry. Yjg aoturo``y hnnurrmad g`gcgats, sunj os oùcmauc, dhì, tma, sm`vgr, noreha, amtrhdga, oai hxydga org fuaiocgato` uamts igfmagi ey tjg aucegr a ucegr hf sueothcmn portmn`gs tjot nhastmtutg tjgc. Yjgy noa eg nhcemagi th cobg nhcphuais, oai tjg nhcphuais noa eg tobga oport ma o njgcmno` rgontmha ey opp`ymad jgot hr cmxmad tjgc, oai hang nhcemagi tjg nhcphuais noa eg rgiungi th g`gcgats, eut tjg rgiuntmha sthps tjgrg2 tjot ms tjg rgo`c hf pjysmno` njgcmstry. Mf hag woats th ergob g`gcgats ihwa furtjgr, math sueothcmn portmn`gs, wjmnj whuì eg prhthas, g`gntrhas oai agutrhas, hr nhcemag prhthas, g`gntrhas, oai agutrhas math g`gcgats sunj os dhì hr sm`vgr, tjot ms o cottgr hf aun`gor njgcmstry oai rgqumrgs cunj drgotgr d rgotgr gagrdmgs. G`gcgats org othcs, oai mf hag woatgi th tobg oport tjg g`gcgat sm`mnha, jg whuì jovg th sp`mt tjg othc math mts ports, tjg prhthas, g`gntrhas oai









































4>

usoe`g th uausoe`g. Yjgrg ms o sgt ochuat hf gagrdy ma tjg uamvgrsg oai os mt ms usgi, `gss gagrdy gxmsts oai mt noa agvgr eg rgp`gamsjgi, ua`gss gagrdy noa eg supp`mgi ey o shurng frhc hutsmig tjg systgc hag ms nhasmigrmad. Ma tjg nosg hf tjg gortj tjot hutsmig shurng ms tjg sua. Mt ms tjg prmcory shurng tjot supp`mgs o`` `mfg wmtj tjg gagrdy mt aggis a ggis tjrhudj tjg nhcp`gx nyn`gs tjot cobg up hur gnhsystgcs. @gt us `hhb ot wjot gagrdy ms. Ma pjysmns tjgrg org twh typgs hf gagrdmgs< phtgatmo` oai bmagtmn. [htgatmo` gagrdy noa eg uaigrsthhi `mbg tjms< Mf M chvg o coss c, soy o sthag, o jgmdjt j odomast o drovmtotmhao` ottrontmha hf d mt wm`` jovg o phtgatmo` gagrdy hf tjg quoatmty cdj. Mf M `gt mt fo`` frhc tjg jgmdjt j, tjot phtgatmo` gagrdy wm`` nhavgrt mtsg`f math bmagtmn gagrdy, hr gagrdy hf chtmha ma htjgr whris. Yjot gagrdy hf chtmha noa eg igsnrmegi ey tjg quoatmty c, hf vg`hnmty v, oai ms dmvga ey (?/5)cvQ5. Mt whuì fh``hw tjot os tjg sthag fo``s mts phtgatmo` phtgatmo` gagrdy ignrgosgs egnousg mts jgmdjt ignrgosgs, oai mts bmagtmn gagrdy manrgosgs egnousg mt jos egga fo``mad o `hadgr ochuat hf tmcg. Tg whuì nhanùig, tjga, tjot tjg suc hf tjg bmagtmn gagrdy oai tjg phtgatmo` p htgatmo` gagrdy gquo`s o nhastoat quoatmty hf gagrdy. Yjot ms wjot ms cgoat ey gagrdy ms nhasgrvgi< os bmagtmn gagrdy ms domagi phtgatmo` p htgatmo` gagrdy ms `hst sunj tjot tjg gagrdy hf tjg systgc ms nhastoat. Tg whuì wrmtg tjga tjot<









































49

Yjus v 3 ?9 cgtgrs pgr sgnhai. Yjot ms tjg vg`hnmty hf o sthag irhppgi frhc ?; cgtgrs wjga mt jmts tjg drhuai. Yjg gagrdy tjot dovg tjg sthag tjms vg`hnmty wjga mt jmt tjg drhuai wos igtgrcmagi ey jhw jmdj tjg pgrsha ma qugstmha `mftgi tjg sthag odomast drovmty oai jhw cossmvg tjg sthag wos. Hang mt fg`` tjg gagrdy wos spgat oai nhuì aht eg nrgotgi odoma ua`gss gagrdy wos supp`mgi frhc hutsmig tjg systgc th rgsthrg mt th mts mamtmo` jgmdjt. Yjg gagrdy frhc hutsmig tjg systgc ms tjg gagrdy o pgrsha spgais ma `mftmad mt th o phtgatmo`. Gnhsystgcs org `mbg tjot. Gnhsystgcs org nhccuamtmgs hf `mfg matgrigpgaigat ha hag oahtjgr oai tjgmr pjysmno` gavmrhacgat. Lust `mbg tjg fo``mad sthag tjgy jovg o phtgatmo` gagrdy tjot ms `hst os tjgy norry hut tjgmr fuantmhao` ports, oai o`chst o`` hf tjg gagrdy frhc hutsmig tjg gnh`hdmno` systgc tjot bggps mt dhmad nhcgs frhc tjg ûa. @mdjt frhc tjg sua ms gagrdy ma tjg fhrc hf g`gntrhcodagtmn roimotmha. Tg bahw tjms mf wg stoai ma tjg sua egnousg wg fgg` tjot mt worcs us< jgot ms oahtjgr fhrc hf gagrdy. Eut mt ms aht gagrdy tjot oamco`s noa usg th chvg









































47

shm` th fmx amtrhdga frhc tjg omr sh pòats noa norry hut tjg prhngssgs tjot o`` hf `mfg aggis. Yjgsg org lust o fgw hf tjg g`gcgats tjot cobg gnhsystgcs whrb, eut wg sgg tjg gatmrg gnhsystgc aggis th gxmst fhr `mfg th gxmst.









































46

Njoptgr 9< Yjg @mvmad Ng`` „ Oa Hvgrvmgw

Hag hf tjg tjmads tjot ms nhccha th o`` `mfg ms tjot mt ms ng`ùòr. ^hcg `mfg ms smad`g ng`ùòr oai htjgr `mfg ms cu`tmng`ùòr. Eontgrmo org smad`g ng``s. Ng``s org cmnrhsnhpmn uamts fu`` hf nhcphagats lust `mbg ha o òrdgr sno`g o jucoa jos coay nhcphagats, o jgort, o `mvgr, o poanrgos, tjot whrb thdgtjgr th cobg tjg gatmrg ehiy whrb, gonj nhcphagat, hr hrdoa, wmtj o imffgrgat fuantmha. Imffgrgat bmais hf ng``s jovg imffgrgat fuantmhas. Ng``s cobg up tmssug os nh``gntmhas hf ng``s, sunj os ng``s tjot cobg up o jgort, j gort, hr o `mvgr, hr o poanrgos. Yjgrg org twh bmais hf ng``s, prhboryhtmn oai guboryhtmn. Yjgmr imffgrgang ms tjot prhboryhtmn ng``s iha”t jovg tjgmr aun`gus jhusgi ey o cgceroag. [òats oai oamco`s org coig up hf guboryhtmn ng``s.











































44

O`` ng``s rgprhiung ey imvmimad th cobg `mvmad nhpmgs hf tjgc sg`vgs. Tjm`g ng``s org `mvmad uamts, tjg ch`gnu`gs tjot cobg tjgc up org aht.









































4:

Njoptgr 7< Igsmda, ^yagrdgtmns, Oai Gvhùtmha

Aoturg prhiungs `mfg tjot ms gxtrohrimaorm`y wg`` igsmdagi fhr tjg purphsg hf fuantmhamad hptmco``y th survmvg. Eunbcmastgr Fu``gr wrhtg ma jms ehhb ^yagrdgtmns< ‐Wamvgrsg ms tgnjah`hdy „ tjg chst nhcprgjgasmvg`y nhcp`gx tgnjah`hdy. Jucoa hrdoamscs org Wamvgrsg”s chst nhcp`gx `hno` tgnjah`hdmgs… ‐Jucoas noaaht sjrmab oai rgtura math tjg whce os ygt









































4=

Eut wg noa mcodmag o cunj egttgr igsmda fhr `gof hrdoamzotmha orhuai o stgc. @gt us soy shcgtmcg cunj òtgr pòats nocg th jovg tjgmr `govgs hrdoamzgi orhuai o stgc sunj tjot tjgy wgrg ha`y rhtotgi hag fhurtj hf tjg woy orhuai tjg stgc. Yjms whuì cgoa tjgrg whuì eg os coay os fhur `govgs hrdoamzgi orhuai tjg stgc egfhrg hag wos pòngi imrgnt`y eg`hw oahtjgr. Yjms whuì eg cunj egttgr fhr tjg sunngss hf tjg pòat, fhr mt nhuì dotjgr chrg gagrdy ma tjg fhrc hf `mdjt gonj ioy i oy tjoa tjg pòat tjot joi gonj sunngssmvg `gof rhtotgi hag jo`f hf tjg woy orhuai tjg stgc. Tg noa ahw osb ms tjgrg oa gvga egttgr sngaormh tjoa tjg hag-









































:;

Yjg hag ma tjg tjmri pòng p òng oftgr tjg ignmco` ms hag hut hf o tjhusoai. ^h wg bahw pm ms vgry n`hsg th tjrgg. Yjms ms o rgsu`t hf hur eosg ?; nhuatmad systgc. Tg nhuat th amag tjga wrmtg hag-zgrh os tga, hag-hag os g`gvga, hag-twh os twg`vg, oai sh hag. Mf wg jovg tjrgg fmdurgs, sunj os ma tjg aucegr ?;;, tjga ey pòng smdamfmnoat ahtotmha wg bahw tjot tjg aucegr a ucegr hag ma tjg fmrst pòng rgprgsgats hag juairgi, tjg zgrh ma tjg sgnhai pòng cgoas ah tgas, oai tjg zgrh ma tjg tjmri pòng cgoas ah hags. Yjg phmat wg org trymad th cobg ms tjot egnousg pm ms mrrotmhao`, mt agvgr imvmigs hut2 tjgrgfhrg mt noaaht eg wrmttga os tjg rotmh hf twh









































:?

ms tjgrgfhrg tjg `gost rgpgtmtmvg, oai tjgrgey prhvmigs wjot ms no``gi ‐n`hsgst ponbmad–, Yjg Dhìga Uotmh, wjmnj ms wrmttga< ?.6?:… Odoma tjg ihts oftgr tjg gmdjt cgoa tjg aucegrs oftgr tjg ignmco` nhatmaug mafmamtg`y, eut gonj sunngssmvg aucegr jos `gss smdamfmnoang tjoa tjg hag egfhrg mt. Eut lust os ;.57 noa eg wrmttga ?/9, tjg dhìga rotmh (o`sh no``gi pjm) pj m) noa eg wrmttga os o fmamtg nhcemaotmha hf aucegrs oai hpgrotmhas no``gi n`hsgi fhrc. @gt us igrmvg tjg dhìga rotmh ma n`hsgi fhrc, sh tjot wg noa uaigrstoai











































:5

# o ? & 5 % " ( $ e 5' o

?

7 3

9

7









































:>

Yjms whuì onnhuat fhr tjg imvgrsmfmnotmha hf spgnmgs. Os Njor`gs Iorwma wrhtg< ‐Yjus, frhc tjg wor hf aoturg, frhc focmag oai igotj, tjg chst









































:9

tmcg. Tjot org coss `gadtj oai tmcg8 [jysmns ms eum`t upha Agwtha's fhuaiotmha, wjmnj usgs< vg`hnmty 3 imstoang/tmcg wjmnj ymgìs< imstoang 3 vg`hnmty x tmcg









































:7

Eut tjms ihgs aht dgt ot tjg rgo` smdamfmnoang hf tjg cgoamad pjysmns pjys mns jos. Yjg rgo` purphsg hf pjysmns, hr snmgang ma dgagro`, ms th fmai uamty ma aoturg wmtj tjg smcp`gst gxprgssmha. Yjot ms mf tjrhudj









































:6

@gt us `hhb ot tjg egouty ma jms rgoshamad. Yjg fhrng ms iug th tjg coss tjgrgfhrg tjg fhrng hf ottrontmha ms imrgnt`y prhphrtmhao` prhph rtmhao` th tjg cossgs, eut mt wgobgas wmtj imstoang oai ey mts squorg smang tjg fhrng ms sprgoi hut hvgr hv gr o drgotgr orgo wmtj chrg imstoang (sgg tjg





























































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































?55

Njoptgr ^mx< Yjg [hmatmad Hf Yjg [òagts M jovg sjhwa jhw Lupmtgr oai ôtura phmat th tjg Gortj, egnousg wmtj ôtura ot oehut = uamts frhc tjg sua ma mts n`hsgst opprhonj, oai Lupmtgr ot oehut fmvg uamts wmtj mts n`hsgst opprhonj th tjg sua, tjot puts tjg gortj ot oehut hag uamt frhc tjg sua, oai, tjot, furtjgr, amag-fmftjs ms tjg rotmh hf tjg shòr roimus th tjg ùaor hremt hf tjg chha orhuai tjg gortj, os wg`` os tjg rotmh hf tjg chòr coss hf dhì th tjot hf sm`vgr. Mt sjhuì o`sh eg cgatmhagi tjot = oai 7 org vhùcgs hf twh hf tjg fmvg rgduòr sh`mis ma tgrcs hf tjg rgduòr sh`mi tjg tgtrojgirha jovmad o vhùcg hf hag ma Eunbcmastgr Fu``gr”s ^yagrdgtmns. M tjga sjhw tjot tjg gortj, ma tura, phmats th Agptuag tjrhudj Vgaus oai Cors ma tjg Agptuag Gquotmha. M wrhtg<

Jg wrhtg ma jms Lhurao` os fh``hws< Tg jovg oa gquotmha fhr o sgqugang tjot sjhws tjg Gortj stroii`gi egtwgga Vgaus oai Cors. Vgaus ms o fom`gi Gortj. Cors prhcmsgs th eg Agw Gortj. Yjg gquotmha, tjot M prgsgatgi prgsgatgi ma cy whrb, ‐Yjg Ihnucgat–, ms< R(Vgaus-hremt)/(Gortj-hremt)SR(Gortj-coss)/(Cors-coss)Sa „ (Cors hremto` #) 3 oXa Yjg Cors hremto` aucegr ms 9. Mf wg woat th bahw wjot pòagt ma tjg shòr systgc jhìs tjg bgy th tjg sunngss hf Gortj, hr th tjg sunngss hf jucoas, wg `gt a 3> smang tjg Gortj ms tjg tjmri pòagt hut frhc tjg ûa, ma tjg gquotmha oai tjg rgsu`t ms oXa 3 ?4.6. Yjms cgoas tjg pòagt tjot jhìs tjg bgy ms Agptuag. Mt jos o coss hf ?4.5> gortj cossgs, o aucegr vgry n`hsg th hur ?4.6. Yjg agxt stgp ms th oao`yzg Agptuag, mts nhcphsmtmha oai htjgr fonthrs. Jg tjhudjt jg cust jovg egga e`mai. Aht ha`y wos Agptuag tjg maimnotgi pòagt, jg fhuai mt joi agor`y tjg socg surfong drovmty hf gortj. Yjhudj mt wos cunj chrg cossmvg tjoa gortj, mt wos cunj òrdgr oai tjgrgfhrg `gss igasg. Yjot wos wjy mt nocg hut th jovg tjg socg surfong drovmty. Yjg Agptuag Gquotmha ms igrmvgi ey nhasmigrmad =/7, wjmnj ms ?.:. M







































?5>

twh sgqugangs< 7, ?9, 5>, >5,… oai ?.:, >.6, 7.9, 4.5,… Nhuì jg fmai tjg nhaagntmha egtwgga tjg twh th `hno`mzg tjg pmvhto` phmat hf tjg shòr systgc8 ]gs jg nhuì, jg thhb tjgmr imffgrgang, suetrontmad rgspgntmvg tgrcs ma tjg sgnhai sgqugang frhc tjhsg ma tjg fmrst sgqugang th hetoma tjg agw sgqugang< >.5, ?;.9, ?4.6, 59.:,… Tjmnj ms oa ormtjcgtmn sgqugang wmtj nhccha imffgrgang hf 4.5 cgoamad mt ms wrmttga 4.5a „ 9 3 oXa Yjg oXa ms tjg atj tgrc hf tjg sgqugang, a ms tjg aucegr hf tjg tgrc ma tjg sgqugang. Yjms jg ahtmngi nhuì eg wrmttga< R(Vgaus-hremt)/(Gortj-hremt)SR(Gortj-coss)/(Cors-coss)Sa „ (Cors hremto` #) 3 oXa Yjgrg wos dhhi rgosha wrmtg tjgsg sgqugangs frhc wjot M wrhtg jgrg< Tg hrmdmao``y tjhudjt tjot ?.: (=/7) hnnurrgi ma tjg shòr systgc oai aoturg, o`hag. Mt ms tjg rotmh hf ôtura hremt th Lupmtgr hremt ma tjgmr n`hsgst opprhonjgs th tjg sua. Mt ms tjg rotmh hf tjg shòr roimus th tjg ùaor hremt. Mt ms rotmh hf tjg chòr coss hf dhì th tjot hf sm`vgr. Yjga M imsnhvgrgi tjot opprhxmcotg`y twmng tjot voùg (>.4) wos rgnurrgat tjrhudjhut tjg shòr systgc oai aoturg. Ywmng ?.: ms >.6. M fhuai mt hnnurrgi ma Lupmtgr, ôtura, Gortj, Cgrnury, oai Vgaus th aocg o fgw os >.4. Ahw M jovg fhuai mt ma Agptuag oai Wroaus, prgnmsg`y<







































?59

;.>4(gortj coss)/(cors coss)3;.>4(?;)3>.4 Mt hnnurs jgrg th cg wg org aht lust igo`mad wmtj ?.: oai >.4, eut oay wjh`g aucegr cu`tmp`g hf ?.:. Tg org igo`mad wmtj< oXa3?.:a oXa3?.:a @gt us try tjrgg tmcgs ?.:. Mt ms 7.9. Mccgimotg`y wg sgg mt ma tjg chst hevmhus, Lupmtgr. Mt ms tjg òrdgst oai chst cossmvg pòagt ma tjg shòr systgc. Mts furtjgst imstoang frhc tjg sua ma mts hremt ms 7.977 OW ~ 7.9. Tg sgg mt ma tjg fh``hwmad (sotura coss)/(agptuag coss)3(=7.?94)/(?4.5>)37.755~7.9 M jovg o`rgoiy ahtgi tjot ôtura oai Agptuag jovg smcmòr man`maotmhas th tjgmr hremt tjot org ha`y nhccha th Gortj oai Cors. Yjus, wg org igo`mad jgrg wmtj tjg sgqugang< ?.:, >.6, 7.9, 4.5,… Furtjgrchrg2 R(vgaus hremt)/(gortj hremt)SR(gortj coss)/(cors coss)S 3 4.5 ^hcg hf tjg chst matgrgstmad hnnurrgangs hf >.4 ma aoturg org< R(vhùcg hf sotura)/(vhùcg hf Lupmtgr)S(vhùcg hf cors) 3(cgrnury roimus)(gortj roimus)Q5 3R(vgaus hremt)/(gortj hremt)(gortj roimus)SQ> 3R(cgrnury hremt)/(gortj hremt)S(gortj roimus)Q> 3;.>4 nuemn gortj roimm ;.>4 noa eg nhavgrtgi th >.4 ey cu`tmp`ymad mt ey tjg rotmh hf gortj coss th







































?57

3 >.4 Yjgrg org oehut os coay ioys ma o ygor os igdrggs ma o nmrn`g. Tjga M soy tjot tjg gortj phmats th Agptuag tjrhudj cors oai Vgaus, wg cmdjt os wg`` soy mt phmats th Agptuag oai Wroaus, egnousg M jovg fhuai tjgy org nhup`gi, wjmnj noa eg sgga ey tjot wjmnj M wrhtg jgrg< M no`nuòtg tjot tjhudj Agptuag ms chrg cossmvg tjoa Wroaus, mts vhùcg ms `gss sunj tjot tjgmr prhiunts org n`hsg th gqumvo`gat. Ma cotj< AXv 3 vhùcg hf Agptuag AXc 3 coss hf Agptuag WXv 3 vhùcg hf Wroaus WXc 3 coss hf Wroaus (AXv)(AXc) 3 (WXv)(WXc) Yjms ms opprhprmotg, egnousg tjgsg twh pòagts org smcmòr ma smzg, coss, oai nhcphsmtmha oai org aht lust dos dmoats `mbg ôtura oai Lupmtgr, eut org o`sh tjg twh mng dmoats.







































?56

M ahw smt jgrg rgoimad tjg snmgang fmntmha whrb [ùthamo. Aoturo``y, M egdma th tjmab oehut tjg pòagt [ùth, hr wjot shcg ostrhahcgrs thioy nhasmigr o pòagt, oai tjg ha`y spjgrg M jovg ygt th nhasmigr. Jhwgvgr, rmdjt hff tjg eot ms mt aht hevmhus tjot Agptuag oai Wroaus phmat th [ùth mf yhu bahw tjg jmsthry hf [ùth8 Mt ms tjms< Yjg Ostrhahcgr, Wreoma Vgrrmgr ma tjg ?:9;”s prgimntgi tjg gxmstgang hf Agptuag Agptuag egnousg hf pgrtureotmhas pgrtureotmhas ma tjg Hremt hf Wroaus. Chrg hesgrvotmhas nhcmad `goi th tjg migo tjot Agptuag o`hag nhuì aht eg tjg nousg. O amatj pòagt wos sgornjgi fhr, oai fmao``y nhafmrcgi ma ?=>;. Yjms nhcp`gtgs o lhuragy tjrhudj tjg shòr systgc tjot tg``s o sthry wmtj cgoamad, eut ms ha`y tjg egdmaamad hf hur mavgstmdotmhas, egnousg tjg snm-fm ehhb [ùthamo, ey Vòimcmr Herunjgv ms oehut oa orntmn gxpgimtmha wjgrg snmgatmsts fmai ma tjg Orntmn oa hpgamad ma tjg gortj th o worc, ùsj whrì worcgi ey o eo`` hf jgot ot tjg ngatgr hf tjg gortj no``gi [ùth. M bahw hf tjhsg wjh eg`mgvg tjot tjg futurg fhr jucoamty ms aht ma spong, eut ma shcgtjmad tjgy no`` ‐prhlgnt dgagsms– frhc o stor trgb chvmg, wjgrgma ùsj, sustomaoe`g gnhsystgcs org nrgotgi egagotj tjg gortj ey jh``hwmad mt hut ma pòngs. Tjgtjgr hr aht sunj o tjmad ms fgosme`g, ihgs aht cottgr th cg. M fmai cysg`f ot prhlgnt dgagsms ma tjg sgasg tjot wg try th uaigrstoai jhw th nrgotg oai comatoma joemtoe`g gnhsystgcs maigfmamtg`y. Moa Egoris`gy Oprm` 55, 5;??









































?54

Njoptgr ^gvga< Yjg Imsnhvgrmgs [rgsgatgi ^h For >.4 rgnurrgat tjrhudjhut aoturg

vhùcg X hf X sotura vhùcg X hf X lupmtgr

(vhùcg X hf X cors)

( cgrnury X roimus)(gortj X roimus)

5

3

3

>

R(vgaus X hremt / gortj X hremt )(gortj X roimus)S

( cgrnury X hremt / / gortj X hremt )(gortj X roimus)

3

>

3

;.>4 nuemn gortj roimm

gortj X roimus chha X roimus

3

9(igd rggs X ma X nmrn`g)

chha X ims toa ng sua X ims toa ng

>.4

@

>.7

3

C

@3?;; shòr ùcmahsmtmgs ms o zgrh codamtuig stor ?;;

>.7

3

C

`hd ?;; 3 >.7 `hd C

3









































?5: O 3 orgo hf o > ey 9 rgntoad`g Aucegr hf > ey 9 rgntoad`gs ma o 6 ey : rgntoad`g 3 a 3 9 [3pgrmcgtgr masnrmegi ma o 6 ey : rgntoad`g 3 5; (>,9,7) ms fmrst [ytjodhrgoa trmp`gt chòr X coss X hf X omr chòr X coss X hf X wotgr

"

jucoa X ehiy X tgcgroturg frggzmad X tgcpgroturg X hf X wotgr

shòr X roimus

Ou 3

Od

3

gortj # chha X ims toa ng

;.>4 noa eg nhavgrtgi th >.4 ey cu`tmp`ymad mt ey tjg rotmh hf gortj coss th cors coss egnousg mt ms n`hsg th tga.

= 3

7









































?5=

Njoptgr Gmdjt< Jhw M Coig Cy Imsnhvgrmgs

Jhw imi M igtgrcmag tjg gquotmha< R(vhùcg hf sotura)/(vhùcg hf Lupmtgr)S(vhùcg hf cors) 3(cgrnury roimus)(gortj roimus)Q5 3R(vgaus hremt)/(gortj hremt)(gortj roimus)SQ> 3R(cgrnury hremt)/(gortj hremt)S(gortj roimus)Q> 3;.>4 nuemn gortj roimm Tjgrg ;.>4 noa eg nhavgrtgi th >.4 ey cu`tmp`ymad mt ey tjg rotmh hf gortj coss th cors coss egnousg mt ms n`hsg th tga. Mt fg`` ha cy òp ey nhasmigrmad fh``hwmad possodgs M wrhtg ma 5;;4<

Amag-fmftjs (=/7) ms gcehimgi ey tjg fochus f ochus [ytjodhrgoa tjghrgc. Mt ms ma tjg fmrst [ytjodhrgoa trmp`gt (>,9,7). Yjg [ytjodhrgoa tjghrgc, wjmnj stotgs tjg rgòtmhasjmp egtwgga twh smigs hf o rmdjt trmoad`g wmtj mts jyphtgausg ms usgi th









































?>;

igsnrmegs, oai, th fmai o dghcgtrmn, hr pmnthrmo` smdamfmnoang hf tjg rotmh. Yjg oanmgat Gdyptmoas, osshnmotgi cunj smdamfmnoang wmtj tjms trmp`gt, nhastruntmad tjg Bmad”s njocegr ma tjg Drgot [yrocmi wmtj tjgsg prhphrtmhas. Dghcgtrmn ^mdamfmnoang Hf amag-fmftjs, tjg nhscmn gquotmha. Ey tjg [ytjodhrgoa tjghrgc Tg jovg xQ5+yQ53jQ5 Yjg fmrst [ytjodhrgoa trmp`gt ms (>,9,7) Oai x39, y3>, j37 Mf O3 orgo hf > ey 9 rgntoad`g [3 pgrmcgtgr masnrmegi ma 6 ey : rgntoad`g 3 5; Oai, a3 aucegr hf > ey 9 rgntoad`gs ma o 6 ey : rgntoad`g.









































?>?

gquotmha jhì fhr gvhùtmhaory iyaocmns hf shòr systgc oai aun`gor njgcmstry imntotgi ey stors th cobg g`gcgats. Yjms pmnturg hut`magi oehvg wm`` ymgì cunj iyaocmns upha oao`ysms. OQ53orgo squorgi3[*[*[*[3[Q9 [3pgrmcgtgr Aucegr 3 a Yjga smang OQ5/[3 [Q>3 vhùcg Vhùcg/a3=/7

ôtura hremt (n`hsgst opprhonj th tjg sua) 3= ostrhahcmno` uamts Lupmtgr hremt (n`hsgst opprhonj th tjg sua)3 7 ostrhahcmno` uamts 9tj pòagt 3 cors Tg jovg<











































?>5

No`nuòtmha hf ônrgi Vhùcg GXr3?3 Gortj roimus CXr3;.7>53 Cors roimus LXr3 ??.543 Lupmtgr roimus ^Xr3=.993 ôtura roimus V 3 9/> (pm)rQ> 3 9/>(>.?)(??.54)Q>3 7==6 39/>(>.?)(=.99)Q>3 >759 39/>((>.?)(;.7>5)Q>3 ;.6>;4









































?>>

ônrgi Vhùcg Oao`yzgi, ônrgi @gadtj Hetomagi, Iyaocmn ^trunturg Hf ^hòr ^ystgc Ugvgo`gi. M no`nuòtgi tjg sonrgi vhùcg th eg ;.>4 nuemn gortj roimm, wjmnj M jovg ahtmngi nhmanmigs wmtj cgrnury imstoang frhc tjg sua, oai cgrnury roimus ma gortj uamts. ^mang vhùcg ms ma nuemn uamt `gadtjs, oai roimm oai imstoangs ma gortj roimm oai gortj-sua imstoangs, wg tobg tjg nueg rhht hf hur sonrgi vhùcg th dgt tjg `gadtj hf hag smig hf o nueg wmtj tjg sonrgi vhùcg. Mt ms ;.45 gortj roimm. Tg wm`` no`` no`` mt tjg tjg sonrgi `gadtj, mt mt ms tjg vgaus-sua imstoang ma gortj uamts (ostrhahcmno` uamts), wjgrg vgaus vgau s ms tjg pòagt oftgr cgrnury, hr tjg sgnhai pòagt.









































?>9

ûccory hf ônrgi Vhùcg M jovg fhuai amag-fmftjs (=/7), wjmnj ms gquo` th ?.: ma tjg chst sonrgi ospgnts th coa, dhì, sm`vgr, chha, sua, wotgr, omr, jucoa ehiy tgcpgroturg, oai jovg jovg igrmvgi frhc tjms sonrgi rotmh, hr nhscmn aucegr, tjg nhscmn vhùcg ey e y gxprgssmad mt dghcgtrmno``y. Yjot sonrgi vhùcg ms< (ôtura/Lupmtgr)cors3;.>4 nuemn gortj roimm Tjgrg ôtura oai Lupmtgr org tjg chst cossmvg pòagts ma tjg shòr systgc, oai Cors ms tjg pòagt tjot noa eg nh`hamzgi ey jucoas. Yobmad tjg nueg rhht hf ;.>4 dmvgs tjg sonrgi `gadtj, mt ms gquo` th tjg imstoang hf tjg pòagt Vgaus frhc tjg sua ma gortj uamts (ostrhahcmno` uamts), wjmnj ms tjg sgnhai pòagt (;.45 Ostrhahcmno` Wamts). Yjg ;.>4 ms tjg cgrnury-sua imstoang ma gortj uamts, oai tjg cgrnury roimus ma gortj uamts. Cgrnury ms tjg fmrst pòagt.









































?>7

Njoptgr Amag< Ywh ^thrmgs Yjot Toat Yh Eg Yhì









































?>6

^thry ? Ywh erhtjgrs, hag oa o`njgcmst tjg htjgr oa ostrhahcgr, cgt fhr ùanj. Yjg womtgr somi th tjgc, ‐Umdjt tjms woy, o toe`g fhr twh.– ^yiagy, tjg ostrhahcgr, somi ‐Yjoab yhu–, Uo`pj, tjg o`njgcmst somi th ^yiagy, ‐]hu iha”t cmai mf M smt ey tjg wmaihw.– ^yiagy somi, ‐Aht ot o``, oftgr o`` yhu jovg o`woys somi M oc ma tjg iorb.– Uo`pj oaswgrgi, ‐]gs, o`` hf tjot rgosha, oai sbgptmnmsc, `govgs ah rhhc fhr matumtmha.– Yjgy ehtj sot ihwa. Uo`pj somi, ‐^yiagy, M jovg egga whrbmad ha o agw prhlgnt oai jovg joi th ih o `mtt`g ostrhahcmno` rgsgornj th igvg`hp mt. Os yhu











































?>4

Uo`pj put tjg qugstmha th jmc, ‐Doòxmgs org nh``gntmhas hf stors tjot fhrcgi hut hf dmoat dos n`huis, oai pòagts org spjgrmno` cossgs tjot fhrc orhuai stors. Yjg stors org vgry for oport, oai tjg pòagts hremt n`hsg math tjg stors, tjg stors org gxtrgcg`y for oport, eut tjg stors oai tjgmr pòagts org aht, ms tjot rmdjt8 ^yiagy somi, ‐]gs, chrg hr `gss.– Uo`pj nhatmaugi, ‐^h tjg pòagts hremtmad tjg ûa, wjmnj ms hag









































?>:

^yiagy somi, ‐]gs, oai sh8– Uo`pj oaswgrgi, ‐Tg``, Cors ms tjg pòagt wg noa tgrrofhrc, tjot ms cobg joemtoe`g fhr jucoa `mfg egnousg tjg maagr pòagts org thh n`hsg th tjg sua cobmad tjgc thh jht, oai tjg hutgr pòagts egyhai Cors orga”t gatmrg`y sh`mi, tjgy org dos dmoats, sh wg cust, mt whuì sggc, sgt som` upha tjg nhscmn hngoa fhr Cors.– ^yiagy somi, ‐Tg`` tjot o`` shuais vgry cystmno`, tjhudj `mvmad ha o pòagt hf `mcmtgi rgshurngs, oai manrgosmad phpuòtmha, wg cust hag ioy nh`hamzg Cors.–









































?>=

Uo`pj wgat ha, ‐Jgrg ms wjot M jovg fhuai. Gortj omr ms oehut 4:% amtrhdga oai 5?% hxydga. Tg noa trgot ehtj os imothcmn ch`gnu`gs. Yjg chòr coss hf amtrhdga dos (A5) ms 5(?9.;?) oai tjg chòr coss hf hxydga dos (H5) ms 5(?6.;;). ^h,– (oai jg wrhtg ha o aopbma)< Gortj Omr 3 5R(?6.;;)(;.5?) + (?9.;?)(;.4:)S 3 5:.7476 ‐Yjg cortmoa otchspjgrg ms chst`y noreha imhxmig (NH5). Yjms









































?9;

^yiagy oaswgrgi, ‐H.B., M oc ah emh`hdmst, eut mt shuais dhhi th cg.– Uo`pj nhatmaugi, ‐Tg`` dùnhsg ms N6J?5H6, wjmnj dmvgs o chòr coss hf,– (oai jg wrhtg ha tjg aopbma)< N6J?5H6 3 6(?5.;?) + ?5(?.;;:) + 6(?6.;;) 3 ?:;.?6 ‐Oai wotgr (J5H) nhvgrs chst hf gortj oai ms gssgatmo` th `mfg, mts chòr coss ms<–









































?9?

^thry 5 ‐Jm Froab, tjoabs fhr cobmad mt ihwa jgrg, M rgo``y opprgnmotg yhu pu``mad owoy frhc yhur whrb ot tjg hesgrvothry. M oc sh dòi yhu nhuì dgt ihwa jgrg sh qumnb, wg rgo``y aggi oa ostrhahcgr, oai M tjmab wjot M oc dhmad th sjhw yhu wm`` jovg coig yhur vmsmt whrtjwjm`g.– Froab osbgi, ‐Tjot ih yhu jovg Loag8– ^jg egdoa, ‐Tg uagortjgi tjgsg wrmtmads ha nòy toe`gts ma o imd ma











































?95

cust eg o ngrtoma woy dmvga tjg nrgothr whuì ha`y cobg aoturg onnhrimad tjot, wjmnj ms imvmag. Oa gxocp`g hf tjms tjms ms tjg chha chha noa rmsg ma tjg gost gost fu`` hag amdjt, amdjt,









































?9>

M soy fhur tmcgs tmcgs >6;, egnousg fhur fhur tmcgs >67 oai oai hag port ma fhur fhur ms gxont`y tjg ioys hf 9 nyn`gs hf tjg sua frhc shutj th ahrtj oai eonb shutj odoma.









































?99

Loag somi, ‐Jms rgvgrgang fhr tjg aucegr ?5 fhr tjg rgoshas jg somi, wjot noa yhu soy oehut tjot8– Froab oaswgrgi, ‐Jg sggcs th eg jovmad oa mab`mad th tjg font tjot









































?97 Njoptgr ?;< Njhhsmad Hag ^tor Hut hf Yjg Em``mhas @ghaori bagw O`pjo Ngatourm wos tjg n`hsgst stor systgc th gortj, oai tjot mt wos o trmp`g systgc shcg 9.5 `mdjt ygors owoy. Jg o`sh bagw tjg prmcory, O`pjo Ngatourm O, wos o D5V coma sgqugang stor, wjmnj cobgs mt tjg socg bmai hf stor os tjg ûa2 smcmòr ma smzg,









































?96



































































































































































































































































































































































































































































































































































Genesis Projects 01, 02, And 03

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