Pythagoras, Archimedes and indian mathematical theories

PMLA e: Hubuyôpus, "Apyyinönz xui Ivöıxös as pulnpurixes Oswpins 157 Dev Opnoxeiuv Evreizotürnv Ékpadov ápiduov te Kai povoikñAs Kai tOv tdo padnpdtey Er’ dxpov ¿A0ów rap abtoic (da te d@5eKa ¿rn ouvôratpiyas, eis Lapov bréotpeye, repi Extov mov Kai nevtnKootov ¿ros ón XPIETINA @IAH, "A0Nvat Punt C., Pythagoras, Archimedes and Indian mathematical theories’ 4Y yeyovms»®. Mera ünö più obvroun rupupovi) oth Lapo takidewe otoüg Ari pos, IIYOATOPAZ, APXIMHAHZ KAI oth AijAo, ory Kpñrn,. ot) Eraprn «dev eis áravra tà navreia raptrafe, INAIKEZ MAOHMATIKEZ OEQNPIEZ Kai év Kpñtn öl Kai Ev Exápty tOv vopov Evexa Stétpiye Kai Tobrwv ünüvtay Úxpoutis te Kai palytis yevopevoc, cis olxov éxavedOdv Öpunoev Èri T@y rapereieppévov Cytnoivy?. Nudauydopugc-Samkhya “Qpipog ma karaknyeı oróv Kpötova tig Káro "Iradiac, éxov iôpôet Ma noAby xupò rà tubidia tod Mudayópa anotédeouy Eva aveEavtAnto Kai ÉAKUOTIKÔ Oépa yiá tobs Proypadpous tov'. “Opms 500 xi liv oí Gvagopéc tHv Proypáguv tov yiù ta tatisia? Sev Exouv Gxodvuty iotopixy GEia, dev npéxer va nepäceı àraparñpntn ñ éxi- Kai dtev0bver tiv LyoAH tov. Mapá mt) puorirórnta? mod nepiéfadrde iv Ardaokadia tig ExoANs tou Kai tiv EAdeıypn ypuntòv Ketpévey tod ¡óLov tod iöpurfj?, répacav ariv Snpoowtyta ôpiopéva onpria tic MvOayoperas Arduoxadiac?, Grws: ôpaon tic "Avarolfis oriv Mudayópeia Audaokukia. “lows axopn tà tagidia 100 Mudayópa «và ÉEnyobv» tiv áróxtnpon ts L'H Mvu@ayopera AtéacKkadia tev ùppiatov à pi0u@v. yr@ans tov Kui tij¢ Oavpactijs Émornpouxs tov Karüprıang?. Zönpova pè th Proypagia tod ‘lapPAizov, 6 Mudayópas Epewe cixoat- Kata tov Mpóxio*”, y dvaxdAuyn tév douppéetpwv Ópeiderar otòv Muduo ypóvia pè tods lepopävteg ris Alyórrov*, kai dtav è Kuußüons, Bact- Oayôpa. Enpepa à üvarakuyn tOv üppiitwv apr0pòv Kai idtaitepa TS Y 2 das tg Nepoiac, rarélafe tiv Atyurto, «eis Bafulova àviyOn, Kaxet toic Mäyoız dopévors ovvdarpiyas Kai éxmardeudeis ta rap’ abtotc cepva Kai uvaunv Kai mod nv abris Eroioüvro yvpvuciav te Kai ÉmpÉAEUV, Ev ye tH puvdáverv où npdtepov apievreg tO diduorxbpevov Éws reprlá former fefaios ext rig nparng palhocasy, I. Tpeig elvas of Proypagies rod Mudayópa rod Stuowdnkuv: rod “lapPAixov, too HMopgupiov Kai tod Atoyévn tod Auepriov. BA. lamblichi, De Vita Pythagorica, Teubner L. Leipzig 1937. Porphyrii, Opuscula Selecta, A. Nauck 2e Auflage, Leipzig 1886. Diogenis Laertius, Vitae Philosophorum, ed. Long H. S. 2 vol. Oxford 1964. 2. B2. F. Wehrli, Die Schule des Aristoteles, 10 Hefte, Basel 1944-1960. 2e H. Aristoxenos fr. 13. 1945 Kai J. Bidez & Cumont F., Les Mages Hellénisés, Paris 1938. "Axöyn D).. Is. Lévy, Les Sources de la légende de Pythagorr, Paris 1926. 6 Mu0uyòpuz tmoxépOnxe mv Alyurro xai Eyive padnrhs t@v iepéwv. BA. H. Diels & W. Kranz, op. cit., 14.4. Tia più avornpurıcn pedérn tv tugidiov tod Mudayópa fà. tò ápOpo toû Th. Höpfner: «Orientalische und griechische Philosophie», «Beihefte zur alten Orient, 4. 1926. 6. lambl., op. cut, Lt cap. V & 25. 7. Bi. E. Zeller and R. Mondolfo, La Filosofia dei Greci, Firenze 1.1, 3e ed., 1951, 3. P. Gorman, Pythagoras. A Life, London 1979. 4. «xai mepì Bedv xitov tt Euaßev...» Porph., Vita Pyth., ed. Nauck «xai cuppitavia tois "Hiiorokitug, ixneup@fvar pév cig Mépoiv, ús rpòs xpcofurépous, ti y a).nOcig axertopevov tv "H}ioro,irdv ta rouubru», ib. oc). 16 1.31. «Kai év Aiyórto pèv roîg lepedor ouviy Kai thy cogiay Éépude, xai ev r@v AiyuRtiwy puvhv ypunpéruv dè tpıooäs dtupopäg, ¿moroorpupixOv te Kai icpoykupıkav Kai cupfodiKdy tav pty xorvoZoyovpévwov Kuta piunow, ròv Se G2.Anyopoupévey Kara tivas aiviypots», ib. 13. 15, t. 18. "EG G)2.0v And rov TayußAıxo puduivoupe: «Tov 15 ötöuakukias tporov oupPodiKdy rowiv Encyeiper lambl., De Vita Pyth., och. 164. 5, lambl. De Vita Pythagorica, 1.1 Cap. IV 5 19. ‘O 'looxpärng && G2.0v dvagépet Gr (6 Mvluyopas) Kai maven Gpotov tots év Aiyórto èidayuaoi Kal’ è érasev0n.., "Novro dè delv Karbyetv Kai Some év ti) vpn nüvta ta diduoxóneva Kal péypr robrov ovoxevúlcoOm tag te pu0noui Kui tas unpodoric, péxpig Grou Suvurui mupudéyeobur tó puvOdvey kai diapyvynpovedov’ Ori Excivd éariv, © det yryv@exciy, Tobro dh riv yvo guidaaniv' Erie yodv agddpu uv 2. 404, n, 4. B2.. àxôun lambl., op. cit., 94. 8, "O Aroyévns è Auéprios âvupépei ón 6 Mudayópas dtv Gonos xavéva obyypappa’ Bd. Diogenis Laertius, Vitae Philosophorum, 2 Vols., Oxford 1964, 8. 6. Môvo 6 "Hpáeros loxupilerar tó avribero. B).. Diels, op. cit., 22 B 129. 9, "Ou Eyive yymord oyetixad pè th Aiôuoxuzia Kul tiv Epevva rod Muluyópa Kai ts ExoAfig tov, ta np@ra Exaró xpóvia arò tiv jöpvon tig Exo?.As, Öyeilerar apyixd oróv 17.0,a0, 400 r.X. Tıa repracórepes Lextopéperes PA. JS. A. Philip, Pythagoras and Karly Pythagorism, Toronto 1966. "Axöyn PA. tó Epyo rod Ed. Chaignet, Pythagore et la philosophie pythagoricienne contenant les fragments de Philolaus et d'Archytas, Ouvrage couronné par l'Institut, Paris 10, «éni Se rodrois Mudayópas mv nepi adrñv (sc. thy yewperpiav) puU.ocopiav cig

Xp. Pin dév drodidetat Gxoxe1otiKa otòv Mvdayópa, di id otobs Ilvbayöpeıovg too Hudayópaz. “Apgyuyens ul lydinds palnpurxes Onopies 159 otolyovacs ÉVVOLES mob anédide 6 Huduyópas ci Kae oteped'*- küBos-yh, El aiove n.X.''. Daivera Gti À avakakvuyn tOv appitov appa kparnünxe rupupnida-nüp, dKtdedpo-anp, cikxoodedpo-témp, dwdexdedpo - TV TOD mav- Hvotiky ano mv aderpórnta tOv TOs opaipu'®, Mudayopeiwv, xalws n GAN Sop rs Deopias Baoiornke othy Evvora tod pytod aprOpod'?. "O ükoyog À Gppytoc üpılnös hrav Katt rob diutapacoe tiv épuovia tod úElmuarirod tous "Ag doüne twpu tig Gvudoyies mov nupovordler i apyarotepy ivôuxi] procogia, y Samkhya, pé tiv Mudayópera. “H ivétkh rupadoon Bewpei tiv ovoethpatos. Xapaxtnpirotixi] eivar Y ppácn tod DPiroAdov: «Peddoc di obdév Séyetat à tH dpi0pò quais obdè ápuovia: où yap oikelov abtots tomi. Tas tH Gxeipm Kai avontw Kui GAdyw pocos tó yebdos Kai è plôvos nepi tov obpuvôv Ocwpñpatu». Porphyr., De Vite Eatin’. piferun ta Téia: «...decimus... apud Acgyptios geometriam primum inventam fuisse quae ab Pythagor., ac). 6. Kai 6 Mpóxos ioyuagrorum emensi ortum habuit. Hace si quidem illis necessaria fuit propter Nili inundatio- 2,"H Aiduoxaldiía tv névtre cotoriyeiwv-tav RÉVTE otepe@y. nem convenientes singulis terminos diluentis... Quemadmodum erat apud Phenicas propier mercaturas atque commertia apud Acgyptios quoque numcrorun certa cognitio sumpsit exortium, ita sane Geometria ob jam memoratam reperta est causam». Proclus, Lib. Il, c. IV. ‘An’ 6,1 Eyer repiowbet paivetar Gti 6 Mudayópas yvópile ta Kavovixd Exò)10 tod Lou PiBiiov av Lrayriew tod EUxAsion avagspei Ott oi Mudayóperor nodvedpa'* Kai tig KatacKevés tous. "O MAovtapyos pic àvugéper tic avtiyvopı$av tpia pôvo xuvovika ro dcôpu, dnd. tov kúflo, ro terpúzdpo Kui TO dwdexdcdpo xui Ott Ô Tiputos dvaxéz.uye tú a do, 5n?.. 16 Oxtácópo Kai tó cixocúzópo. 15. «Tludayöpus rövte cxnuúrov Ovrwv otepràv, üncp cu.ritar Kai paßnparıxa, éx oxiuu ruócias &rudépov peréornorv úvedev tac Gpzas airis Exioxonobpevws Kai pév rod xüßou enol yeyovevar thy yi, Ex dè ts mupupido; tó rüp, Ex de rod ékruéôpou “blos ta Ocopnpara Ötepcvvopevos 65 6h xui thy tOv dlóyov npaypurziav Kai thy tav zöv dépu, Ex SÈ tot cixocutépovu tó Üéwp, Ex Sè tod öwdexusöpou thy tod ravrò; oguipuv». KOCHIKO@Y cynpdtav Plut. Pew. II, 65. Bi. axdpn Ocdgpuctos - ‘Aéro, Diels, op. cit., 44 [32], 15. oboracsıv avedpe», Mpóxiov cic a’ Etxicibov, £xó. Friedicin, "Apkerous vives ápyótepa 6 J. Kepler —éxnpeucpévos arò tiv rudayópera xui ni.u- Leipzig 1873, or. 65. Enprerwovovpr òri ord Kai Gdoyo riva à ÉAnvxh dvopecia yá ö,rı ofpepa dvont- TavikH puU.ocopiu— zpoorulnoe va EEnynact ric nußuyöpeıe; Kui xarwvixds avriotor- Coupe antò Kai doonro Gvticrotza. "H dnptoupyi« Kal i avarrufn tis Oewpiag rv douppexies. Méou ano rpoP).muutu neyiorov Kai Ehuxiorou otepedy (fi. Nova stereometria doliotpv rirora bros thy Ppioxouge ord X Biflio av Frurzeimr tod Etxicidou dpyice ano rum cinarivrum imprimis Austriaci supplementum, Linz 1615, y Opera Omnia, ed. Ch. Frist Frankofurti a.M. und Erlangae 1858-70, vol. IVe, 551-646) UmoBiter Gti tO terpacdpo mv éxoxh 100 Miurwvos. SacKaiog tot Matmvosg ora Ma0nparixà (Aroy. Auép- REPIKALIEN tov pixpdtcpo 6yxo yiù mv Exipaveta tov, Evo avriletu vò eixocúzdpo tov peyu- 103 IH, 6) áoxodeirar pè rò npößinuu tOv àppirev Óxi Óuos pe tó yevixò, 2.2.0 Kura- Júrepo. Tig oxtccis abris Óyxov xui Émipuvcius tig ouvdéci pé tic jörörntes Enpörntus miaverai pè tobs Gpphtous and Y3 fw; y 17 Kai Excira oraperá. Bi. Márovos Orairyra: Kai bypotntas. "Era ágod N ponia elvur rò Enporepo ùnò ta névte crorgeia Kai tò vepò "0 Ocódepoz è Kupnvatog tó onpeio ubrò 100 Orarrijrov éxifefiaid@ver Gu À 10 byporcpo, avrıiotorgei tO rerpúcópo oth wwrid Kai ro cixooücôpo otò vepó. "O xúflos y2 Arav non voor. BA. W. Burkert: Weisheit und Wissenschaft. Studien zu l'ythago- 2.670 tis cbotabcius tov, üvriororgei ati) yi) Eves Gvrilera tó Oxtdedpo nov cdKoka mepiras, Philolas und Platon, Nürnberg 1962, 02).. 437. orpepetat, üvriororgei oröv dépu. To dwéexdcipo üvriororgei oto obprav, yuri Exet 147d 148b. Kara tov W. Burkert "O xalnyntns x. Eby. Lrapatns brootnpileı Gti à M.atov LOyw rs iepdtnras rod ùpi0pod 17 otupurà tov Ocódopo arnv áródción tod Gouppétpov ris Y 17. Bi. Mouxrixd ‘xadypias "On, topos 31, Eros 1956, avaxoivmats 12-1-1956. "Axöyun 6 inpòg àpi0pòg 17 tHv Tivdayopeiov Exaile anpavrıxö pólo ativ xuruoxevn tio rnoduyóperas povorntiig KAipaxuc. BR. MA. Tiras, 36 6.8. Il. ‘H aròdriGn uom ov Mudaropeiov fluoiornke navw ony rexvinm 100 dpriou ówmdexa Eöpes, Grws ómbexa oùdyfloiu Exer Kai 6 GwdiaKds kurios. Tıü più yevixotepn uriétn Pi. ro x.uowò Epyo tis Eva Sachs: Die fünf platonischenKörper, Berlin 1917. 16. Tid tó dudexázópo cidixa Ovpitovpe Stet ol ESpez tou civat xuvovikà nevräyova kai Örı of Stayaviat adtHyv tüv revrayovov cynuuritovv Eva ozipa, dvaxoyo pè thy mevtaza, nov Édcopeito oùyufloio dvayvOpionsg Onxe Kui cè Pafurwviuxà oyédia, tv Muduyopciov. To axfina ubró fipé- Ónos avupéper Ó B. L. van Wacrden, BA. Science Kui tod repirrod, «Aobppetpos À btapetpos Sua tO yiveoOat tà repitta Tau trois dptiotc Awakening, I, 4n éK6., 1975, och. 101, ovupirpov rebeiong». "Aptor., ‘Aravrixa Modreva 23, 41 a 26. Lyetixa pè to oa ubro —ox da rod Jupiter dpretà tò yvoord onpitixd obpfpoko— 12. Pid nepioodtepeg Aertopéperes BA. E, R. Dodds, The Greeks and the Irrational, Berkeley 1951, Kathys Kal Arpad Szabo, Hi dogai ren éme Munari, "Alva 1973, 13, Diels, op. cit., ach. 244. fii. J. Marquès-Rivière: «.lmulettes, talismans et pentacles», Paris 1938, 082. 49, 0%. 9 kai Hammer-Purgstall Literaturgeschichte der Araber, Wien 1854, of). 10. Eùv pd aneıxövion tod yxwpoypovov —oè ¿En Sruoráccig— tò fpunvever 6 P. D, Ouspensky, PA. P, D. Ouspensky, „I new Model of the Universe, London, 3d ed. 1948,0€2.. 445-446, oy. 18. 14. Eröv Proypago tov Moppúpro Srußaloune: «Peoperpias pév ex nav xpovov “AGiCer va onperboovpe bri td 1885 fipéOnxe Eva Kavovixd Gwôekdcôpo Erpovoxixiig Ener Oivar Alyurtioug tà 5é mepi dpiOpobs Kai Loyianods Polvixas: Xaddalovg de rá «utuyoyAs, stò Monte-Loffa xovtà ornv Padova, nob ypovod.oynOnKke vapitepu amò tó

Xp. Pin Hutluyôpus, "Apyıyunönz xui "Ivöıxds padnpatixés Ocmpies 161 Sämkhya oüv thy mó üpyaia Oewpia (darçana). "H XéEn Sàmkhya ¿EnyiOnxe pè ti) oeipa tov tv rupidide otòv Pancaçikha, kai dx’ abröv tiv rapérafe uè Giapgôpous tpörovc. "O R. Garbe!? Oewpei ón i AéEn Sämkhya rapéyetur 6 Içvarakrsna**. ünö ti AEEN samkhyá rod onpaiver üpıdpös, Kai morever Ón onpaiver ‘Ar’ adrû yiveraı puvepò nöco Súcxodo elvar va S@covupe thy axpr bh üxöun, árapidunon, Epevva, ávádvon. ‘O Oldenberg'* morever ón Exppülcı nepiocôtepo tiv Evvora tic npaöng tod ¿Zerálerv, 100 Aoyıcpod i) arapi0non tov dadoyix®v otorzeiov. "Evi 6 Jacobi’? moteder Gti onpaiver tov xa0opiopò mäg Evvorag and tiv Grapibunon tod repieyopévov tov. “lows Ökeg abres ol èEnyNoerg va Nrav yvwotÈs Kai Gnodextés otiv apyaia ‘Ivôia, önora Önwg xt div elvar à EEHyNoN?? 6 xbprog oróxos tig Sämkhya elvar Evas, 6 oupñc diayompropòs tod rveúparos (purusha) ano tiv dan (prakrti)?!. "Töpurg tod praocopiroû avrod S6ypatos civar 6 uubixos Kapila?? rob dturunwoe tic piLocogikés tov doEaaies E€ywpa and tods ayloug Kai copobs ypovodoyia this ovotnpatixi)g iôpuons tij¢ Sämkhya, rod ñ aGpzh ths npéner vá tonoderndel pepuxods aidves n.X., otòv ET” ij E’ aióva ?*. “Opws, of piles tod ovotijnurog Sämkhya npéner va civar noAb Paberés. “Avayovrat othv roy nov ol úvOporor, úvaldovras tú otorXETU TG CucoMpEvpévNes neipag, apocorúbncav va dtaxwpicovy ta otoryeta Exelva mov pè tov Odvato «éyKatakeinovv» tov dvOpwnxo Kui ¿xelva mov elvar «a0avata» Kai ovvodevovv THY yuyn. "Eror y Kataymyi tig Simkhya elvat dvandonaocta ovvöcdeutvn pè tO peyúldo rpopinpa tòv oroiyeiov rod rapupévouv GBavata otòv üvOpuro. épunveutés tOv PedixGv xerpévov. "H mo nadia ypanti xpaypateia rapa- "H Sämkhya üvalntü Kai ornpileı «tov Avtpwpò» ünoxkeıorıkü or never y Sämkhya Kärikä tot Igvarakrsna??. "Orwoôñnote Spws, 6 Içvarakrsna dév eivar 6 rpòrog ovyypapéas ts Samkhya. "O copds Kapila, pubixós idpuris tod ovorijnarog, naptimoe Th Gewpia otòv Asuri, Kai Exeivoc yvoaon. “H únelevdepwon ùpyiter va yivetat Krijpa ¿xeivov rod üpyiler vá yvopiter cè Pádos tiv odcia Kai tH pope? tic pbang (prakrti), önwg Kai TOUS vopous rod ÖLenouv tiv ÉÉÉALEN ng. Mé tòv tpdxo abtò 6 Avrpwpòg Epyetar Órav n dıavora (buddhi), öönyei tov GvOpwxo otd xat@ghi tod EvRvHpatoc. "Apxeroi pelerntes napadéyovtar örı 6 Povdiopds àrotekei Gueon 500 n.X. Fiá nepicaórepes 2enronépeuc BA. F. Lindemann: Stzungber, Bayerische Akad. IViss., 26, 1897 ae). 625-768. 17. R. Garbe, Die Simkhya - Philosophie. Eine Darstellung des indischen Hationalismus, Leipzig 1894. 18. Die Lehre der Upanishaden und die Anfänge des Buddhismus, Göttingen 1915. rpoéxtuon tig Sämkhya. “O Garbe x.y. üvapäpeı èkt® xorvà onpeia peraEd Bovdicpod Kai Sämkhya?*. Tú mò onpavtixà elvar Gti 6 Povdicpds Önwg Kai à Sämkhya elvar «capiOpntixés pu.ocopiec» yrati ypynoimonoioby ovyva 19. Göttingische Gelehrte Anzeigen, 1919, 20. ‘O xa0nynuig M. Eliade ¿Enyet tm 2£3n Sämkhya oûv «discrimination» (diugwpionös) Kai «discernement» (Sráxpron). BR. M. Eliade: «Patanjali et le Yoga» coll. Maitres spirituels, Seuil 1976 cel. 13. 21. Bhagavad-Gita Keo. Y, otix. $, uerapp. A. Fudavob, "/rdixai peragodariz. “ADi- 24. Bd. R. Garbe Die Simkhya Philosophie. Eine Darstellung des indischen Rationalismus, Leipzig. 1894, Kai V. Sovani, A critical study of the Sánkhya System on the lines of Sankhya-Karika, Sämkhya-Sûtra and their commentaries. Allahabad University vat 1845. Studies, Vol. VII, 1931. Cid pià rmeprnnux pedétn PR. 10 ápOpo tod Th. Goldsticker, 22. 'H Ouvparovupyırn) tov Öbvayn avayvmpiterar Kai at éxixd Epyo Mahäbhärata peragp. A. Tudavod, op. cit. (BA. HI, 107). Sankhya ot “Eyxrxdonuidera 23. BA. Gymnosophista sive Indicae philosophiae documenta collegit. edidit, enarravit Christianus Lassen. Voluminis I Fasciculus Isvaracrishnae Sänkhya - Caricam tenens, London Chambers. "AvaSnpocievon otö Literary Remains. 1879, vol. I, aed. 170-176 Öönwg Kui tó Epyo tod Madhava Acharya, The Sarvadarsana samgraha or review of the different systems of Hindu Philosophie, transl. by E.B. Cowell and A.E. Gough, Tribner’s Oriental Series, London 1822, chapter XIV, The Bonn 1832 ñ The Sankhya Karika or memorial verses on the Sänkhya philosophy by Iswarakrishna; translated from the Sanscrit by Henry Thomas Colebrooke. Also the bhäshya Sänkhya-darsana, 0). 221-230. 'Axópn pia covroun replänyn As Simkhya Bpioxoupe or commentary of Gaurapäda; translated, and illustrated by an original comment, by account of the Sàmkhya, Journal of Indian History, vol. VII, Dec. 1929, ari. 5-7. Horace Hayman Wilson, Oxford 1837. "Axóun P).. John Davies, Hindu Philosophy. The Sánkhya Karika of Iswarakrishna, Eliade, ioyupiloveaı Gt: ypüpınke tov 50 p.X. ai@va, Pi. M. Eliade, op. cit., och. 13, Kai ord émxd roinuu Manimékalai. Bi. S.S. Suryanarayana Sastri, «The Manimékalai 25. “Ojos yá Th oùvruën tod Epyou dev brüpxeı Spogwvia. “Addor, Gros 6 M. An erposition of the system of Kapila, With an appendir on the Nydya and Vaiseshika systems. Trübner's Oriental Series, London 1881, i) The Sánkhyakáriká, with an exposition called Chandrika by Náráyana Tirtha, and Gandapadacharya's commentary, Edited by @ 2.01, Gr; 6 Belvalkar, riotevovv Gr ypagrnxe tòv lo i) tov 20 p.X. al@va. BA. Bel- Pandit Bechanarama Tripathi. Benares Sanskrit Series No. 9, Benares 1883, # S.S. Souryats Simkhya [9.. tó Gp0po tod Haraprasad Shastri, «Chronology of the Simkhya System», narayana Sastri, The Sámkhya Káriká of Isvarakrsna, With an Introduction, translation and notes, University of Madras 1930. Journal of Bihar-Orissa Research Society, June 1923. valkar, «Mátharavratti». Annales of the Bhandarkar Institut, vol. V, Poona 1924, 133- 168, Tid pu ción peréty, oxetiKy pè té npoßAnpara tod xpovokoyikod mpocdiopicpob 26. B). R. Garbe, op. cit., ach. 3-5, DIAOIOGIA 15-16 (1985-1986)

Xp. bin ta&ıvonnoeig, drapiOpijoers Kai oynpara, Gxwc Kai tt ta Slo ouotipatu miatevouv Gti À Abrpwon elvar è brépratos avOpmmivoc GKonöc. "O Jacobi?” ¿nions Séyetar ta oupnepdopata tod Garbe Kai broypappiter tig orevés oxéoetc tv nidäna Kai tv «xatnyopi®v» this Sämkhya, Kai onevOvpiter ón 6 np@rog Saoxahos toh Boúda, 6 Aräda, rav Önuöög Fubuyôpus, Apyipndng Kai ‘Ivôixés nn paßnparırds copies 163 rpoxakoüge tiv òpyil tv Vedy, i) ypappatiKy Kai 7) ètvporoyia elyav oùv xupio xu0ffxov va fonOngovv tiv xaravonon tóv iep@v xeipévov. ‘Akôun Kai î otevi) oxéon puocopias Kai Ocoloyias, pè axabdpiota cúvopa tg más ind tiv dii in ovveßais onpavnxé, otre Sha abtà va tovicouv thy rpwtorunia tv ivétkOv padnpatiKdy. tig Sämkhya, cippwva pè tm) paptupia tod Acvaghosa, army Buddhacarita. Ta keipeva tOv teketovupyixOv Kavévwv Kalpasutras kai tú cvupxAnpo- Lé pra Gn tov épyacia éxavépyetat otd idro Dépa Kui onperdver: «è PovSiopòg div ¿upavilerar oùv pra Avrıypapn) di iù ody più rpocwmxr ¿Eñynon puta tous Sulvasitras*' —Keipevu rpoopiopéva GTV reprypugi xavovov dia civ Püon nave otiy Önoia ytiotnKen*®. *H Sämkhya rapovandleı apxetic dvadloyies pè ta owLöpeva otoryela us Mudayóperas drdaoxakias. "Era ori Sämkhya Bpicxoupe thy yvOpiun 6oEaoia tic perevoápkoons?”, Seapnon rod suvavräne otiv 'Ivöia axd tov LT’ x.X. aióva. Tis árayopeúceis Spicpévwv tpopayv, x.y. THY xapaxtnpiori) yuá tods ‘Ivôods àroy darò tò xpéac, i tiv árayópevon tov xvapwv, ärayöpevon roù tiv ouvavräpe ón and tov I x.X. aióva?”. Oi palnpanrès yvhoes orhv Ivéia —xpiv Kai peta thy Exoz tod Mudayópa— Frav Gbiayapiota cuvdedeuéves pè ti Opnoxeia. Où O8).ape va broypappicovpe Sti À Kowvovixy Kai % rod Con tis *Ivdiag éEovoraLôtav and th Opnoxeia. "H Erıdupia va Beorıotoüv cwotoi dizAaciacpod pudix®v Popev i) Katackevh fopòv yu Karanolfunon tic Katacxevils Popav— pac tovilouv Sti of pa0npatrixîg üvakaküyeıs tOv ris Sämkhya. ‘H Sämkhya dtv ypnoiuevos oùv rpôturo yiù tó Bovdtopod “lvé@v rnyálovv and pepikes Aarpevrıxös Gxaithoess. Arúpopa xpofAnpata, mknavovKAuc, pac Ovpitovv pè Ouupaari) üvakoyia 16 Añdiov npößinpe. ‘Hyvooti «urvdayòperu rporuon» Kai of äppnror üpılpoi (kaanra), joav yvootoi. Múliora Lrfpye kai iötaitepn Svopacia, x.y. y2 = dvikarani, Y3 = trikarani, Y10 = dacakarani, Y40 = catvaringatkarani x2x.??. Tédos à xocpoyovixi] rupudogn tv révte otoryziov —adp, údop, 7h, anp, aidip*?— ñrav t6c0 nod) dudedouévn Kai oikeia ctots 'Ivdoüg ote va Bewpotv tó Bavaro ovv@vuno pè thy dxocúvdeon cè xévte otoryeia?*. "Axópn à cavoxpitixh LÉEN akaca (ai0ñp) péperar oùv rapagBopà ris £M.nvikijs Ólxáúc?*. “O rpütos rod rapatiipnoe tiv üvukoyia Gvapeca otò oùotnquu Sämk- Kavoves yià tv ieporeAeotia mov Ovotdv ¿dwce tiv np&rn SOnon yiù tic äotpovouxës napatnpioets. Ol pwwntixoi xavóves ExivonOnxav yrati ñ hya kai oth Mudayòpera paocogia itav è Sir William Jones’, ddoúuevos LavOacpivn rpopopú Évès Kai póvo ypappatoc tHv Opnokeutikdv TOR@V, 31. BR. tò kiuoixd Keipevo tod G. Thibaut, «On the Sulvasútras», Journal Asiatic Bengal, vol. 44 (1), 1875, oe). 227-274. Ma rò p6Ao rob Enarfuv ol Sulvasütras otàv TE LETOUPYKT Katay@yh tig Femperpiag 27. BX. Jacobi, Der Ursprung des Buddhismus aus dem Sämkhya Nach. Konigl, fix. tó Évôiugépov äpÜpo tod A. Seidenberg, «The Ritual Origin of Geometry», Archive Ges. Wissen, zu Göttingen, 1896 oc. 43-58. 28. BA. Jacobi, «Uber der Verhältnis der buddhistischen Philosophie zu Sämkhya Yonga und die Bedeutung des Nidänas», Zet. Deut, Gesell., vol. 52, 1900, och. 1. 29, [ud neprocórepes Acntopéperes PA. H. Oldenberg Zur Geschichte der Simkhya Philosophie». Nach. Gótting. 1917, a. 218-237. i Satischandra Vidyäbhüsana: «Sámkhya Philosophie in the Land of Lamas», Journal of the Asiatic Society of Bengal, 1907, och. 571-577. BA. axöyın J. Gonda: Change and Continuity in Indian Religion, The Hague 1965. “Opus è peadropds tig Sämkhya, önwg kai ñ Dion ing yiù TV TpaypaTiKdétnta TOD tEwrepixod Koopov, kpl0nxe Evrova and tods ieadtatés Povdiotés. Bd. Vijnaptimatratäsiddhi rod Vasubandhu. Metagpacn ano ta xivétika Kai oyó and tov L. de la ValléePoussin, tom. I, Paris 1928, 23-26. Tékos BA. tm yevixbtepn pearctn yıa thy Sámkhya tod J.A.B. van Buítenen, «Studies in Sámkhya», Journal of American Oriental Society, LXXX (1956), 153-157, LXXXII (1957), 15-25. 30. Erhv Mäiträyani Samhita, mv ápxarórepn Yajurveda, ouvavräne tig anayopevorts oyeriKis uè roùs xuapoug Mäitrâyani. 1.4.10. "Eridns ka otiy Käthakam Yajurveda tig lóms änayopeborıg. Bi. Käthakam 32,7. for the History of Exact Sciences, I, 1962, ach. 488-527. 32. B).. M. Cantor, Vorlesungen über Geschichte der Mathematik, 1 Band, Leipzig 1907°, arci. 638-639. 33. «npôg dè rois tirtupoi otorzcions yeren tic tori guorc, EE hg 6 obpavós Kai tà úctpa». Megasth, Fragm. XLI 17. 34. B).. Max Müller, “«Beitrigen zur Kenntiniss der indischen Philosophie», Zeitschrift der deutschen Morgenkl. Gesellschaft, VI, 1892. 35. «Solle am Ende gar in der... Stelle des Philolaus (160)» nip, Üdop, xai ya xal dp Kui 6 tag apuipas Gixug ($ OAKGS) répreuz, «in dem seltsamen ÖAxag als Bezeichnung des A——_—_m6 fünften Elementes, das schon so viele Conjekturen, aber keine befridigende hervorgerufen hat, sich eine Verstiimmelung der indischen Bezeichnung des Acthers, d.i. dkáca erhalten huben ®» L.B,v. Schröder, op. cit,, 084. 65, onu. 2. BA. Entlang tv dvuroivwon tod A, Weber, «Die Griechen in Indien», Sitzunberichte der Kgl. Preussischen Akademie der Wissenschaften zu Berlin XXXVII, cer. 923-926 & Literar. Zentralblatt 1884, 02). 1563-65, 36. Bd. Works, 8 Vols., Vol. IM, 1799 oe).. 236

Xp. pin Muduyôpu;, "Apzıunön; sui ‘lvôixés palbnyarixés Ucwpics 165 and 16 ón à AEN samkhyà —roù onpaiver dpidpò ord cavoxpitixa— eiye Geperk@dn onpacia atò Ilvdayöpsıo procopixd obornua”, ‘Apyòrepu aröv Frwartxionö Kai iórairepa toviler tiv èribpaon ris Sämkhya otóv $ Colebrooke?** ypáper Sti of 'Ivdol Adokakoı Erarfav üropaoiatikd pólo Miorivo**, oti) Siatin@on tg paocopias tod peytiov Lapiov**®. Mé tH ovyyéver tOv Ivdırav Kai rvdayopriov Bewpıöv doyoAHOnxe Kai 6 Barthélemy SuintHilaire*®. "Exeivos pws rod cvommpatixà doyokHOnxe pi abró td Dépa civar 6 L. v. Schröder, rod napovoiace tò 1884 più guyxpırıcn) perétn tv 500 Dewpidv*'. E abrò tó BıßAio è Schröder perderà kai avrinapabéter Kowa an neia th Sämkhya Kai tig Mudayóperas Audaokakiag**. "H ovozétion Kai n ämppor) tod avotijnarog Sámkhya*? EaxoAovOnoe va ouvövdLerun pè tH Suruki) 'O Lassen** bnoypappitet tiv ¿niópaon tod ovoriparos Sämkhya Lalitavistara - Pappitys "Ag REPÜOODHE twpa GE jua OXETIKÜ vebtepn ¿roy í, Kai Gc Oavpacovpe Eva brépoyo pa0npartixò ivdtxd Keipevo*®. “Orav 6 Bodhisattva, yiós tod Bacıkıa Cönddhödana, Epyetat cè Axia yàpov diaymvitetar pè nevtaxdarous GAAouG véous ott) ypapí, ony apiOpnTiki), OTH MGAN, otò THEO, yiù TO YEpr This Ovyatépas tod Cakya Dandapäni, quocogia. Göpä. Kepôilovrus, ywpig Övoxokia tole Gove àvrayoviotés, 6 Bödhisattva Kadettat va ouvayoviobel tov peyúdo pa0nparixò Ardjouna rod Arav 37. «gaivovrar Si Kal odror tov GpiOpdv vopifovres épyñv riva». *Aprar. Mera rà voi, I, 5986a 15. 38. H. T. Colebrooke: «On the Philosophy of the Hindu», Part I. On the Sankhya system. Transactions of the Royal Asiatic Society, I, 19-43, 1823. Bd. axopn Miscellaneous Essays, by M.T. Colebrooke, new ed. with notes by E. B. Cowelle, London 1873, Vol. I, kai Kpttis tod Siayoviopod*”. "O Ardjouna tov pwrä oyetixa pè toùg tpdRoug Exppacyns tOv dpi0ypòv rod civar peyadótepor drò 100 kótis (1 kôti igodtar pè Sera Exatoppopia) Kai 6 Bodhisattva üravrä pè tiv napaxdro KAipaxa, pè ecixoaitpeic dvopacies SuadoyixOv Spwv rod oynpartitovy | otk, 239-279. 39, «adverting to what has come to us of the history of Pythagoras, | shall not hesitate to acknowledge an inclination to consider the Grecian to have been... indebted to Indian instructors. Nobody needs to be reminded, that Pythagoras and his successors held the doctrine of metempsychosis, as the Hindus universally do held the doctrine of transmigration of souls. They agree likewise generally in distinguishing the sensitive material organ (manas), from the rational and concious living soul Givatman): Gund; and gpùv of Pythagoras; one perishing with the body, the other immortal. Like the Hindus, Pythagoras with other Greek philosophers, assigned a subtle etherial clothing to the soul apart from the corporeal part, and a grasser clothing to it when united with body; the sukshma (or linga) sárira and sthúla sárira of the Sänkhyas and the rest... 1 should be disposed to conclude that the Indians were in this instance teachers rather than learners», T.H. Colebrooke, Mise. Ess., I, ori. 241, | 40. Barthélemy Saint-Hilaire, «Premier Mémoire sur le Sämkhya». Mémoires de l'Académie des Sciences Morales et Politiques, tom. VI, Paris 1852, ot). 105-560, Première partie: bibliographie du Sàmkhya, oe). 107-121. Deuxième partie: analyse du Sänkhya arà..123-366. Troisième partie: examen critique du Sánkhya ac. 369-488. Quatrième partic: histoire du Sänkhya, a. 489-502. 41. Pythagoras und die Inder, Eine Untersuchung über Herkunft und Abstamung der Pythagorischen Lehren, Leipzig 1884. Kav axokibv diatund@vet 6 W. Jones: «Of the Philosophical School it will be sufficient, here, to remark that the first Nyäya seems analogous to the Peripatetik; the second, sometimes called Vaiseshika to the Ionic; the two Mimänsäs, of which the second is often distinguished by the name of Vedanta, to the Platonic; the first Sänkhya to the Italic; and the second, or Pätanjala to the Stoic Philosophs so that Gautama corresponds with Aristotle; Kanáda with Thales; Jaim with Socrates; Vyasa with Plato; Kapila, with Pythagoras; and Patanjali with Zeno. But an accurate comparison between the Grecian and Indian Schools would require a considerable volume». Sir William Jones, Works, 4th ed, 1799, val. 4, cel. 360-361. Mid àvéoyu ovyxpr eisen &inviriig Kai ivdtxijs pthocogias rapovandfcı è B. Burouëñs orö [prio tov: Plato and the Upanisades, Arnold Heinemann 1977 (New Delhi), 44. Lasseu, op. cit., ocd. 384, 45. Tia neprocórepes Acrropéperes Pi. mv Gtôuxropixn Ötarpıpı) tod Georg Biedenkapp: «Beitrage zu den Problemen des Selbstwusstseins, der Willensfreinheit und der Giesetzmässigkeit des Geistes, teilweise mit Bezug auf die Philosophie der Inder, Halle a/S. 1893, 46. Ilpöxcıtur yià Thy Lalitavistara, Eva áró ra icpà ivóncá fiflia. Td xeipevo abrò Kura tov Woepke xui tov Menninger elvar rob IM #.X. aióva. BA. F. Woepke, «Mémoire Sur la propagation des chiffres indiens», Journal Asiatique, ler semestre, Paris 1863. K. Menninger, Zahlwort und Ziffer, Line Kulturgeschichte der Za, 2e Auflage, Göttingen 42. 'H rpocwroromptvn Ocdtnta dv naifer xavéva pózo ath Simkhya Kal oti Tlvdaydpeıa Arduorakia. ñ Îpovouà KAipaxa rav Entrá QUoyywy brdpyer hön ota Ciksgá (rá np@ra EEn Vedänjas) Snag Kal 6 cvpPodropos tOv Séxa npotov Apıduav m.x. | = pra- Shing House (rep.) 1962. yelve Spioxerat oroús orixous rod Pratyanc, Athaweveda, 13, 1, 56. 6 drayaviapes, Y pira «eferaon» tod Bodhisattva xariyeı, onpuivovou Géon, dood jäpati, 7 = Metra. Kai à yvwotà nudayspeiu gpdon: «npòs hAtov tetpuppévov pn) bpi- 43. Mid tokpnpt du@movooqpavty Avrıcrorgia "Ivdıxav xai "EAAnvixdy Q1.00091- 1958. B2.. áxóun B. Datta and A.N, Sing, //tstory of Hindu Mathematics, | vol., Asia Publi47. Etig Sexartoorpris ochiöeg tod Ouvarpırıkod xemévov Órov meprypagetat Ólos sutuZupflaver oxcóóv rò mod xcipevo 6 '/, achiörs. BX. F. Woepke, op. cit., ot. 75.

Xp. Din Hudarópas, "Apxıpnöng xui “Ivéinés palqpatixés Ocewpics 167 YEMpETpIKH np6050 pè Adyo 100, Kai Sxov è npúros Ópos elvar 16 köti Kai 6 oxnpatiCovtac Kata tov ió tpóro più yemperpix mp6odo pè Ayo 100, teXevtatosg tó tallakchana: paver 6 Bodhisattva otòv dpi0pò 17+°*#) = 10*!. Tére 6 Ardjouna, rob and xpıriig perapoppo@verar cè padnti tod Bodhisattva [nrá va tod I ayouta = 100 kôtis = 100 ayoutas | niyouta = 100 niyoutas I kangara = 100 kangaras | vivara = 100 vivaras | akchóbhya I viväha = 100 akchöbhyas 1 outsanga = 100 vivähas = 100 outsangas | bahoula = 100 bahoulas I nágabala = 100 nägabalas I titilambha | vyavasthänapradjnapti = 100 titilambhas = 100 vyavasthanapradjnaptis I hétouhila ì karahou = 100 hétouhilas = 100 karahous 1 hétvindriya = 100 hétvindriyas 1 samäptalambha = 100 samäptalambhas | gananágati I niravadya = 100 gananägatis = 100 niravadyas | moudräbala | sarvabala = 100 moudräbalas 1 visandjiàgati = 100 sarvabalas | sarvasandjità = 100 visandjñágatis L vibhoütangamä = 100 sarvasandjnas I tallakchana = 100 vibhoütangamäs = Jo = 10"! = 10% == 10 = 10 = 10" Fe = 107 = 10% = 10% == 10° = 10 = 10” =: 10% = 19°? = 10" = 10*! = 10% = 10 = 10 = 19 ==. 10° = 1993 4* ¿Enoc rog oxnparilerar ñ ápidunon rod pláver péxpt th oxdvy Tüv rpótv üröumv’ Kabas Kai róca ürona dnépyouv a” Eva yôdjana. "O Bódhisattva Gpyiber va oynparileı tiv rapaxáto x)ipaxa: I xöxkog noÂd Aenti}¢ OKOVNS = 7 KÉKKOUS OKÖVNS Tpatwv Arölav = | KOKKOSG Aeris GKÔVNG = 7 k6kkovg KOAD denti okôvnc = 7X I = = 7a, x Ta=T’a KOKKOS akövng mob tiv pépver 6 dvepoc | xòxxog oxóvnc Aayod = PE = 7 KOKKOUS OKÓVNC mob mv pépver è (oxövn nod onxóvetar and úvepos = 7*a. 10 nodi Evdc Auyob) I KOKKOS oxdévns Kpioü = 7 xöxkous oxövng Aayod = 7%a. I KOKKOS OKÓVNS tabpou = 7 kòkkovg GKÔVNS Kkpioù = 7°a. I xéxxog GKÔVNG KÓKKIVNS = 7 KOKKovg Gkòvng tubpov = Tu, rarapobvas*' | KÓKKOS otvandonopov = 7 xòxkoug OKÓVNS KÓKKIVNS nanapov- I Köxkog xpılapı = 7 KOKKOUG olvandonopov = 7°a. vas = 7*a, I pálayya ivòg durtbkou = 7 x6kkovc Kpiläpı I map = 7 qádayyes évds Saxtúlov = 12K7!%q, I mijyus I t6Eo Dôävovtras a” adrdv tov dpidpò, 6 Bodhisattva npooGérer ón din adth ñ KAipaxa oynparileı tiv ápi0yunon tallakchana —dvopacia rod rpoépyetar ünd tov rekevraio dpidpò this KAipaxac— kai Ott peta an” adtiv Bpicxerat 7 xöxkoug Aentüg oxOvng = 7x7x7a 7'%. 2 mBapés = 2x12x7'%u, = 4 mie I kröga rs xbpus rv Magadha = I yödjana = = 4X2X12X7100. 1000 röfa = 1000x4x2x12x7!%a. = 4 krögas = 4x1000x4x2x12x7!°%a. Wie pera*®. "Yrodkrovrag Ón ot kúde pia ax” adrés tic apirOumoerg avri- Mé th Pondera avriis tig kAipaxas 6 Bodhisattva Katakïñyer otò rapaKat@ cvurépacpa: «Eror tO RAMPES pijxos Evög yódjana, mod elvar évrel Ge ororyei Eva rAñ0oc Spwv Tao pè tiv apórn apidpnon, tiv tallakchana, Kai Yenüto GRO KOKKOUS OXÓVIS Xpwtwv Gropev elvat: Eva niyouta akchôbhyas ñ ápi0unon dvadjägravati, Kai peta À àpiOunon dvadjägranigämani Kai EEN Kai tpuavia Exatovrúdes Kıkıades ano kötis tHv niyouta Kai ¿Eñvra éxatovtúdes kôtis Kai cikootdbo kòtis Kai névre Sexúdes tv ÉkatovréSwv tov 48. “HL Ex0erix ypapñ —éritevEn mob Snproopynoe Y Avon pô tov 170 alava— dtv tupavifcrar otd davoxpitixò Kelpevo, 49, Evupova pè ti Operravi) «Ekôoon» nob perégpace 6 Ed. Foucaux Higya teh'er rol pa, perapp. Ed. Foucaux, Ile partie, Paris 1848, ced. 141. Enuerovovpe Sti à “EOviKA BiPà100fxn ord Mapiot Exc: S00 cavoxpitixad xerpoypapa fig Lalitavistara. 50. Tid ouvropia è Woepke, op. cit., och. 77, xpnogorotel tò ypaupa a yá vá ouplPolícar ra mp@ra Gronau, SI. "Opo nob tov cuvavrape otòv «Pappitn» tod ‘Apxiuñôn.

Xp. Pin giov Kai d@dexa Xıkıdöeg, adtd elvat tó GAporcpa évos yódjana kòkkov OKOVNS TOV TPOtOV Atönwv»??. Td keipevo adrd tig Lalitavistara pùg diver Hubuyopus, “Apximndns Kui Ivóixés publnyuarixes Onopies 169 ts unKwvog ioodrar pè 10.000 x6kxovg dupov Kai dti Eva Súxtuio loodtut pè capávra popès tiv Siúperpo ÉVOS KÔKKOU uñkovos**, Eva KatarAnKtiKkd mapaderypa broloyiguod peyúdov apiWpadv nod Eyıve Mé tig bro0éoerg abris 6 "Apyınnöng gpredover ta reparto ovprepaotiv ‘Ivéia tov I n.X. albva. IIpiv npoxwpnoovuue otàv obyKpıon pè tov «Pappity» tod "Apyınnön tig ovykpatioovye Stt 16 Gxdonacpa abtò TAG Lalitavistara Eyer oùv avtiKeipevo tov Kadopıond tod dpi@poî tHv kóxkov TIIS oxóvnc, Kai Gti kabiepovet pid KAipaxa diadoyxiK@v sldv oxóvns diupopov peye0Ov*?. To Oéna tod «'Pappitn» —ñ póvn owLöuevn npaypateia tod ‘Apyipnôn, pè dapiOpntixò neprexdpevo— napovorder pid Oavpacth advadoyia pè tó oyo o tñc oxóvns tod Bodhisattva. "O oróxos ris nei&rng abris tod "Apyıunön elvar v' anodeiEer Sti 6 apidpòg tHv KÖKKWV TG dppov À yappov Ts rpaynareias —Atön and tiv dnoia rpogpyetar dvopacia—, mod rnepié- YOVTAL or opuipa tHv árlavóv dotépwv nob mepikAcie: TO OUUTAV, civat pikpdtepos And Evav Ópicipo apidpò. Tia va kataX@Bovpe kaibtepa tiv Önorörnta tod ivüikod Aoyiopod oyara: I. opaipa diapétpov vos SaxtbAov ioodtut pé 640.000.000 x6xxovs Gppou Kai elvat pıkpötepn tòv 10 novadwv tov dSevtépwv apidpov. 2. cpaipa dSiapétpov 100 daktiAwv igodrar pè 1.000.000 apaipes dtapétpov Evòg SaxtbAov, Kai civat pixpotepy t@v Xıkiov pupradov (10.000.000) trav devtépwv ùpi0p@v. 3. oquipa Suapérpov 10.000 daxtbAwy ioodtur pè 1.000.000 opaipes dupétpov 100 daxtbAwy Kai eivat puxpdtepy t@v 10 pupiddmv tv tpitwv üpıOnov. 4. opaipa Stapétpov Evög oradiov £ivur puxpótepn Gxo ın opaipa rod Exel Ötdnerpo pupiwv dartbAwv Kai elvat pukpôtepn tóv 10 pupiadov tüv tpitwv appv. ar bra tic 5. opaípa Siapétpov 100 otuôiwv ioodtut pù 1.000.000 opuipes diapétpov évos otudiov, Kai civat pixpdtepy t@v Low povadov tHv TETÚPTOV api- 2. Stu n dtéuetpos this yig elvar peyadvdtepy ano nv Sidpetpo TAG oeANvnG 6. opaipa pè Srúnerpo 10.000 otadia icodrat pè 1.000.000 opaipes diapétpov dic Sodue ano mod xovtà tiv pébodo tod "Apyxınnön. Mpóra dodpe tic brodécetc tod neydkov LupaKovotov: I. Gu à nepipetpos tg yÎfg elvar 3.000.000 otúdu. Ouv. Önwg Kai Stt À SiaGpetpos tod Aou elvar peyaX.vtepn And tiv diapetpo 100 otadimv Kai elvat pukpôtepn t@v 10 povadov tOv réurrov apt0p@v. TS YA Kai nadıora elvar 30 popÈès peyadótepn aro Exeivyy tig GeAN- 7. opaipa pè Siapetpo 1.000.000 otddia icoütuı pè 1.000.000 opuipec diapétpov 10.000 cradiwv kai pixpotepyn tOv Xıkiov pupiddwv tov rÉUTTOV vnc. ME abra aroderkvber ta ÉEñG: api0uov. I. Sti y Stapetpos tod Kdéopov elvar pixpotepyn and 10.000 Siapétpovg ts yAs Kai Gkdpyn Str elvar md prxph 100.000.000.000 aradıu. Lyetika pè tods Kk6kkovg Gppov broßkreı ta nupuxatw.: 8. opaipa pi Stdpetpo 100.000.000 orádia ioobrar pé 1.000.000 opuipes Siapétpov 1.000.000 otadiov Kai civur pixpótepn tov 10 pupiúdov tov | kóxkOc Extwv apıdu@v. 9. spaipa pè Srúperpo 10.000.000.000 oradıa ioodtur pé 1.000.000 opuipes Siapéetpov 100,000,000 otuôiwv kai eivat pukpôtepn t@v 1000 povádwv tov EPSdpov apiOpav**, 52. Anzasm 10.000.000.000.000.000.000.000.000.000 = 60.000.000.000 + 220,000,000 + 5.000.000 t 12.000 Tıa vá Statun@cer ta napandvw ovpnepdopata 6 "Apxıunöng kadiepover, önwg Kai oi ‘IvSoi, ju KAipaKxa dvopaciag apOpav*®®. ME adrôv tov tporo, KUTaAyEt otò cvprépaopa Ón TO nAndos Th PA. Woepke, op. cit., aed. 79. 53. "O brohoyionds tig oxóvns Atay ¿vas ápxera diadedopevog Aoyiapds cè npoßın- 54. Bd. Aoguodors "Ararra, top. B, petagpaots - oxdAıa Evy. Lrapatn, éxd. T.E.E., pata ápriluntixAs, lows rodó nplv and tv ovvraEn fig Lalitavistara. Duoiké, Stay ma "An var 1973, ocd. 180-215, H. 220 30-9, H 233 1-4, H 236, 6-9. 55. ib. H 244 16-20, H 244 21-24, H 248 6-10, H 249 8-10, H 251 1-4, 252 12, H 253 ypáptnxe ord lepa PiPria rg Opnoxelas 51ad60nKke axon neproodtepo. Elvat nod nıdavn à ¿Eñynon, dti an’ adróv td Aoyıayd, of "Apaßes tig "Avutoifis òvopavav tic pe0ddous th¢ mpaxtiKfis "ApıduntiKfig tv ‘Ivô@v, Loyiouò th oxdync. 12-15, 254, 14, H 254 11-17. 56, ib. HI H 237 1-2

Xp. Din Gov loobdrat pù th opaipa thy ankavav dotépwv!” Kai sivar pixpdtepo and 1000 pupiddes tv dydówv dpWpav>*. peyadúrepns taEng. “Ero. napurnpet Ste à KAipaKa tv npotwv, Sevtépwv, tpitav dpidpov propel va ovvexiodet péxpr tobs Exkatoppwproctods üptOpoùs, rob Vewpodvrat ody tehevralos 6pos abris tic xAipurag Kai tautóody pováda puäç Katvobpiag raöng npwroug dpidpods lg debrepng nepıödov. pel pè robs debrepoug dpidpovs, robs Ania à paocomiwxh nAcupü rod Oépatog div dphvet Gdiapopo TÓV auyypuota®', 'Axóun 6 ‘Apyyning, Grwg kai 6 Bodhisattva, napadéxetar apıdunasız ypova 171 Muduròpas, "Apxıinhäng Kai ‘Ivins pu0npurixèg Onaping dpi0pòv nod tobs dvopater Mé tó iso okentikò rpoywtpitovs, ... péxpt 100.000.000 povádes TOV Exatoppuprtoct@y apiOpav tic Ékaronpupiootis nepiddov*”. Méoa ünd tiv ovyKpitiKy abr pedéry, OcAñoape vá beiSoupe tiv Spowrtyta Spropévov ivdiKav pu0nputiròv Oewprdy pè tig avriotorgss ¿Minvixec. "Opos népa dnd th Sopuxi) Önorörnra À tows üxöun Kai «rd Saveropo» tov Oewpdy, exeivo nob Eyer ovoraco iy onpuoia elvar Ór tú aveúpata tod Mudayópa kai tod "Apyınndovz peraoynpatitovv Kai avaraAúrtovv poa dnd mv ivdıcı) oxéyn tobs SiKobs tous Öpönovg, avartiodovNS diavonons. Tí tus repioootepo, ixelvo nob Eye tó Kévtpo tig ÉAANVIK Quocgogia. Tedixú Pérouse Gun, T600 è Aoyıopög nob bräpyer ot Lalitavistara, 600 Kai 6 Aoyiopds tod "Apyxınidoug Exovv tòv Té10 otóxo. AnAaëñ npoonadodv va xulopioouv tòv dpi0pò tOv KOKKwV TG oxóvns rod uropeí vá nepiéyovtat otd obprav nod Kai otic 50 npaypatetes Oewpettat merepa- PYTHAGORAS, ARCHIMEDES AND INDIAN MATHEMATICAL THEORIES opévo. Kai oi 500 xadopitovv ju dvoparodoyia apiWpav. Kai otods dúo at fi dvopatoAoyia änoteketrur dxd S00 Padpideg. Erijv Lalitavistara ñ Summary rporn fadpida neprrapPdver thy KAipaxa tOv apwWpdyv nob oynpatitovv mv GplOpnon tallakchana, dvriororza oröv Vappityn Exoupe tods np@roug, The article deals with the parallelism between the theories of Pythagoras dedtepous, dktepiOpovg 1 rpórng nepıödov. Mid pováda Sevrépwv àp10- and Archimedes and the Indian theories of Simkhya and Lalitavistara, pòv ¡cobrar pè 10%, pià pováda pè 100%, pid povaba rüv tecodpwv üpıd- The common points between the Pythagorean teachings and the older, Indian Sämkhya philosophy are: the knowledge of the irrational numbers the doctrine of the five elements of matter, the founding of both teachings nov ioodrat pè 10°? KAR, "H bebtepy Padpida ory Lalitavistara nepirapfdver rig Siapopes diadoyikég apıßunaeig: avrloroıya atdv Vappityn Exoupe tiv äkokoudia tay on the concept of number and others, repwodov trav dpioòpòv. pévo pè ti) yAbooa tous kai ti) Aoyotexvia tous. "H napddoon abri bxo- Archimedes, with his calculation in Psammites, and Lalitavistara have as a common aim the measurement of dust particles contained in the universe. They both specify an enumeration of numbers on two scales. The difference between these two mathematical treatises lies in their implementation, The Indians confine themselves solely to calculus whereas Archimedes adds a ypappiterar philosophical dimension. “Optws 1) Sopuri Önorörnta nob yapurtnpiter tig duo abres padnpatixés npaypatetec, dev üxoAovdeltar and tiv Téa pédodo. Oi 'Ivdoi elyav rapà- Soon atd aynnarıond KAaKOV óvopacias apiOpdv, Oépa otevà ouvôcdc—péoa and tiv dinynpatiKxy dphynon tod xeipévov— pò tov TpwtapyiKd poco tig Aoyıarırf)s. “Avrideta, div kai y Ovopacia tHv peya- Awv dpidp®v Arav Kati tó Evo yıd tig ouvhDewes tig ¿22 vis yAdoous”®, Chr. Phili Athens 6 «Pappitng» ünoredel più Kalaph naßnparızı) npaypareia, ¿vo napú)- AN 57. YXpuipa nov brobéret 6 'Apiorapxos PA. "Apxınhöng, op. cit., H 218, 1-4. 58. ib. H 258 15-20. LaiLo SORA ene ces KVEXVI SLL Y Re are 59. ib. H 239 1-20, H 240. 60. Geneviève Guitel, //istoire comparée des numérations écrites, chap. MI, Grèce 1, chap. IV, Les numérations alphabétiques, Grèce Il, Paris 1975, 61. N. Lusin, Lecons sur les ensembles anolyliques et leurs applications, Paris 1930, ach. 322.