De animae procreatione in Timaeo Machine readable text Plutarch Gregorius N. BernardakisPerseus Project, Tufts University Gregory Crane Prepared under the supervision of Lisa Cerrato William Merrill Elli Mylonas David Smith The National Endowment for the Humanities Trustees of Tufts University Medford, MA Perseus Project

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You credit Perseus, as follows, whenever you use the document: Text provided by Perseus Digital Library, with funding from The National Endowment for the Humanities. Original version available for viewing and download at http://www.perseus.tufts.edu/hopper/. You leave this availability statement intact. You use it for non-commercial purposes only. You offer Perseus any modifications you make. Plutarch Moralia Gregorius N. Bernardakis Leipzig Teubner 1895 6

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e)pei\ ta\ polla/kis ei)rhme/na kai\ gegramme/na spora/dhn e)n e(te/rois e(/tera, th\n *pla/twnos e)chgoume/nois do/can h(\n ei)=xen u(pe\r yuxh=s, w(s u(penoou=men h(mei=s, oi)/esqe dei=n ei)s e(\n sunaxqh=nai kai\ tuxei=n i)di/as a)nagrafh=s to\n lo/gon tou=ton, ou)/t' a)/llws; eu)metaxei/riston o)/nta kai\ dia\ to\ toi=s plei/stois tw=n a)po\ *pla/twnos u(penantiou=sqai deo/menon paramuqi/as, proekqh/somai th\n le/cin, w(s e)n *timai/w| ge/graptai. th=s a)merou=s kai\ a)ei\ kata\ tau)ta\ e)xou/shs ou)si/as kai\ th=s au)= peri\ ta\ sw/mata gignome/nhs meristh=s tri/ton e)c a)mfoi=n e)n me/sw| sunekera/sato ou)si/as ei)=dos, th=s te tau)tou= fu/sews au)= pe/ri kai\ th=s qate/rou: kai\ kata\ tau=ta sune/sthsen e)n me/sw| tou= t' a)merou=s au)th\n kai\ tou= kata\ ta\ sw/mata meristou=. kai\ tri/a labw\n au)ta\ o)/nta sunekera/sato ei)s mi/an pa/nta i)de/an, th\n qate/rou fu/sin du/smikton ou)=san de a)nimae procreatione i)n timaeo. ei)s tau)to\ sunarmo/ttwn bi/a|: mignu\s de\ meta\ th=s ou)si/as, kai\ e)k triw=n poihsa/menos e(\n pa/lin o(/lon tou=to moi/ras ei)s a(\s prosh=ke die/neimen: e(ka/sthn de\ tou/twn e)/k te tau)tou= kai\ qate/rou kai\ th=s ou)si/as memigme/nhn h)/rxeto de\ diairei=n w(=de tau=ta prw=ton o(/sas pare/sxhke toi=s e)chgoume/nois diafora/s, a)/pleton e)/rgon e)sti\ dielqei=n e)n tw=| paro/nti, pro\s d' u(ma=s e)ntetuxhko/tas o(mou= tai=s plei/stais kai\ peritto/n. e)pei\ de\ tw=n dokimwta/twn a)ndrw=n tou\s me\n *cenokra/ths proshga/geto, th=s yuxh=s th\n ou)si/an a)riqmo\n au)to\n u(f' e(autou= kinou/menon a)pofhna/menos oi( de\ *kra/ntori tw=| *solei= prose/qento, mignu/nti th\n yuxh\n e)/k te th=s nohth=s kai\ th=s peri\ ta\ ai)sqhta\ docasth=s fu/sews: oi)=mai/ ti th\n tou/twn a)nakalufqe/ntwn safh/neian w(/sper e)ndo/simon h(mi=n pare/cein.

e)/sti de\ braxu\s u(pe\r a)mfoi=n o( lo/gos. oi( me\n ga\r ou)de\n h)\ ge/nesin a)riqmou= dhlou=sqai nomi/zousi th=| mi/cei th=s a)meri/stou kai\ meristh=s ou)si/as: a)me/riston me\n ga\r ei)=nai to\ e(\n meristo\n de\ to\ plh=qos, e)k de\ tou/twn gi/gnesqai to\n a)riqmo\n tou= e(no\s o(ri/zontos to\ plh=qos kai\ th=| a)peiri/a| pe/ras e)pitiqe/ntos, h(\n kai\ dua/da kalou=sin a)o/riston. kai\ *zara/tas o( *puqago/rou dida/skalos tau/thn me\n e)ka/lei tou= a)riqmou= mhte/ra to\ d' e(\n pate/ra: dio\ kai\ belti/onas ei)=nai tw=n a)riqmw=n o(/soi th=| mona/di proseoi/kasi, tou=ton de\ mh/pw yuxh\n to\n a)riqmo\n ei)=nai: to\ ga\r kinhtiko\n kai\ to\ kinhto\n e)ndei=n au)tw=|. tou= de\ tau)tou= kai\ tou= e(te/rou summige/ntwn, w(=n to\ me/n e)sti kinh/sews a)rxh\ kai\ metabolh=s to\ de\ monh=s, yuxh\n gegone/nai, mhde\n h(=tton tou= i(sta/nai kai\ i(/stasqai du/namin h)\ tou= kinei=sqai kai\ kinei=n ou)=san. oi( de\ peri\ to\n *kra/ntora ma/lista th=s yuxh=s i)/dion u(polamba/nontes e)/rgon ei)=nai to\ kri/nein ta/ te nohta\ kai\ ta\ ai)sqhta\ ta/s te tou/twn e)n au(toi=s kai\ pro\s a)/llhla gignome/nas diafora\s kai\ o(moio/thtas, e)k pa/ntwn fasi/n, i(/na pa/nta gignw/skh|, sugkekra=sqai th\n yuxh/n: tau=ta d' ei)=nai te/ttara, th\n nohth\n fu/sin a)ei\ kata\ tau)ta\ kai\ w(sau/tws e)/xousan kai\ th\n peri\ ta\ sw/mata paqhtikh\n kai\ metablhth/n, e)/ti de\ th\n tau)tou= kai\ tou= e(te/rou dia\ to\ ka)kei/nwn e(kate/ran mete/xein e(tero/thtos kai\ tau)to/thtos.

o(malw=s de\ pa/ntes ou(=toi xro/nw| me\n oi)/ontai th\n yuxh\n mh\ gegone/nai mhd' ei)=nai genhth/n, plei/onas de\ duna/meis e)/xein, ei)s a(\s a)nalu/onta qewri/as e(/neka th\n ou)si/an au)th=s lo/gw| to\n *pla/twna gignome/nhn u(poti/qesqai kai\ sugkerannume/nhn ta\ d' au)ta\ kai\ peri\ tou= ko/smou dianoou/menon e)pi/stasqai me\n a)i/dion o)/nta kai\ a)ge/nhton, to\ d' w(=| tro/pw| sunte/taktai kai\ dioikei=tai katamaqei=n ou) r(a/|dion o(rw=nta toi=s mh/te ge/nesin au)tou= mh/te tw=n genhtikw=n su/nodon e)c a)rxh=s prou+poqeme/nois tau/thn th\n o(do\n *i)n timaeo platonis. trape/sqai. toiou/twn de\ tw=n kaqo/lou legome/nwn, o( me\n *eu)/dwros ou)dete/rous a)moirei=n oi)/etai tou= ei)ko/tos: e)moi\ de\ dokou=si th=s *pla/twnos a)mfo/teroi diamarta/nein do/chs, ei) kano/ni tw=| piqanw=| xrhste/on, ou)k i)/dia do/gmata perai/nontas a)ll' e)kei/nw| ti boulome/nous le/gein o(mologou/menon. h( me\n ga\r e)k th=s nohth=s kai\ th=s ai)sqhth=s ou)si/as legome/nh mi=cis ou) diasafei=tai ph= pote yuxh=s ma=llon h)\ tw=n a)/llwn, o(/ ti a)/n tis ei)/ph|, ge/nesi/s e)stin. au)to/s te ga\r o( ko/smos ou(=tos kai\ tw=n merw=n e(/kaston au)tou= sune/sthken e)/k te swmatikh=s ou)si/as kai\ nohth=s, w(=n h( me\n u(/lhn kai\ u(pokei/menon h( de\ morfh\n kai\ ei)=dos tw=| genome/nw| pare/sxe: kai\ th=s me\n u(/lhs to\ metoxh=| kai\ ei)kasi/a| tou= nohtou= morfwqe\n eu)qu\s; a(pto\n kai\ o(rato/n e)stin, h( yuxh\ de\ pa=san ai)/sqhsin e)kpe/feugen. a)riqmo\n ge mh\n o( *pla/twn ou)de/pote th\n yuxh\n prosei=pen, a)lla\ ki/nhsin au)toki/nhton a)ei\ kai\ kinh/sews phgh\n kai\ a)rxh/n: a)riqmw=| de\ kai\ lo/gw| kai\ a(rmoni/a| diakeko/smhke th\n ou)si/an au)th=s u(pokeime/nhn kai\ dexome/nhn to\ ka/lliston ei)=dos u(po\ tou/twn e)ggigno/menon. oi)=mai de\ mh\ tau)to\n ei)=nai tw=| kat' a)riqmo\n sunesta/nai th\n yuxh\n to\ th\n ou)si/an au)th=s a)riqmo\n u(pa/rxein: e)pei\ kaq' a(rmoni/an sune/sthken, a(rmoni/a d' ou)/k e)stin, w(s au)to\s e)n tw=| peri\ *yuxh=s a)pe/deicen. e)kfanw=s de\ tou/tois h)gno/htai to\ peri\ tou= tau)tou= kai\ tou= e(te/rou: le/gousi ga\r w(s to\ me\n sta/sews to\ de\ kinh/sews sumba/lletai du/namin ei)s th\n th=s yuxh=s ge/nesin, au)tou= *pla/twnos e)n tw=| *sofisth=| to\ o)\n kai\ to\ tau)to\n kai\ to\ e(/teron, pro\s de\ tou/tois sta/sin kai\ ki/nhsin, w(s e(/kaston e(ka/stou diafe/ron kai\ pe/nte o)/nta xwri\s a)llh/lwn tiqeme/nou kai\ diori/zontos

o(/ ge mh\n ou(=toi/ te koinh=| kai\ oi( plei=stoi tw=n xrwme/nwn *pla/twni fobou/menoi kai\ paramuqou/menoi pa/nta mhxanw=ntai kai\ parabia/zontai kai\ stre/fousin, w(/s ti deino\n kai\ a)/rrhton oi)o/menoi dei=n perikalu/ptein kai\ a)rnei=sqai, th/n te tou= ko/smou th/n te th=s yuxh=s au)tou= ge/nesin kai\ su/stasin, ou)k e)c a)idi/ou sunestw/twn ou)de\ to\n a)/peiron xro/non ou(/tws e)xo/ntwn, i)di/a| te lo/gou te/teuxe kai\ nu=n a)rke/sei r(hqe/n, o(/ti to\n peri\ qew=n a)gw=na kai\ lo/gon, w(=| *pla/twn o(mologei= filotimo/tata kai\ par' h(liki/an pro\s tou\s a)qe/ous kexrh=sqai, sugxe/ousi, ma=llon d' o(/lws a)nairou=sin. ei) ga\r a)ge/nhtos o( ko/smos e)sti/n, oi)/xetai tw=| *pla/twni to\ presbu/teron tou= sw/matos th\n yuxh\n ou)=san e)ca/rxein metabolh=s kai\ kinh/sews pa/shs, h(gemo/na kai\ prwtourgo/n, w(s au)to\s ei)/rhken, e)gkaqestw=san. ti/s d' ou)=sa kai\ ti/nos o)/ntos h( yuxh\ tou= sw/matos prote/ra kai\ presbute/ra le/getai gegone/nai, proi+w\n o( lo/gos e)ndei/cetai tou=to ga\r h)gnohme/non e)/oike th\n plei/sthn a)pori/an kai\ a)pisti/an pare/xein th=s a)lhqou=s do/chs.

prw=ton ou)=n h(\n e)/xw peri\ tou/twn dia/noian e)kqh/somai, pistou/menos; tw=| ei)ko/ti kai\ paramuqou/menos, w(s e)/nesti, to\ a)/hqes tou= lo/gou kai\ para/docon: e)/peit' au)tai=s le/cesin e)pa/cw sunoikeiw=n a(/ma th\n e)ch/ghsin kai\ th\n a)po/deicin. e)/xei ga\r ou(/tw kata/ ge th\n e)mh\n ta\ pra/gmata do/can. ko/smon to/nde fhsi\n *(hra/kleitos ou)/te tis qew=n ou)/te a)nqrw/pwn e)poi/hsen w(/sper fobhqei\s mh\ qeou= a)pogno/ntes; a)/nqrwpo/n tina gegone/nai tou= ko/smou dhmiourgo\n u(ponoh/swmen. be/ltion ou)=n *pla/twni peiqome/nous to\n me\n ko/smon u(po\ qeou= gegone/nai le/gein kai\ a(/|dein: o( me\n ga\r ka/llistos tw=n gegono/twn o( d' a)/ristos tw=n ai)ti/wn: th\n d' ou)si/an kai\ u(/lhn, e)c h( ge/gonen, ou) genome/nhn a)ll' u(pokeime/nhn a)ei\ tw=| dhmiourgw=| ei)s dia/qesin kai\ ta/cin au(th=s kai\ pro\s au)to\n e)comoi/wsin w(s dunato\n h)=n e)mparasxei=n. ou) ga\r e)k tou= mh\ o)/ntos h( ge/nesis a)ll' e)k tou= mh\ kalw=s mhd' i(kanw=s e)/xontos, w(s oi)ki/as kai\ i(mati/ou kai\ a)ndria/ntos. a)kosmi/a ga\r h)=n ta\ pro\ th=s tou= ko/smou gene/sews: a)kosmi/a d' ou)k a)sw/matos ou)d' a)ki/nhtos ou)d' a)/yuxos a)ll' a)/morfon me\n kai\ a)su/staton to\ swmatiko\n e)/mplhkton de\ kai\ a)/logon to\ kinhtiko\n e)/xousa tou=to d' h)=n a)narmosti/a yuxh=s ou)k e)xou/shs lo/gon. o( ga\r qeo\s ou)/te sw=ma to\ a)sw/maton ou)/te yuxh\n to\ a)/yuxon e)poi/hsen, a)ll' w(/sper a(rmoniko\n a)/ndra kai\ r(uqmiko\n ou) fwnh\n poiei=n ou)de\ ki/nhsin e)mmelh= de\ fwnh\n kai\ ki/nhsin eu)/ruqmon a)ciou=men, ou(/tws o( qeo\s ou)/te tou= sw/matos to\ a(pto\n kai\ a)nti/tupon ou)/te th=s yuxh=s to\ fantastiko\n kai\ kinhtiko\n au)to\s e)poi/hsen: a)mfote/ras de\ ta\s a)rxa\s paralabw/n, th\n me\n a)mudra\n kai\ skoteinh\n th\n de\ taraxw/dh kai\ a)no/hton a)telei=s de\ tou= prosh/kontos a)mfote/ras kai\ a)ori/stous, e)/tace kai\ dieko/smhse kai\ sunh/rmose, to\ ka/lliston a)pergasa/menos kai\ teleio/taton e)c au)tw=n zw=|on. h( me\n ou)=n sw/matos ou)si/a th=s legome/nhs u(p' au)tou= pandexou=s fu/sews e(/dras te kai\ tiqh/nhs tw=n genhtw=n ou)x e(te/ra ti/s e)stin.

th\n de\ th=s yuxh=s e)n *filh/bw| me\n a)peiri/an ke/klhken, a)riqmou= kai\ lo/gou ste/rhsin ou)=san, e)llei/yew/s te kai\ u(perbolh=s kai\ diafora=s kai\ a)nomoio/thtos e)n au(th=| pe/ras ou)de\n ou)de\ me/tron e)/xousan: e)n de\ *timai/w| th\n th=| a)meri/stw| sugkerannume/nhn fu/sei kai\ peri\ ta\ sw/mata gi/gnesqai legome/nhn meristh\n ou)/te plh=qos e)n mona/si kai\ stigmai=s ou)/te mh/kh kai\ pla/th le/gesqai nomiste/on, a(\ sw/masi prosh/kei kai\ swma/twn ma=llon h)\ th=s yuxh=s e)stin, a)lla\ th\n a)/takton kai\ a)o/riston au)toki/nhton de\ kai\ kinhtikh\n a)rxh\n e)kei/nhn, h(\n pollaxou= me\n a)na/gkhn e)n de\ toi=s *no/mois a)/ntikrus yuxh\n a)/takton ei)/rhke kai\ kakopoio/n: au(/th ga\r h)=n yuxh\ kaq' e(auth/n, nou= de\ kai\ logismou= kai\ a(rmoni/as e)/mfronos mete/sxen, i(/na ko/smou yuxh\ ge/nhtai. kai\ ga\r to\ pandexe\s kai\ u(liko\n e)kei=no me/geqos me\n e)ke/kthto kai\ dia/sthma kai\ xw/ran, ka/llous de\ kai\ morfh=s kai\ sxhma/twn metrio/thtos e)ndew=s ei)=xen: e)/laxe de\ tou/twn, i(/na gh=s kai\ qala/tths kai\ ou)ranou= kai\ a)ste/rwn futw=n te kai\ zw/|wn pantodapa\ sw/mata kai\ o)/rgana gi/gnhtai kosmhqe/n. oi( de\ th\n e)n *timai/w| legome/nhn a)na/gkhn, e)n de\ *filh/bw| peri\ to\ ma=llon kai\ h(=tton e)llei/yews kai\ u(perbolh=s a)metri/an kai\ a)peiri/an th=| u(/lh| prostiqe/ntes a)lla\ mh\ th=| yuxh=|, pou= qh/sontai to\ th\n u(/lhn a)ei\ me\n a)/morfon kai\ a)sxhma/tiston u(p' au)tou= le/gesqai kai\ pa/shs poio/thtos kai\ duna/mews oi)kei/as e)/rhmon, ei)ka/zesqai d' a)w/desin e)lai/ois, a(\ pro\s ta\s bafa\s oi( mureyoi\ lamba/nousin; ou) ga\r oi(=o/n te to\ a)/poion kai\ a)rgo\n e)c au(tou= kai\ a)rrepe\s ai)ti/an kakou= kai\ a)rxh\n u(poti/qesqai to\n *pla/twna kai\ kalei=n a)peiri/an ai)sxra\n kai\ kakopoio/n, au)=qis d' a)na/gkhn polla\ tw=| qew=| dusmaxou=san kai\ a)fhnia/zousan. h( ga/r a)nastre/fousa to\n ou)rano/n, w(/sper e)n *politikw=| le/getai, kai\ a)neli/ttousa pro\s tou)nanti/on a)na/gkh kai\ su/mfutos e)piqumi/a kai\ to\ th=s pa/lai pote\ fu/sews su/ntrofon pollh=s mete/xon a)taci/as, pri\n ei)s to\n nu=n ko/smon a)fike/sqai, po/qen e)gge/gone toi=s pra/gmasin, ei) to\ me\n u(pokei/menon a)/poios h)=n u(/lh kai\ a)/moiros ai)ti/as a(pa/shs, o( de\ dhmiourgo\s a)gaqo\s kai\ pa/nta boulo/menos au(tw=| kata\ du/namin e)comoiw=sai, tri/ton de\ para\ tau=ta mhde/n; ai( ga\r *stwikai\ katalamba/nousin h(ma=s a)pori/ai, to\ kako\n e)k tou= mh\ o)/ntos a)naiti/ws kai\ a)genh/tws e)peisa/gontas e)pei\ tw=n g' o)/ntwn ou)/te ta)gaqo\n ou)/te to\ a)/poion ei)ko/s e)stin ou)si/an kakou= kai\ ge/nesin parasxei=n a)lla\ tau)to\ *pla/twn ou)k e)/paqe toi=s u(/steron, ou)de\ paridw\n w(s e)kei=noi th\n metacu\ th=s u(/lhs kai\ tou= qeou= tri/thn a)rxh\n kai\ du/namin u(pe/meine tw=n lo/gwn to\n a)topw/taton, e)peiso/dion ou)k oi)=d' o(/pws poiou=nta th\n tw=n kakw=n fu/sin a)p' au)toma/tou kata\ sumbebhko/s. *)epikou/rw| me\n ga\r ou)d' a)kare\s e)gkli=nai th\n a)/tomon sugxwrou=sin, w(s a)nai/tion e)peisa/gonti ki/nhsin e)k tou= mh\ o)/ntos: au)toi\ de\ kaki/an kai\ kakodaimoni/an tosau/thn e(te/ras te peri\ sw=ma muri/as a)topi/as kai\ dusxerei/as, ai)ti/an e)n tai=s a)rxai=s ou)k e)xou/sas, kat' e)pakolou/qhsin gegone/nai le/gousin.

o( de\ *pla/twn ou)x ou(/tws, a)lla\ th\n g' u(/lhn diafora=s a(pa/shs a)palla/ttwn kai\ tou= qeou= th\n tw=n kakw=n ai)ti/an a)pwta/tw tiqe/menos tau=ta peri\ tou= ko/smou ge/grafen e)n tw=| *politikw=| para\ me\n ga\r tou= cunqe/ntos pa/nta ta\ kala\ ke/kthtai para\ de\ th=s e)/mprosqen e(/cews o(/sa xalepa\ kai\ a)/dika e)n ou)ranw=| gi/gnetai, tau=t' e)c e)kei/nhs au)to/s te e)/xei kai\ toi=s zw/|ois e)naperga/zetai. kai\ mikro\n e)/ti proelqw\n proi+o/ntos de/ fhsi tou= xro/nou kai\ lh/qhs e)ggignome/nhs e)n au)tw=|, ma=llon dunasteu/ei to\ th=s palaia=s a)narmosti/as pa/qos kai\ kinduneu/ei dialuqei\s ei)s to\n th=s a)nomoio/thtos a)/peiron o)/nta to/pon du=nai pa/lin a)nomoio/ths de\ peri\ th\n u(/lhn, a)/poion kai\ a)dia/foron ou)=san, ou)k e)/stin. a)lla\ meta\ pollw=n a)/llwn kai\ *eu)/dhmos a)gnoh/sas kateirwneu/etai tou= *pla/twnos, w(s ou)k eu)= th\n polla/kis u(p' au)tou= mhte/ra kai\ tiqh/nhn prosagoreuome/nhn ai)ti/an kakw=n kai\ a)rxh\n a)pofai/nontos. o( ga\r *pla/twn mhte/ra me\n kai\ tiqh/nhn kalei= th\n u(/lhn, ai)ti/an de\ kakou= th\n kinhtikh\n th=s u(/lhs kai\ peri\ ta\ sw/mata gignome/nhn meristh\n a)/takton kai\ a)/logon ou)k a)/yuxon de\ ki/nhsin, h(\n e)n *no/mois w(/sper ei)/rhtai yuxh\n e)nanti/an kai\ a)nti/palon th=| a)gaqourgw=| prosei=pe. yuxh\ ga\r ai)ti/a kinh/sews kai\ a)rxh/, nou=s de\ ta/cews kai\ sumfwni/as peri\ ki/nhsin. o( ga\r qeo\s ou)k a)ne/sthse th\n u(/lhn a)rgou=san a)ll' e)/sthsen u(po\ th=s a)noh/tou tarattome/nhn ai)ti/as: ou)d' a)rxa\s th=| fu/sei metabolh=s kai\ paqw=n pare/sxen, a)ll' ou)/shs e)n pa/qesi pantodapoi=s kai\ metabolai=s a)ta/ktois e)cei=le th\n pollh\n a)oristi/an kai\ plhmme/leian, a(rmoni/a| kai\ a)nalogi/a| kai\ a)riqmw=| xrw/menos o)rga/nois: w(=n e)/rgon e)sti\n ou) metabolh=| kai\ kinh/sei e(tero/thtos pa/qh kai\ diafora\s pare/xein toi=s pra/gmasin, a)lla\ ma=llon a)planh= kai\ sta/sima kai\ toi=s kata\ tau)ta\ w(sau/tws e)/xousin o(/moia poiei=n. h( me\n ou)=n dia/noia toiau/th, kata/ ge th\n e)mh\n do/can, tou= *pla/twnos.

a)po/deicis de\ prw/th me\n h( th=s legome/nhs kai\ dokou/shs au)tou= pro\s e(auto\n a)sumfwni/as kai\ diafora=s lu/sis. ou)de\ ga\r sofisth=| kraipalw=nti, po/qen ge dh\ *pla/twni, toiau/thn a)/n tis a)naqei/h, peri\ ou(\s e)spouda/kei ma/lista tw=n lo/gwn, taraxh\n kai\ a)nwmali/an, w(/ste th\n au)th\n fu/sin o(mou= kai\ a)ge/nhton a)pofai/nein kai\ genome/nhn, a)ge/nhton me\n e)n *fai/drw| th\n yuxh\n e)n de\ *timai/w| genome/nhn. h( me\n ou)=n e)n *fai/drw| dia/lektos o)li/gou dei=n a(/pasi dia\ sto/mato/s e)sti, tw=| a)genh/tw| to\ a)nw/leqron tw=| d' au)tokinh/tw| pistoume/nh to\ a)ge/nhton au)th=s: e)n de\ *timai/w| th\n de\ yuxh/n fhsin ou)x w(s nu=n u(ste/ran e)pixeirou=men le/gein ou(/tws e)mhxanh/sato kai\ o( qeo\s newte/ran ou) ga\r a)\n a)/rxesqai presbu/teron u(po\ newte/rou sune/rcas ei)/asen: a)lla/ pws h(mei=s polu\ mete/xontes tou= prostuxo/ntos te kai\ ei)kh=| tau/th| ph kai\ le/gomen o( de\ kai\ gene/sei kai\ a)reth=| prote/ran kai\ presbute/ran th\n yuxh\n sw/matos, w(s despo/tin kai\ a)/rcousan a)rcome/nou, sunesth/sato. kai\ pa/lin, ei)pw\n w(s au)th\ e)n e(auth=| strefome/nh qei/an a)rxh\n h)/rcato a)pau/stou kai\ e)/mfronos bi/ou, to\ me\n dh\ sw=ma/ fhsin o(rato\n ou)ranou= ge/gonen, au)th\ d' a)o/ratos me\n logismou= de\ mete/xousa kai\ a(rmoni/as yuxh/, tw=n nohtw=n a)ei\ t' o)/ntwn u(po\ tou= a)ri/stou a)ri/sth genome/nh tw=n gennhqe/ntwn e)ntau=qa ga\r to\n me\n qeo\n a)/riston ei)pw\n tw=n a)ei\ o)/ntwn, th\n de\ yuxh\n a)ri/sthn tw=n gennhqe/ntwn, safesta/th| tau/th| th=| diafora=| kai\ a)ntiqe/sei to\ a)i/dion au)th=s kai\ to\ a)ge/nhton a)fh/|rhtai.

ti/s ou)=n tou/twn e)pano/rqwsis e(te/ra plh\n h(=s au)to\s di/dwsi toi=s de/xesqai boulome/nois; a)ge/nhton me\n ga\r a)pofai/nei yuxh\n th\n pro\ th=s ko/smou gene/sews plhmmelw=s pa/nta kai\ a)ta/ktws kinou=san genome/nhn de\ kai\ genhth\n pa/lin, h(\n o( qeo\s e)/k te tau/ths kai\ th=s moni/mou te kai\ a)ri/sths ou)si/as e)kei/nhs e)/mfrona kai\ tetagme/nhn a)pergasa/menos kaqa/per ei)=dos, kai\ tw=| ai)sqhtikw=| to\ noero\n kai\ tw=| kinhtikw=| to\ tetagme/non a)f' au(tou= parasxw\n h(gemo/na tou= panto\s e)gkate/sthsen. ou(/tw ga\r kai\ to\ sw=ma tou= ko/smou ph=| me\n a)ge/nhton a)pofai/nei ph=| de\ genhto/n: o(/tan me\n ga\r ei)/ph| pa=n o(/son h)=n o(rato\n ou)x h(suxi/an a)/gon a)lla\ kinou/menon a)ta/ktws to\n qeo\n paralabo/nta diakosmei=n kai\ pa/lin ta\ te/ttara ge/nh, pu=r kai\ u(/dwr kai\ gh=n kai\ a)e/ra, pri\n h)\ to\ pa=n u(p' au)tw=n diakosmhqe\n gene/sqai, seismo\n e)mpoiei=n th=| u(/lh| kai\ u(p' e)kei/nhs tina/ssesqai dia\ th\n a)nwmali/an: o)/nta pou poiei= kai\ u(pokei/mena ta\ sw/mata pro\ th=s tou= ko/smou gene/sews. o(/tan de\ pa/lin le/gh| th=s yuxh=s new/teron gegone/nai to\ sw=ma kai\ to\n ko/smon ei)=nai genhto/n, o(/ti o(rato\s kai\ a(pto\s kai\ sw=ma e)/xwn e)sti\ ta\ de\ toiau=ta gigno/mena kai\ genhta\ e)fa/nh panti\ dh=lon w(s ge/nesin th=| fu/sei tou= sw/matos a)podi/dwsin. a)lla\ pollou= dei= ta)nanti/a le/gein kai\ diafe/resqai pro\s au(to\n ou(/tws e)kfanw=s e)n toi=s megi/stois. ou) ga\r w(sau/tws ou)de\ tau)to\ sw=ma gi/gnesqai\ te/ fhsin u(po\ tou= qeou= kai\ ei)=nai pri\n h)\ gene/sqai tau=ta ga\r a)/ntikrus farmakw=nto/s e)stin. a)lla\ ti/ dei= noei=n kai\ th\n ge/nesin, au)to\s dida/skei. to\ me\n ga\r pro\ tou/tou fhsi\ tau=ta pa/nta ei)=xen a)lo/gws kai\ a)me/trws: o(/te d' e)pexeirei=to kosmei=sqai to\ pa=n, pu=r prw=ton kai\ u(/dwr kai\ gh=n kai\ a)e/ra, i)/xnh me\n e)/xonta a)/tta au(tw=n, panta/pasi mh\n diakei/mena, w(/sper ei)ko\s e)/xein a(/pan, o(/tan a)ph=| tinos qeo/s ou(/tw dh\ to/te pefuko/ta tau=ta prw=ton diesxhmati/sato ei)/desi kai\ a)riqmoi=s, e)/ti de\ pro/teron ei)pw\n w(s ou) mia=s e)/rgon h)=n a)nalogi/as a)lla\ duei=n to\ sundh=sai stereo\n o)/nta kai\ ba/qos e)/xonta to\n tou= panto\s o)/gkon kai\ dielqw\n o(/ti puro\s kai\ gh=s u(/dwr a)e/ra te o( qeo\s e)n me/sw| qei\s sune/dhse kai\ sunesth/sato to\n ou)rano/n, e)/k te dh\ tou/twn fhsi\ toiou/twn kai\ to\n a)riqmo\n tetta/rwn to\ tou= ko/smou sw=ma e)gennh/qh di' a)nalogi/as o(mologh=san, fili/an t' e)/sxen e)k tou/twn, w(/st' ei)s tau)to\n au(tw=| sunelqo\n a)/luton u(po\ tw=n a)/llwn plh\n u(po\ tou= sundh/santos gene/sqai: safe/stata dida/skwn w(s ou)xi\ sw/matos a(plw=s ou)d' o)/gkou kai\ u(/lhs, a)lla\ summetri/as peri\ sw=ma kai\ ka/llous kai\ o(moio/thtos h)=n o( qeo\s path\r kai\ dhmiourgo/s. tau=ta dh\ dei= dianoei=sqai kai\ peri\ yuxh=s, w(s th\n me\n ou)/q' u(po\ tou= qeou= genome/nhn ou)/te ko/smou yuxh\n ou)=san, a)lla/ tina fantastikh=s kai\ docastikh=s a)lo/gou de\ kai\ a)ta/ktou fora=s kai\ o(rmh=s du/namin au)toki/nhton kai\ a)eiki/nhton: th\n d' au)to\s o( qeo\s diarmosa/menos toi=s prosh/kousin a)riqmoi=s kai\ lo/gois e)gkate/sthsen h(gemo/na tou= ko/smou gegono/tos genhth\n ou)=san.

o(/ti de\ peri\ tou/twn dienoei=to tau=ta kai\ ou) qewri/as e(/neka, tou= te ko/smou mh\ genome/nou kai\ th=s yuxh=s o(/mws u(peti/qeto su/stasin kai\ ge/nesin, e)kei=no pro\s polloi=s tekmh/rio/n e)sti to\ th\n me\n yuxh\n u(p' au)tou= kai\ a)ge/nhton w(/sper ei)/rhtai kai\ genhth\n le/gesqai, to\n de\ ko/smon a)ei\ me\n gegono/ta kai\ genhto\n a)ge/nhton de\ mhde/pote mhd' a)i/dion. ta\ me\n ou)=n e)n *timai/w| ti/ dei= profe/rein; o(/lon ga\r kai\ pa=n to\ su/ggramma peri\ ko/smou gene/sews; a)/xri te/lous a)p' a)rxh=s e)sti. tw=n d' a)/llwn e)n me\n *)atlantikw=| proseuxo/menos o( *ti/maios o)noma/zei to\n pa/lai me\n e)/rgw| gegnono/ta nu=n de\ lo/gw| qeo/n, e)n *politikw=| d' o( *parmeni/deios ce/nos to\n ko/smon u(po\ tou= qeou= sunteqe/nta fhsi\ pollw=n a)gaqw=n metalabei=n, ei) de/ ti flau=ro/n e)stin h)\ xalepo/n, e)p th=s prote/ras e(/cews a)narmo/stou kai\ a)lo/gou summemigme/non e)/xein: e)n de\ th=| *politei/a| peri\ tou= a)riqmou=, o(\n ga/mon e)/nioi kalou=sin, o( *swkra/ths a)rxo/menos le/gein e)/sti de/ fhsi qei/w| me\n genhtw=| peri/odos h(\n a)riqmo\s perilamba/nei te/leios, ou)k a)/llo kalw=n qei=on genhto\n h)\ to\n ko/smon.

kata\ tau)ta\ e)/xon w(s morfh\n kai\ ei)=dos, to\ de\ peri\ ta\ sw/mata gigno/menon meristo\n w(s u(podoxh\n kai\ u(/lhn, to\ de\ mi=gma koino\n e)c a)mfoi=n a)potetelesme/non. h( me\n ou)=n a)me/ristos ou)si/a kai\ a)ei\ kata\ tau)ta\ kai\ w(sau/tws e)/xousa mh\ mikro/thti, kaqa/per ta\ e)la/xista tw=n swma/twn, noei/sqw feu/gousa to\n merismo/n: to\ ga\r a(plou=n kai\ a)paqe\s kai\ kaqaro\n au)th=s kai\ monoeide\s a)mere\s ei)/rhtai kai\ a)me/riston w(=| kai\ tw=n sunqe/twn kai\ meristw=n kai\ diaferome/nwn a(mwsge/pws qigou=sa pau/ei to\ plh=qos kai\ kaqi/sthsin ei)s mi/an di' o(moio/thtos e(/cin. th\n de\ peri\ ta\ sw/mata gignome/nhn meristh\n ei) me/n tis e)qe/loi kalei=n u(/lhn, w(s kai\ u(pokeime/nhn e)kei/nh| kai\ metalhptikh\n e)kei/nhs fu/sin, o(mwnumi/a| xrw/menos, ou) diafe/rei pro\s to\n lo/gon: oi( de\ swmatikh\n a)ciou=ntes u(/lhn summi/gnusqai th=| a)meri/stw| diamarta/nousi prw=ton me\n o(/ti tw=n e)kei/nhs o)noma/twn ou)deni\ nu=n o( *pla/twn ke/xrhtai decamenh\n ga\r ei)/wqe kai\ pandexh= kai\ tiqh/nhn a)ei\ kalei=n e)kei/nhn, ou) peri\ ta\ sw/mata meristh/n, ma=llon de\ sw=ma merizo/menon ei)s to\ kaq' e(/kaston. e)/peita ti/ dioi/sei th=s tou= ko/smou gene/sews h( th=s yuxh=s, ei)/per a)mfote/rois e)/k te th=s u(/lhs kai\ tw=n nohtw=n ge/gonen h( su/stasis; au)to/s ge mh\n o( *pla/twn, w(/sper a)pwqou/menos th=s yuxh=s th\n e)k sw/matos ge/nesin, e)nto\s au)th=s fhsin u(po\ tou= qeou= teqh=nai to\ swmatiko/n, ei)=t' e)/cwqen u(p' e)kei/nhs perikalufqh=nai: kai\ o(/lws, a)pergasa/menos tw=| lo/gw| th\n yuxh\n u(/steron e)peisa/gei th\n peri\ th=s u(/lhs u(po/qesin, mhde\n au)th=s pro/teron, o(/te th\n yuxh\n e)ge/nna, dehqei/s, w(s xwri\s u(/lhs genome/nhn.

o(/moia de\ tou/tois e)/stin a)nteipei=n kai\ toi=s peri\ *poseidw/nion ou) ga\r makra\n th=s u(/lhs a)pe/sthsan: a)lla\ deca/menoi th\n tw=n pera/twn ou)si/an peri\ ta\ sw/mata le/gesqai meristh\n kai\ tau=ta tw=| nohtw=| mi/cantes a)pefh/nanto th\n yuxh\n i)de/an ei)=nai tou= pa/nth| diastatou= kat' a)riqmo\n sunestw=san a(rmoni/an perie/xonta ta/ te ga\r maqhmatika\ tw=n prw/twn nohtw=n metacu\ kai\ tw=n ai)sqhtw=n teta/xqai, th=s te yuxh=s; tw=n nohtw=n to\ a)i/dion kai\ tw=n ai)sqhtw=n to\ paqhtiko\n e)xou/shs, prosh=kon e)n me/sw| th\n ou)si/an u(pa/rxein. e)/laqe ga\r kai\ tou/tous o( qeo\s toi=s tw=n swma/twn pe/rasin u(/steron, a)peirgasme/nhs h)/dh th=s yuxh=s, xrw/menos e)pi\ th\n th=s u(/lhs diamo/rfwsin, to\ skedasto\n au)th=s kai\ a)su/ndeton o(ri/zwn kai\ perilamba/nwn tai=s e)k tw=n trigw/nwn sunarmottome/nwn e)pifanei/ais. a)topw/teron de\ to\ th\n yuxh\n i)de/an poiei=n: h( me\n ga\r a)eiki/nhtos h( d' a)ki/nhtos, kai\ h( me\n a)migh\s pro\s to\ ai)sqhto\n h( de\ tw=| sw/mati suneirgme/nh. pro\s de\ tou/tois o( qeo\s th=s me\n i)de/as w(s paradei/gmatos ge/gone mimhth/s, th=s de\ yuxh=s w(/sper a)potele/smatos dhmiourgo/s. o(/ti d' ou)d' a)riqmo\n o( *pla/twn th\n ou)si/an ti/qetai th=s yuxh=s a)lla\ tattome/nhn u(p' a)riqmou=, proei/rhtai.

pro\s d' a)mfote/rous tou/tous koino/n e)sti to\ mh/te toi=s pe/rasi mh/te toi=s a)riqmoi=s mhqe\n i)/xnos e)nupa/rxein e)kei/nhs th=s duna/mews, h(=| to\ ai)sqhto\n h( yuxh\ pe/fuke kri/nein: nou=n me\n ga\r au)th=| kai\ nohtiko\n h( th=s nohth=s me/qecis a)rxh=s; e)mpepoi/hke: do/cas de\ kai\ pi/steis kai\ to\ fantastiko\n kai\ to\ paqhtiko\n u(po\ tw=n peri\ to\ sw=ma poioth/twn, o(\ ou)k a)/n tis e)k mona/dwn ou)de\ grammw=n ou)d' e)pifaneiw=n a(plw=s noh/seien e)ggigno/menon. kai\ mh\n ou) mo/non ai( tw=n qnhtw=n yuxai\ gnwstikh\n tou= ai)sqhtou= du/namin e)/xousin, a)lla\ kai\ th\n tou= ko/smou fhsi\n a)nakukloume/nhn au)th\n pro\s e(auth/n, o(/tan ou)si/an skedasth\n e)/xonto/s tinos e)fa/pthtai kai\ o(/tan a)me/riston, le/gein kinoume/nhn dia\ pa/shs e(auth=s, o(/tw| t' a)/n ti tau)to\n kai\ o(/tou a)\n e(\teron, pro\s o(/ ti te ma/lista kai\ o(/ph kai\ o(/pws sumbai/nei kata\ ta\ gigno/mena pro\s e(/kaston e(/kasta ei)=nai kai\ pa/sxein e)n tou/tois a(/ma kai\ tw=n de/ka kathgoriw=n poiou/menos u(pografh\n e)/ti ma=llon toi=s e)fech=s diasafei=. lo/gos ga/r fhsin a)lhqh/s, o(/tan me\n peri\ to\ ai)sqhto\n gi/gnhtai kai\ o( tou= qate/rou ku/klos o)rqo\s i)w\n ei)s pa=san au)tou= th\n yuxh\n diaggei/lh|, do/cai kai\ pi/steis gi/gnontai be/baioi kai\ a)lhqei=s: o(/tan d' au)= peri\ to\ logistiko\n h)=| kai\ o( tou= tau)tou= ku/klos eu)/troxos w)\n au)ta\ mhnu/sh|, e)pisth/mh e)c a)na/gkhs a)potelei=tai tou/tw d' e)n w(=| tw=n o)/ntwn e)ggi/gnesqon, e)a\n pote/ tis au)to\ a)/llo plh\n yuxh\n prosei/ph|, pa=n ma=llon h)\ to\ a)lhqe\s e)rei=. po/qen ou)=n e)/sxen h( yuxh\ th\n a)ntilhptikh\n tou= ai)sqhtou= kai\ docastikh\n tau/thn ki/nhsin, e(te/ran th=s nohtikh=s e)kei/nhs kai\ teleutw/shs ei)s e)pisth/mhn, e)/rgon ei)pei=n, mh\ qeme/nous bebai/ws, o(/ti nu=n ou)x a(plw=s yuxh\n a)lla\ ko/smou yuxh\n suni/sthsin e)c u(pokeime/nwn, th=s te krei/ttonos. ou)si/as kai\ a)meri/stou kai\ th=s: xei/ronos, h(\n peri\ ta\ sw/mata meristh\n ke/klhken, ou)x e(te/ran ou)=san h)\ th\n docastikh\n kai\ fantastikh\n kai\ sumpaqh= tw=| ai)sqhtw=| ki/nhsin, ou) genome/nhn a)ll' u(festw=san a)i/dion w(/sper h( e(te/ra. to\ ga\r noero\n h( fu/sis e)/xousa kai\ to\ docastiko\n ei)=xen, a)ll' e)kei=no me\n a)ki/nhton a)paqe\s kai\ peri\ th\n a)ei\ me/nousan i(drume/non ou)si/an, tou=to de\ meristo\n kai\ planhto/n, a(/te dh\ ferome/nhs kai\ skedannume/nhs e)fapto/menon u(/lhs. ou)/te ga\r to\ ai)sqhto\n ei)lh/xei ta/cews a)ll' h)=n a)/morfon kai\ a)o/riston, h(/ te peri\ tou=to tetagme/nh du/namis ou)/te do/cas e)na/rqrous ou)/te kinh/seis a(pa/sas ei)=xe tetagme/nas, a)lla\ ta\s polla\s e)nupniw/deis kai\ parafo/rous kai\ tarattou/sas to\ swmatoeide/s, o(/sa mh\ kata\ tu/xhn tw=| belti/oni perie/pipten: e)n me/sw| ga\r h)=n a)mfoi=n kai\ pro\s a)mfo/tera sumpaqh= kai\ suggenh= fu/sin ei)=xe, tw=| me\n ai)sqhtikw=| th=s u(/lhs a)ntexome/nh tw=| de\ kritikw=| tw=n nohtw=n.

ou(/tw de/ pws kai\ au)to\s diasafei= toi=s o)no/masin: ou(=tos ga/r fhsi para\ th=s e)mh=s yh/fou logisqei\s e)n kefalai/w| dedo/sqw lo/gos, o)/n te kai\ xw/ran kai\ ge/nesin ei)=nai tri/a trixh= kai\ pri\n ou)rano\n gene/sqai. xw/ran te ga\r kalei= th\n u(/lhn w(/sper e(/dran e)/stin o(/te kai\ u(podoxh/n, o)\n de\ to\ nohto/n, ge/nesin de\ tou= ko/smou mh/pw gegono/tos ou)demi/an a)/llhn h)\ th\n e)n metabolai=s kai\ kinh/sesin ou)si/an, tou= tupou=ntos kai\ tou= tupoume/nou metacu\ tetagme/nhn, diadidou=san e)ntau=qa ta\s e)kei=qen ei)ko/nas. dia/ te dh\ tau=ta : meristh\ proshgoreu/qh kai\ o(/ti tw=| ai)sqhtw=| to\ ai)sqano/menon kai\ tw=| fantastw=| to\ fantazo/menon a)na/gkh sundiane/mesqai kai\ sumparh/kein h( ga\r ai)sqhtikh\ ki/nhsis, i)di/a yuxh=s ou)=sa, kinei=tai pro\s to\ ai)sqhto\n e)kto/s o( de\ nou=s au)to\s me\n e)f' e(autou= mo/nimos h)=n kai\ a)ki/nhtos, e)ggeno/menos de\ th=| yuxh=| kai\ krath/sas ei)s e(auto\n e)pistre/fei kai\ sumperai/nei th\n e)gku/klion fora\n peri\ to\ me/non a)ei\ ma/lista yau/ousan tou= o)/ntos. dio\ kai\ dusana/kratos h( koinwni/a ge/gonen au)tw=n, tw=| a)meri/stw| to\ meristo\n kai\ tw=|: mhdamh=| kinhtw=| to\ pa/nth| forhto\n mignu/ousa kai\ katabiazome/nh qa/teron ei)s tau)to\n sunelqei=n. h)=n de\ to\ qa/teron ou) ki/nhsis w(/sper ou)de\ tau)to\n sta/sis, a)ll' a)rxh\ diafora=s kai\ a)nomoio/thtos. e(ka/teron ga\r a)po\ th=s e(te/ras a)rxh=s ka/teisi, to\ me\n tau)to\n a)po\ tou= e(no\s to\ de\ qa/teron a)po\ th=s dua/dos: kai\ me/miktai prw=ton e)ntau=qa peri\ th\n yuxh/n, a)riqmoi=s kai\ lo/gois sundeqe/nta kai\ meso/thsin e)narmoni/ois, kai\ poiei= qa/teron me\n e)ggeno/menon tw=| tau)tw=| diafora/n, to\ de\ tau)to\n e)n tw=| e(te/rw| ta/cin, w(s dh=lo/n e)stin e)n tai=s prw/tais th=s yuxh=s duna/mesin: ei)si\ d' au(=tai to\ kritiko\n kai\ to\ kinhtiko/n. h( me\n ou)=n ki/nhsis eu)qu\s e)pidei/knutai peri\ to\n ou)rano\n e)n me\n th=| tau)to/thti th\n e(tero/thta th=| perifora=| tw=n a)planw=n, e)n de\ th=| e(tero/thti th\n tau)to/thta th=| ta/cei tw=n planh/twn e)pikratei= ga\r e)n e)kei/nois to\ tau)to\n e)n de\ toi=s peri\ gh=n tou)nanti/on. h( de\ kri/sis a)rxa\s; me\n e)/xei du/o, to/n te nou=n a)po\ tou= tau)tou= pro\s ta\ kaqo/lou kai\ th\n ai)/sqhsin a)po\ tou= e(te/rou pro\s ta\ kaq' e(/kasta. me/miktai de\ lo/gos e)c a)mfoi=n, no/hsis e)n toi=s nohtoi=s kai\ do/ca gigno/menos e)n toi=s ai)sqhtoi=s: o)rga/nois te tai=s metacu\ fantasi/ais te kai\ mnh/mais xrw/menos, w(=n ta\ me\n e)n tw=| tau)tw=| to\ e(/teron ta\ d' e)n tw=| e(te/rw| poiei= to\ tau)to/n. e)/sti ga\r h( me\n no/hsis ki/nhsis tou= noou=ntos peri\ to\ me/non, h( de\ do/ca monh\ tou= ai)sqanome/nou peri\ to\ kinou/menon fantasi/an de\ sumplokh\n do/chs pro\s ai)/sqhsin ou)=san i(/sthsin e)n mnh/mh| to\ tau)to\n de\ qa/teron kinei= pa/lin e)n diafora=| tou= pro/sqen kai\ nu=n, e(tero/thtos a(/ma kai\ tau)to/thtos; e(fapto\menon.

dei= de\ th\n peri\ to\ sw=ma tou= ko/smou genome/nhn su/nthcin ei)ko/na labei=n th=s a)nalogi/as e)n dihrmo/sato yuxh/n. e)kei= me\n ga\r h)=n a)/kra to\ pu=r kai\ h( gh=,: xaleph\n pro\s a)/llhla kraqh=nai fu/sin e)/xonta, ma=llon d' o(/lws a)/kraton kai\ a)su/staton o(/qen e)n me/sw| qe/menos au)tw=n to\n me\n a)e/ra pro\ tou= puro\s to\ d' u(/dwr pro\ th=s gh=s, tau=ta prw=ton a)llh/lois e)ke/rasen, ei)=ta dia\ tou/twn e)kei=na pro/s te tau=ta kai\ pro\s a)/llhla sune/mice kai\ sunh/rmosen. e)ntau=qa de\ pa/lin to\ tau)to\n kai\ to\ qa/teron, e)nanti/as duna/meis kai\ a)kro/thtas a)ntipa/lous, sunh/gagen, ou) di' au(tw=n, a)ll' ou)si/as e(te/ras metacu/, th\n me\n a)me/riston pro\ tou= tau)tou= pro\ de\ tou= qate/rou th\n meristh/n, e)/stin prosh/kousan e(kate/ran e(kate/ra| ta/cas, ei)=ta mixqei/sais e)kei/nais e)pegkerannu/menos, ou(/tw to\ pa=n sunu/fhne e(\n th=s yuxh=s ei)=dos, w(s h)=n a)nusto/n, e)k diafo/rwn o(/moion e)/k te pollw=n e(\n a)peirgasme/nos. ou)k eu)= de/ tines ei)rh=sqai le/gousi du/smikton u(po\ tou= *pla/twnos th\n qate/rou fu/sin, ou)k a)/dekton ou)=san a)lla\ kai\ fi/lhn metabolh=s ma=llon de\ th\n tou= tau)tou=, mo/nimon kai\ dusmeta/blhton ou)=san, ou) r(a|di/ws prosi/esqai mi=cin a)ll' a)pwqei=sqai kai\ feu/gein, o(/pws a(plh= diamei/nh| kai\ ei)likrinh\s kai\ a)nalloi/wtos. oi( de\ tau=t' e)gkalou=ntes a)gnoou=sin o(/ti to\ me\n tau)to\n i)de/a tw=n w(sau/tws e)xo/ntwn e)sti\ to\ de\ qa/teron tw=n diafo/rws: kai\ tou/tou me\n e)/rgon, w(=n a)\n a(/yhtai, diista/nai kai\ a)lloiou=n kai\ polla\ poiei=n: e)kei/nou de\ suna/gein kai\ sunista/nai di' o(moio/thtos e)k pollw=n mi/an a)nalamba/nonta morfh\n kai\ du/namin.

au(=tai me\n ou)=n duna/meis th=s tou= panto\s ei)si yuxh=s ai(\ d' ei)s qnhta\ kai\ paqhta\ pareisi/asin o)/rgana a)/fqartoi fqartw=n au)tai\ swma/twn, e)n tau/tais to\ th=s duadikh=s kai\ a)ori/stou meri/dos e)pifai/netai ma=llon ei)=dos, to\ de\ th=s a(plh=s kai\ monadikh=s a)mudro/teron u(pode/duken. ou) mh\n r(a|di/ws a)/n tis ou)/te pa/qos a)nqrw/pou panta/pasin a)phllagme/non logismou= katanoh/seien ou)/te dianoi/as ki/nhsin, mhde\n e)piqumi/as h)\ filotimi/as h)\ tou= xai/rontos h)\ lupoume/nou pro/sesti. dio\ tw=n filoso/fwn oi( me\n ta\ pa/qh lo/gous. poiou=sin, w(s pa=san e)piqumi/an kai\ lu/phn kai\ o)rgh\n kri/seis ou)/sas: oi( de\ ta\s a)reta\s a)pofai/nousi paqhtika/s: kai\ ga\r a)ndrei/a| to\ fobou/menon kai\ swfrosu/nh| to\ h(do/menon kai\ dikaiosu/nh| to\ kerdale/on ei)=nai. kai\ mh\n qewrhtikh=s ge th=s yuxh=s ou)/shs a(/ma kai\ praktikh=s kai\ qewrou/shs de\ ta\ kaqo/lou kai\ ta\ kaq' e(/kasta kai\ noei=n me\n e)kei=na tau=ta d' ai)sqa/nesqai dokou/shs, o( koino\s lo/gos a)ei\ peri/ te tau)to\n e)ntugxa/nwn tw=| qate/rw| kai\ tau)tw=| peri\ qa/teron e)pixeirei= me\n o(/rois kai\ diaire/sesi xwri/zein to\ e(\n kai\ ta\ polla\ kai\ to\ a)mere\s kai\ meristo/n, ou) du/natai de\ kaqarw=s e)n ou)dete/rw| gene/sqai dia\ to\ kai\ ta\s a)rxa\s e)nalla\c e)mpeple/xqai kai\ katamemi=xqai di' a)llh/lwn. kai\ dia\ tou=to th=s ou)si/as th\n e)k th=s a)meri/stou kai\ th=s meristh=s o( qeo\s u(podoxh\n tw=| tau)tw=| kai\ tw=| qate/rw| sune/sthsen, i(/n' e)n diafora=| ta/cis ge/nhtai tou=to ga\r h)=n gene/sqai e)pei\ xwri\s tou/twn to\ me\n tau)to\n ou)k ei)=xe diafora/n, w(/st' ou)de\ ki/nhsin ou)de\ ge/nesin: to\ qa/teron de\ ta/cin ou)k ei)=xen, w(/st' ou)de\ su/stasin ou)de\ ge/nesin. kai\ ga\r ei) tw=| tau)tw=| sumbe/bhken e(te/rw| ei)=nai tou= e(te/rou kai\ tw=| e(te/rw| pa/lin au(tw=| tau)to/n, ou)de\n h( toiau/th me/qecis a)llh/lwn poiei= go/nimon, a)lla\ dei=tai tri/ths tino\s oi(=on u(/lhs u(podexome/nhs kai\ diatiqeme/nhs u(p' a)mfote/rwn. au(/th d' e)sti/n, h(\n prw/thn sune/sthse tw=| peri\ ta\ nohta\ moni/mw| tou= peri\ ta\ sw/mata kinhtikou= to\ a)/peiron o(ri/sas

w(s de\ fwnh\ ti/s e)stin a)/logos kai\ a)sh/mantos lo/gos de\ le/cis e)n fwnh=| shmantikh=| dianoi/as, a(rmoni/a de\ to\ e)k fqo/ggwn kai\ diasthma/twn, kai\ fqo/ggos me\n e(\n kai\ tau)to\n dia/sthma de\ fqo/ggwn e(tero/ths kai\ diafora/, mixqe/ntwn de\ tou/twn w)|dh\ gi/gnetai kai\ me/los: ou(/tw to\ paqhtiko\n th=s yuxh=s a)o/riston h)=n kai\ a)sta/qmhton, ei)=q' w(ri/sqh pe/ratos e)ggenome/nou kai\ ei)/dous tw=| meristw=| kai\ pantodapw=| th=s kinh/sews. sullabou=sa de\ to\ tau)to\n kai\ to\ qa/teron, o(moio/thsi kai\ a)nomoio/thsin a)riqmw=n e)k diafora=s o(mologi/an a)pergasame/nwn zwh/ te tou= panto/s e)stin e)/mfrwn kai\ a(rmoni/a kai\ lo/gos a)/gwn peiqoi= memigme/nhn a)na/gkhn, h(\n ei(marme/nhn oi( polloi\ kalou=sin, *)empedoklh=s de\ fili/an o(mou= kai\ *nei=kos, *(hra/kleitos de\ pali/ntonon a(rmoni/hn ko/smou o(/kwsper lu/rhs kai\ to/cou *parmeni/dhs de\ fw=s kai\ sko/tos, *)anacago/ras de\ nou=n kai\ a)peiri/an, *zwroa/strhs de\ qeo\n kai\ dai/mona, to\n me\n *)wroma/sdhn kalw=n to\n d' *)areima/nion. *eu)ripi/dhs d' ou)k o)rqw=s a)nti\ tou= sumplektikou= tw=| diazeuktikw=| ke/xrhtai *zeu\s ei)/t' a)na/gkh fu/seos ei)/te nou=s brotw=n: kai\ ga\r a)na/gkh kai\ nou=s e)stin h( dih/kousa dia\ pa/ntwn du/namis. *ai)gu/ptioi me\n ou)=n muqologou=ntes ai)ni/ttontai, tou= *(/wrou di/khn o)flo/ntos, tw=| me\n patri\ to\ pneu=ma kai\ to\ ai(=ma th=| de\ mhtri\ th\n sa/rka kai\ th\n pimelh\n prosnemhqh=nai. th=s de\ yuxh=s ou)de\n me\n ei)likrine\s ou)d' a)/kraton ou)de\ xwri\s a)polei/petai tw=n a)/llwn a(rmoni/h ga\r a)fanh\s fanerh=s krei/ttwn kaq' *(hra/kleiton, e)n h(=| ta\s diafora\s kai\ ta\s e(tero/thtas o( mignu/wn qeo\s e)/kruye kai\ kate/dusen e)mfai/netai d' o(/mws au)th=s tw=| me\n a)lo/gw| to\ taraxw=des, tw=| de\ logikw=| to\ eu)/takton, tai=s d' ai)sqh/sesi to\ kathnagkasme/non, tw=| de\ nw=| to\ au)tokrate/s. h( d' o(ristikh\ du/namis to\ kaqo/lou kai\ to\ a)mere\s dia\ sugge/neian a)gapa=|: kai\ tou)nanti/on h( diairetikh\ pro\s ta\ kaq' e(/kasta fe/retai tw=| meristw=|: xai/rei d' o(/lon th=| dia\ to\ tau)to\n e)f' a(\ dei=tai metabolh=| dia\ to\ qa/teron. ou)x h(/kista d' h(/ te pro\s to\ kalo\n diafora\ kai\ to\ ai)sxro\n h(/ te pro\s to\ h(du\ kai\ to\ a)lgeino\n au)=qis oi(/ te tw=n e)rw/ntwn e)nqousiasmoi\ kai\ ptoh/seis kai\ diama/xai tou= filoka/lou pro\s to\ a)ko/laston e)ndei/knuntai to\ mikto\n e)/k te th=s qei/as kai\ a)paqou=s e)/k te th=s qnhth=s kai\ peri\ ta\ sw/mata paqhth=s meri/dos: w(=n kai\ au)to\s o)noma/zei to\ me\n e)piqumi/an e)/mfuton h(donw=n, to\ d' e)pei/sakton do/can e)fieme/nhn tou= a)ri/stou. to\ ga\r paqhtiko\n a)nadi/dwsin e)c e(auth=s h( yuxh/, tou= de\ nou= mete/sxen a)po\ th=s krei/ttonos a)rxh=s e)ggenome/nou.

th=s de\ diplh=s koinwni/as tau/ths ou)d' h( peri\ to\n ou)rano\n a)ph/llaktai fu/sis, a)ll' e(terorrepou=sa nu=n me\n o)rqou=tai th=| tau)tou= perio/dw| kra/tos e)xou/sh| kai\ diakuberna=| to\n ko/smon: e)/stai de/ tis xro/nou moi=ra kai\ ge/gonen h)/dh polla/kis, e)n to\ me\n fro/nimon a)mblu/netai kai\ katadarqa/nei lh/qhs e)mpipla/menon tou= oi)kei/ou, to\ de\ sw/mati su/nhqes e)c a)rxh=s kai\ sumpaqe\s e)fe/lketai kai\ baru/nei kai\ a)neli/ssei th\n e)n decia=| tou= panto\s porei/an, a)narrh=cai d' ou) du/natai panta/pasin, a)ll' a)nh/negken au)=qis ta\ belti/w kai\ a)ne/bleye pro\s to\ para/deigma qeou= sunepistre/fontos kai\ sunapeuqu/nontos. ou(/tws e)ndei/knutai pollaxo/qen h(mi=n to\ mh\ pa=n e)/rgon ei)=nai qeou= th\n yuxh\n a)lla\ su/mfuton e)/xousan e)n e(auth=| th\n tou= kakou= moi=ran u(p' e)kei/nou diakekosmh=sqai, tw=| me\n e(ni\ th\n a)peiri/an o(ri/santos, i(/n' ou)si/a ge/nhtai pe/ratos metasxou=sa, th=| de\ tau)tou= kai\ th=| e(te/rou duna/mei ta/cin kai\ metabolh\n kai\ diafora\n kai\ o(moio/thta summi/cantos, pa=si de\ tou/tois, w(s a)nusto\n h)=n, koinwni/an pro\s a)/llhla kai\ fili/an e)rgasame/nou di' a)riqmw=n kai\ a(rmoni/as.

peri\ w(=n ei) kai\ polla/kis a)khko/ate kai\ polloi=s e)ntetuxh/kate lo/gois kai\ gra/mmasin, ou) xei=ro\n e)sti ka)me\ braxe/ws dielqei=n, proekqe/menon to\ tou= *pla/twnos: mi/an a)fei=le to\ prw=ton a)po\ panto\s moi=ran, meta\ de\ tau/thn a)fh/|rei diplasi/an tau/ths: th\n d' au)= tri/thn, h(mioli/an me\n th=s deute/ras triplasi/an de\ th=s prw/ths teta/rthn de\ th=s deute/ras diplh=n, pe/mpthn de\ triplh=n th=s tri/ths, th\n d' e(/kthn th=s prw/ths o)ktaplasi/an, e(bdo/mhn d' e(ptakaieikosaplasi/an th=s prw/ths. meta\ de\ tau=ta suneplhrou=to ta/ te dipla/sia kai\ tripla/sia diasth/mata, moi/ras e)/ti e)kei=qen a)pote/mnwn kai\ tiqei\s ei)s to\ metacu\ tou/twn, w(/st' e)n e(ka/stw| diasth/mati du/o ei)=nai meso/thtas, th\n me\n e(kate/rw| tw=n a)/krwn i)/sw| te u(pere/xousan kai\ u(perexome/nhn, th\n de\ tau)tw=| me/rei tw=n a)/krwn au)tw=n u(pere/xousan kai\ u(perexome/nhn: h(mioli/wn de\ diasta/sewn kai\ e)pitri/twn kai\ e)pogdo/wn genome/nwn e)k tou/twn tw=n desmw=n e)n tai=s pro/sqen diasta/sesi, tw=| tou= e)pogdo/ou diasth/mati ta\ e)pi/trita pa/nta suneplhrou=to, lei/pwn au)tw=n e(ka/stou mo/rion, th=s tou= mori/ou tau/ths diasta/sews leifqei/shs a)riqmou= pro\s a)riqmo/n, e)xou/shs tou\s o(/rous e(\c kai\ penth/konta kai\ diakosi/wn pro\s tri/a kai\ tessara/konta kai\ diako/sia. e)n tou/tois zhtei=tai prw=ton peri\ th=s poso/thtos tw=n a)riqmw=n, deu/teron peri\ th=s ta/cews, tri/ton peri\ th=s duna/mews: peri\ me\n th=s poso/thtos ti/nes ei)si/n, ou(\s e)n toi=s diplasi/ois kai\ triplasi/ois diasth/masi lamba/nei peri\ de\ th=s ta/cews po/teron e)f' e(no\s sti/xou pa/ntas e)kqete/on w(s *qeo/dwros, h)\ ma=llon w(s: *kra/ntwr e)n tw=| *l sxh/mati, tou= prw/tou kata\ korufh\n tiqeme/nou kai\ xwri\s me\n tw=n diplasi/wn xwri\s de\ tw=n triplasi/wn e)n dusi\ sti/xois u(potattome/nwn. peri\ de\ th=s: xrei/as kai\ th=s duna/mews ti/ poiou=si paralambano/menoi pro\s th\n su/stasin th=s yuxh=s.

prw=ton ou)=n peri\ tou= prw/tou paraithso/meqa tou\s le/gontas, w(s e)pi\ tw=n lo/gwn au)tw=n a)po/xrh qewrei=n h(\n e)/xei ta/ te diasth/mata fu/sin ai(/ te tau=ta sumplhrou=sai meso/thtes, e)n oi(=s a)/n tis a)riqmoi=s u(po/qhtai xw/ras e)/xousi dektika\s metacu\ tw=n ei)rhme/nwn a)nalogiw=n, o(moi/ws perainome/nhs th=s didaskali/as. ka)\n ga\r a)lhqe\s to\ lego/menon, a)mudra\n poiei= th\n ma/qhsin a)/neu paradeigma/twn, a)/llhs; te qewri/as a)pei/rgei xa/rin e)xou/shs ou)k a)filo/sofon. a)\n ou)=n a)po\ th=s mona/dos a)rca/menoi tou\s diplasi/ous kai\ triplasi/ous e)n me/rei tiqw=men, w(s au)to\s u(fhgei=tai, genh/sontai kata\ to\ e(ch=s, o(/pou me\n to\ deu/teron kai\ to\ te/tarton kai\ o(\gdoon o(/pou de\ tri/ton kai\ e)/nnaton kai\ ei)kostoe/bdomon, suna/pantes me\n e(pta/, koinh=s de\ lambanome/nhs th=s mona/dos, a)/xri tessa/rwn tw=| pollaplasiasmw=| proio/ntwn. ou) ga\r e)ntau=qa mo/non a)lla\ pollaxo/qi th=s tetra/dos h( pro\s th\n e(bdoma/da sumpa/qeia gi/gnetai kata/dhlos. h( me\n ou)=n u(po\ tw=n *puqagorikw=n u(mnoume/nh tetraktu/s, ta\ e(\c kai\ ta\ tria/konta, qaumasto\n e)/xein dokei= to\ sugkei=sqai me\n e)k prw/twn a)rti/wn tessa/rwn kai\ prw/twn perissw=n tessa/rwn, gi/gnesqai de\ suzugi/a teta/rth tw=n e)fech=s sunteqeime/nwn: prw/th me\n ga/r e)sti suzugi/a h( tou= e(no\s kai\ tw=n duei=n, deute/ra.

d' h( tw=n triw=n kai\ tetta/rwn, tri/th d' h( tw=n e' kai\ s' w(=n ou)demi/a poiei= tetra/gwnon ou)/t' au)th\ kaq' e(auth\n ou)/te meta\ tw=n a)/llwn: h( de\ tw=n z' kai\ h' teta/rth me/n e)stin, suntiqeme/nh de\ tai=s prote/rais triakontae\c tetra/gwnon pare/sxen. h( de\ tw=n u(po\ *pla/twnos e)kkeime/nwn a)riqmw=n tetraktu\s e)nteleste/ran e)/sxhke th\n ge/nesin, tw=n me\n a)rti/wn a)rti/ois diasth/masi tw=n de\ perittw=n perittoi=s pollaplasiasqe/ntwn: perie/xei de\ th\n me\n mona/da, koinh\n ou)=san a)rxh\n a)rti/wn kai\ perittw=n, tw=n d' u(p' au)th=| ta\ me\n du/o kai\ tri/a prw/tous e)pipe/dous, ta\ de\ te/ttara kai\ e)nne/a prw/tous tetragw/nous, ta\ d' o)ktw\ kai\ ei)kosiepta\ prw/tous ku/bous e)n a)riqmoi=s, e)/cw lo/gou th=s mona/dos tiqeme/nhs h(=| kai\ dh=lo/s e)sti boulo/menos ou)k e)pi\ mia=s eu)qei/as a(/pantas a)ll' e)nalla\c kai\ i)di/a| ta/ssesqai tou\s a)rti/ous met' a)llh/lwn kai\ pa/lin tou\s perissou/s, w(s u(poge/graptai. ou(/tws ai( suzugi/ai tw=n o(moi/wn e)/sontai pro\s tou\s o(moi/ous kai\ poih/sousin a)riqmou\s e)pifanei=s kata/ te su/nqesin kai\ pollaplasiasmo\n e)c a)llh/lwn.

kata\ su/nqesin ou(/tws: ta\ du/o kai\ ta\ tri/a pe/nte gi/gnetai, ta\ te/ssara kai\ ta\ e)nne/a triakai/deka, ta\ d' o)ktw\ kai\ ei)kosiepta\ pe/nte kai\ tria/konta. tou/twn ga\r tw=n a)riqmw=n oi( *puqagorikoi\ ta\ me\n e' trofo/n, o(/per e)sti\ fqo/ggon, e)ka/loun: oi)o/menoi tw=n tou= to/nou diasthma/twn prw=ton ei)=nai fqegkto\n to\ pe/mpton: ta\ de\ triskai/deka lei=mma, kaqa/per *pla/twn, th\n ei)s i)/sa tou=, to/nou dianomh\n a)pogignw/skontes: ta\ de\ pe/nte kai\ tria/konta a(rmoni/an, o(/ti sune/sthken e)k duei=n ku/bwn prw/twn a)p' a)rti/ou kai\ perittou= gegono/twn, e)k tessa/rwn d' a)riqmw=n, tou= s' kai\ tou= h' kai\ tou= q' kai\ ib', th\n a)riqmhtikh\n kai\ th\n a(rmonikh\n a)nalogi/an periexo/ntwn. e)/stai de\ ma=llon h( du/namis e)kfanh\s e)pi\ diagra/mmatos. e)/stw to\ a b g d parallhlo/grammon o)rqogw/nion, e)/xon tw=n pleurw=n th\n a b pe/nte, th\n de\ a d e(pta/: kai\ tmhqei/shs th=s me\n e)la/ttonos ei)s du/o kai\ tri/a kata\ to\: k th=s de\ mei/zonos ei)s tri/a kai\ te/ttara kata\ to\ l, dih/xqwsan a)po\ tw=n tomw=n eu)qei=ai te/mnousai, a)llh/las, kata\ to\ k m n kai\ kata\ to\ l m c, kai\ poiou=sai to\ me\n a k m l e(\c, to\ de\ k b c m e)nne/a, to\ de\ l m n d o)ktw/, to\ de\ m c g n dw/deka to\ d), o(/lon parallhlo/grammon tria/konta kai\ pe/nte tou\s tw=n sumfwniw=n tw=n prw/twn lo/gous e)n toi=s tw=n xwri/wn a)riqmoi=s, ei)s a(\ dih/|rhtai, perie/xon. ta\ me\n ou)=n e(\c kai\ o)ktw\ to\n e)pi/triton e)/xei; lo/gon, e)n w(=| to\ dia\ tessa/rwn ta\ d' e(\c kai\ e)nne/a to\n h(mio/lion, e)n to\.. dia\ pe/nte: ta\ d' e(\c kai\ ib' to\n dipla/sion, e)n to\ dia\ pasw=n. e)/nesti de\ kai\ o( tou= to/nou lo/gos e)po/gdoos w)\n e)n toi=s e)nne/a kai\ o)ktw/: dia\ tou=to kai\ a(rmoni/an to\n perie/xonta tou\s lo/gous tou/tous a)riqmo\n e)ka/lesan.

e(ca/kis de\ geno/menos to\n tw=n de/ka poiei= kai\ diakosi/wn a)riqmo/n, e)n o(/sais h(me/rais le/getai ta\ e(pta/mhna tw=n brefw=n teleogonei=sqai.

pa/lin d' a)f' e(te/ras a)rxh=s, kata\ pollaplasiasmo\n o( me\n di\s g' to\n s' poiei=, o( de\ tetra/kis e)nne/a to\n triakontae/c, o( d' o)kta/kis kz' to\n sis' kai\ e)/stin o( me\n s' te/leios, i)/sos w)\n toi=s e(autou= me/resi kai\ ga/mos kalei=tai dia\ th\n tou= a)rti/ou kai\ perittou= su/mmicin e)/ti de\ sune/sthken e)/k te th=s a)rxh=s kai\ tou= prw/tou a)rti/ou kai\ tou= prw/tou perittou=. o( de\ ls' prw=to/s e)sti tetra/gwnos a(/ma kai\ tri/gwnos, tetra/gwnos me\n a)po\ th=s e(ca/dos tri/gwnos d' a)po\ th=s o)gdoa/dos: kai\ ge/gone pollaplasiasmw=| me\n tetragw/nwn duei=n, tou= te/ssara to\n e)nne/a pollaplasia/santos, sunqe/sei de\ triw=n ku/bwn to\ ga\r e(\n kai\ ta\ o)ktw\ kai\ ta\ ei)kosiepta\ sunteqe/nta poiei= to\n progegramme/non a)riqmo/n. e)/ti d' e(teromh/khs a)po\ duei=n pleurw=n, tw=n me\n dw/deka tri\s ginome/nwn tw=n d' e)nne/a tetra/kis. a)\n ou)=n

e)kteqw=sin ai( tw=n sxhma/twn pleurai/, tou= tetragw/nou ta\ s' kai\ tou= trigw/nou ta\ o)ktw\ kai\ parallhlogra/mmwn tou= me\n e(te/rou ta\ e)nne/a tou= d' e(te/rou ta\ ib', tou\s tw=n sumfwniw=n poih/sousi lo/gous. e)/stai ga\r ta\ dw/deka pro\s me\n ta\ e)nne/a dia\ tessa/rwn w(s nh/th pro\s parame/shn, pro\s de\ ta\ o)ktw\ dia\ pe/nte w(s nh/th pro\s me/shn, pro\s de\ ta\ s' dia\ pasw=n w(s nh/th pro\s u(pa/thn. o( de\ tw=n sis' ku/bos e)sti\n a)po\ e(ca/dos i)/sos th=| e(autou= perime/trw|.

toiau/tas de\ duna/meis tw=n e)kkeime/nwn a)riqmw=n e)xo/ntwn, i)/dion tw=| teleutai/w| sumbe/bhke, tw=| kz', to\ toi=s pro\ au)tou= suntiqe/menon i)/son ei)=nai pa=sin, e)/sti de\ kai\ periodiko\s selh/nhs. kai\ tw=n e)mmelw=n diasthma/twn oi( *puqagorikoi\ to\n to/non e)n tou/tw| tw=| a)riqmw=| ta/ttousi dio\ kai\ ta\ triskai/deka lei=mma kalou=sin a)polei/pei ga\r mona/di tou= h(mi/seos. o(/ti d' ou(=toi kai\ tou\s tw=n sumfwniw=n lo/gous perie/xousi, r(a/|dion katamaqei=n. kai\ ga\r dipla/sios lo/gos e)sti\n o( tw=n du/o pro\s to\ e(\n e)n w(=| to\ dia\ pasw=n, kai\ h(mio/lios o( pro\s ta\ du/o tw=n triw=n e)n w(=| to\ dia\ pe/nte, kai\ e)pi/tritos o( pro\s; ta\ tri/a tw=n tessa/rwn e)n w(=| to\ dia\ tessa/rwn, kai\ tripla/sios o( pro\s ta\ tri/a tw=n e)nne/a e)n w(=| to\ dia\ pasw=n kai\ dia\ pe/nte, kai\ tetrapla/sios o( pro\s ta\ du/o tw=n h' e)n w(=| to\ di\s dia\ pasw=n: e)/nesti de\ kai\ e)po/gdoos o( pro\s ta\ o)ktw\ tw=n e)nne/a e)n w(=| to\ toniai=on. a)\n toi/nun h( mona\s e)pi/koinos ou)=sa kai\ toi=s a)rti/ois sunariqmh=tai kai\ toi=s perittoi=s, o( me\n a)/pas a)riqmo\s to\ th=s deka/dos pare/xetai plh=qos: oi( ga\r a)po\ mona/dos me/xri tw=n de/ka suntiqe/menoi pentekai/deka, tri/gwnon a)po\ penta/dos: o( de\ peritto\s to\n tessara/konta kata\ su/nqesin me\n e)k tw=n dekatriw=n kai\ tw=n kz' gennw/menon, oi(=s ta\ melw|dou/mena metrou=sin eu)sh/mws oi( maqhmatikoi\ diasth/mata, to\ me\n di/esin to\ de\ to/non kalou=ntes: kata\ to\n pollaplasiasmo\n de\ th=| th=s tetraktu/os duna/mei gigno/menon tw=n ga\r prw/twn tessa/rwn kaq' au(to\n e(ka/stou tetra/kis lambanome/nou gi/gnetai te/ssara kai\ h' kai\ ib' kai\ is' : tau=ta to\n m' sunti/qhsi, perie/xonta tou\s tw=n sumfwniw=n lo/gous: ta\ me\n ga\r is' e)pi/trita tw=n dekadu/o e)sti\n tw=n d' o)ktw\ dipla/sia, tw=n de\ tessa/rwn tetrapla/sia: ta\ de\ ib' tw=n o)ktw\ h(mio/lia, tw=n de\ tessa/rwn tripla/sia ou(=toi d' oi( lo/goi to\ dia\ tessa/rwn kai\ to\ dia\ pe/nte kai\ to\ dia\ pasw=n kai\ to\ di\s dia\ pasw=n perie/xousin. i)/sos ge mh/n e)stin o( tw=n tessara/konta dusi\ tetragw/nois kai\ dusi\ ku/bois o(mou= lambanome/nois: to\ ga\r e(\n kai\ ta\ te/ssara kai\ ta\ o)ktw\ kai\ ta\ kz' ku/boi kai\ tetra/gwnoi m' gi/gnontai sunteqe/ntes. w(/ste polu\ th=s *puqagorikh=s th\n *platwnikh\n tetraktu\n poikilwte/ran ei)=nai th=| diaqe/sei kai\ teleiote/ran.

a)lla\ tai=s ei)sagome/nais meso/thsi tw=n u(pokeime/nwn a)riqmw=n xw/ras ou) dido/ntwn, e)de/hse mei/zonas o(/rous labei=n e)n toi=s au)toi=s lo/gois: kai\ lekte/on ti/nes ei)si\n ou(=toi. pro/teron de\ peri\ tw=n mesoth/twn: w(=n th\n me\n i)/sw| kat' a)riqmo\n u(pere/xousan i)/sw| d' u(perexome/nhn a)riqmhtikh\n oi( nu=n kalou=si, th\n de\ tau)tw=| me/rei tw=n a)/krwn au)tw=n u(pere/xousan kai\ u(perexome/nhn u(penanti/an. o(/roi d' ei)si\ th=s me\n a)riqmhtikh=s s' kai\ q' kai\ ib': ta\ ga\r e)nne/a tw=| i)/sw| kat' a)riqmo\n tw=n e(\c u(pere/xei kai\ tw=n ib' lei/petai: th=s d' u(penanti/as s' h' ib': ta\ ga\r o)ktw\ dusi\ me\n tw=n s' u(pere/xei te/ttarsi de\ tw=n ib' lei/petai, w(=n ta\ me\n du/o tw=n e(\c ta\ de\ te/ssara tw=n dw/deka trithmo/rio/n e)sti. sumbe/bhken ou)=n e)n me\n th=| a)riqmhtikh=| tau)tw=| me/rei tw=n a)/krwn to\ me/son u(pere/xesqai kai\ u(pere/xein, e)n de\ th=| u(penanti/a| tau)tw=| me/rei tw=n a)/krwn tou= me\n a)podei=n to\ d' u(perba/llein e)kei= me\n ga\r ta\ tri/a tou= me/sou tri/ton e)sti\ me/ros, e)ntau=qa de\ ta\ d' kai\ ta\ b' tw=n a)/krwn e(ka/teron e(kate/rou: o(/qen u(penanti/a ke/klhtai. tau/thn d' a(rmonikh\n o)noma/zousin, o(/ti toi=s o(/rois ta\ prw=ta su/mfwna pare/xetai, tw=| me\n megi/stw| pro\s to\n e)la/xiston to\

dia\ pasw=n tw=| de\ megi/stw| pro\s to\n me/son to\ dia\ pe/nte, tw=| de\ me/sw| pro\s to\n e)la/xiston to\ dia\ tessa/rwn o(/ti tou= megi/stou tw=n o(/rwn kata\ nh/thn tiqeme/nou tou= d' e)laxi/stou kaq' u(pa/thn, o( me/sos gi/gnetai o( kata\ me/shn, pro\s me\n to\n me/giston to\ dia\ pe/nte poiou=san pro\s de\ to\n e)la/xiston to\ dia\ tessa/rwn w(/ste gi/gnesqai ta\ o)ktw\ kata\ th\n me/shn ta\ de\ dw/deka kata\ nh/thn ta\ d' e(\c kaq' u(pa/thn.

to\n de\ tro/pon, w(=| lamba/nousi ta\s ei)rhme/nas meso/thtas, a(plw=s kai\ safw=s *eu)/dwros a)podei/knusi. sko/pei de\ pro/teron e)pi\ th=s a)riqmhtikh=s. a)\n ga\r e)kqei\s tou\s a)/krous la/bh|s e(kate/rou to\ h(/misu me/ros kai\ sunqh=|s, o( sunteqei\s e)/stai me/sos e)/n te toi=s diplasi/ois kai\ toi=s triplasi/ois o(moi/ws. e)pi\ de\ th=s u(penanti/as, e)n me\n toi=s diplasi/ois a)\n tou\s a)/krous e)kqei\s tou= me\n e)la/ttonos to\ tri/ton tou= de\ mei/zonos to\ h(/misu la/bh|s, o( sunteqei\s gi/gnetai me/sos: e)n de\ toi=s triplasi/ois a)na/palin, tou= me\n e)la/ttonos h(/misu dei= labei=n tou= de\ mei/zonos tri/ton: o( ga\r sunteqei\s ou(/tw gi/gnetai me/sos. e)/stw ga\r e)n triplasi/w| lo/gw| ta\ s' e)la/xistos o(/ros ta\ d' ih' me/gistos: o(e\n ou)=n tw=n s' to\ h(/misu labw\n ta\ tri/a kai\ tw=n o)ktw\ kai\ de/ka to\ tri/ton ta\ s' sunqh=|s, e(/ceis to\n e)nne/a tau)tw=| me/rei tw=n a)/krwn u(pere/xonta kai\ u(perexo/menon. ou(\tw me\n ai( meso/thtes lamba/nontai. dei= d' au)ta\s e)kei= parenta/cai kai\ a)naplhrw=sai ta\ dipla/sia kai\ tripla/sia diasth/mata. tw=n d' e)kkeime/nwn a)riqmw=n oi( me\n ou)d' o(/lws metacu\ xw/ran e)/xousin oi( d' ou)x i(kanh\n au)/contes ou)=n au)tou/s, tw=n au)tw=n lo/gwn diameno/ntwn, u(podoxa\s poiou=sin a)rkou/sas tai=s ei)rhme/nais meso/thsi. kai\ prw=ton me\n e)la/xiston a)nti\ tou= e(no\s ta\ e(\c qe/ntes, e)pei\ prw=tos h(/misu/ te kai\ tri/ton e)/xei me/ros, a(/pantas e(caplasi/ous tou\s u(potetagme/nous e)poi/hsan, w(s u(poge/graptai, dexome/nous

ta\s meso/thtas a)mfote/ras kai\ toi=s diplasi/ois kai\ toi=s triplasi/ous diasth/masin. ei)rhko/tos de\ tou= *pla/twnos h(mioli/wn de\ diasta/sewn kai\ e)pitri/twn kai\ e)pogdo/wn genome/nwn, e)k tou/twn tw=n desmw=n e)n tai=s pro/sqen diasta/sesi tw=| tou= e)pogdo/ou diasth/mati ta\ e)pi/trita pa/nta suneplhrou=to, lei/pwn au)tw=n e(ka/stou mo/rion, th=s de\ tou= mori/ou tau/ths diasta/sews leifqei/shs a)riqmou= pro\s a)riqmo\n e)xou/shs tou\s o(/rous s' kai\ n' kai\ s' pro\s g' kai\ m' kai\ s' dia\ tau/thn th\n le/cin h)nagka/zonto pa/lin tou\s a)riqmou\s e)pana/gein kai\ mei/zonas poiei=n. e)/dei me\n ga\r e)fech=s e)po/gdoa gi/gnesqai du/o: th=s d' e(ca/dos ou)/t' au)to/qen e)po/gdoon e)xou/shs, ei)/ te te/mnoito, kermatizome/nwn ei)s mo/ria tw=n mona/dwn, dusqewrh/tou th=s maqh/sews e)some/nhs, au)to\ to\ pra=gma to\n pollaplasiasmo\n u(phgo/reusen, w(/sper e)n a(rmonikh=| metabolh=| tou= diagra/mmatos o(/lou sunepiteinome/nou tw=| prw/tw| tw=n a)riqmw=n. o( me\n ou)=n *eu)/dwros e)pakolouqh/sas *kra/ntori prw=ton e)/labe to\n tpd', o(\s gi/gnetai tou= e(\c e)pi\ ta\ cd' pollaplasiasqe/ntos e)phga/geto d' au)tou\s o( tw=n cd' a)riqmo\s e)po/gdoon e)/xwn to\n ob'. toi=s d' u(po\ tou= *pla/twnos legome/nois sumfwno/tero/n e)stin u(poqe/sqai to\ h(/misu tou/tou ga\r to\ lei=mma to\ tw=n e)pogdo/wn e(/cei lo/gon e)n a)riqmoi=s, ou(\s o( *pla/twn ei)/rhken s' kai\ n' kai\ s' pro\s tri/a kai\ m' kai\ s', tw=n e(kato\n e)nenh/konta du/o prw/twn tiqeme/nwn. a)\n d' o( tou/tou dipla/sios teqh=| prw=tos, e)/stai to\ lei=mma lo/gon me\n e)/xon to\n au)to\n a)riqmo\n de\ to\n dipla/sion, o(\n e)/xei ta\ fib' pro\s ups': gi/gnetai ga\r e)pi/trita tw=n me\n e(kato\n e)nenh/konta du/o ta\ sns', tw=n de\ tpd' ta\ fib'. kai\ ou)k a)/logos h( e)pi\ tou=ton a)nagwgh\ to\n a)riqmo/n, a)lla\ kai\ toi=s peri\ to\n *kra/ntora parasxou=sa to\ eu)/logon ta\ ga\r cd' kai\ ku/bos e)sti\n a)po\ prw/tou tetragw/nou kai\ tetra/gwnos a)po\ prw/tou ku/bou: geno/menos d' e)pi\ to\n g', prw=ton o)/nta perisso\n kai\ prw=ton tri/gwnon kai\ prw=ton te/leion o)/nta kai\ h(mio/lion, e(kato\n e)nenh/konta du/o pepoi/hken, e)/xonta kai\ au)to\n e)po/gdoon, w(s dei/comen.

pro/teron de\ ti/ to\ lei=mma/ e)sti kai/ ti/s h( dia/noia tou= *pla/twnos, ma=llon kato/yesqe, tw=n ei)wqo/twn e)n tai=s *puqagorikai=s sxolai=s le/gesqai braxe/ws u(pomnhsqe/ntes. e)/sti ga\r dia/sthma e)n melw|di/a| pa=n to\ periexo/menon u(po\ duei=n fqo/ggwn a)nomoi/wn th=| ta/sei: tw=n de\ diasthma/twn e(\n o( kalou/menos to/nos, w(=| to\ dia\ pe/nte mei=zo/n e)sti tou= dia\ tessa/rwn. tou=ton oi( me\n a(rmonikoi\ di/xa temno/menon oi)/ontai du/o diasth/mata poiei=n, w(=n e(ka/teron h(mito/nion kalou=sin oi( de\ *puqagorikoi\ th\n me\n ei)s i)/sa tomh\n a)pe/gnwsan au)tou=, tw=n de\ tmhma/twn a)ni/swn o)/ntwn lei=mma to\ e)/latton o)noma/zousin, o(/ti tou= h(mi/seos a)polei/pei. : dio\ kai\ tw=n sumfwniw=n th\n dia\ tessa/rwn oi( me\n duei=n to/nwn kai\ h(mitoni/ou poiou=sin oi( de\ duei=n kai\ lei/mmatos. marturei=n de\ dokei= toi=s me\n a(rmonikoi=s h( ai)/sqhsis toi=s de\ maqhmatikoi=s h( a)po/deicis, h(=s toiou=tos o( tro/pos e)sti/n: e)lh/fqh dia\ tw=n o)rga/nwn qewrhqe/n, o(/ti to\ me\n dia\ pasw=n to\n dipla/sion lo/gon e)/xei, to\ de\ dia\ pe/nte to\n h(mio/lion, to\ de\ dia\ tessa/rwn to\n e)pi/triton, o( de\ to/nos to\n e)po/gdoon. e)/cesti de\ kai\ nu=n basani/sai ta)lhqe/s, h)\ ba/rh duei=n a)/nisa xordw=n e)carth/santas h)\ duei=n i)sokoi/lwn au)lw=n to\n e(/teron mh/kei dipla/sion tou= e(te/rou poih/santas: tw=n me\n ga\r au)lw=n o( mei/zwn baru/teron fqe/gcetai w(s u(pa/th pro\s nh/thn, tw=n de\ xordw=n h( tw=| diplasi/w| katateinome/nh ba/rei th=s e(te/ras o)cu/teron w(s nh/th pro\s u(pa/thn tou=to d' e)sti\ dia\ pasw=n. o(moi/ws de\ kai\ tri/a pro\s du/o lhfqe/nta mh/kh kai\ ba/rh to\ dia\ pe/nte poih/sei kai\ te/ssara pro\s tri/a to\ dia\ tessa/rwn, w(=n tou=to me\n e)pi/triton e)/xei lo/gon e)kei=no d' h(mio/lion. e)a\n d' w(s e)nne/a pro\s o)ktw\ ge/nhtai tw=n barw=n h)\ tw=n mhkw=n h( a)niso/ths, poih/sei dia/sthma toniai=on ou) su/mfwnon a)ll' e)mmele\s w(s ei)pei=n e)/mbraxu, tw=| tou\s fqo/ggous, a)\n a)na\ me/ros krousqw=si, pare/xein h(du\ fwnou=ntas kai\ proshne/s a)\n d' o(mou=, traxu\ kai\ luphro/n: e)n de\ tai=s sumfwni/ais ka)\n o(mou= krou/wntai ka)\n e)nalla/c, h(de/ws prosi/etai th\n sunh/xhsin h( ai)/sqhsis. ou) mh\n a)lla\ kai\ dia\ lo/gou tou=to deiknu/ousin. e)n me\n ga\r a(rmoni/a| to\ dia\ pasw=n e)/k te tou= dia\ pe/nte su/gkeitai kai\ tou= dia\ tessa/rwn, e)n d' a)riqmoi=s to\ dipla/sion e)/k te tou= h(mioli/ou kai\ tou= e)pitri/tou: ta\ ga\r dw/deka tw=n me\n e)nne/a e)sti\n e)pi/trita tw=n d' o)ktw\ h(mio/lia tw=n de\ s' dipla/sia. su/nqetos ou)=n o( tou= diplasi/ou lo/gos e)sti\n e)k tou= h(mioli/ou kai\ tou= e)pitri/tou, kaqa/per o( tou= dia\ pasw=n e)k tou= dia\ pe/nte kai\ tou= dia\ tessa/rwn a)lla\ ka)kei= to\ dia\ pe/nte tou= dia\ tessa/rwn to/nw| ka)ntau=qa to\ h(mio/lion tou= e)pitri/tou tw=| e)pogdo/w| mei=zo/n e)sti. fai/netai toi/nun, o(/ti to\ dia\ pasw=n to\n dipla/sion lo/gon e)/xei kai\ to\ dia\ pe/nte to\n h(mio/lion kai\ to\ dia\ tessa/rwn to\n e)pi/triton kai\ o( to/nos to\n e)po/gdoon.

*)apodedeigme/nou de\ tou/tou, skopw=men ei) di/xa te/mnesqai pe/fuke to\ e)po/gdoon: ei) ga\r mh\ pe/fuken, ou)d' o( to/nos. e)pei\ de\ prw=toi to\n e)po/gdoon lo/gon o( q' kai\ o( h' poiou=ntes ou)de\n dia/sthma me/son e)/xousi, diplasiasqe/ntwn d' a)mfote/rwn o( parempi/ptwn metacu\ du/o poiei= diasth/mata dh=lon o(/ti tou/twn me\n i)/swn o)/ntwn di/xa te/mnetai to\ e)po/gdoon. a)lla\ mh\n dipla/sia gi/gnetai tw=n me\n q' ta\ ih' tw=n d' h' ta\ is', de/xontai d' ou(=toi metacu\ ta\ iz' kai\ gi/gnetai tw=n diasthma/twn to\ me\n mei=zon to\ d' e)/latton: e)/sti ga\r to\ me\n pro/teron e)feptakaide/katon to\ de\ deu/teron e)feckaide/katon. ei)s a)/nisa toi/nun te/mnetai to\ e)po/gdoon ei) de\ tou=to, kai\ o( to/nos. ou)de/teron a)/ra gi/gnetai diaireqe/ntos au)tou= tw=n tmhma/twn h(mito/nion, a)ll' o)rqw=s u(po\ tw=n maqhmatikw=n lei=mma proshgo/reutai. kai\ tou=t' e)sti\n o(/ fhsin o( *pla/twn ta\ e)pi/trita toi=s e)pogdo/ois sumplhrou=nta to\n qeo\n lei/pein e(ka/stou mo/rion au)tw=n, ou(= lo/gos e)sti/n, o(\n e)/xei ta\ s' kai\ n' kai\ s' pro\s ta\ g' kai\ m' kai\ s'. ei)lh/fqw ga\r to\ dia\ tessa/rwn e)n a)riqmoi=s dusi\ to\n e)pi/triton lo/gon perie/xousi, toi=s sns' kai\ toi=s e(kato\n e)nenh/konta du/o: w(=n o( me\n e)la/ttwn, ta\ e(kato\n e)nenh/konta du/o, kei/sqw kata\ to\n baru/taton tou= tetraxo/rdou fqo/ggon o( de\ mei/zwn, ta\ sns', kata\ to\n o)cu/taton: a)podeikte/on o(/ti, tou/tou sumplhroume/nou dusi\n e)pogdo/ois, lei/petai dia/sthma thlikou=ton, h(li/kon w(s e)n a)riqmoi=s ta\ s' kai\ n' kai\ s' e)/xei pro\s ta\ g' kai\ m' kai\ s'. tou= ga\r barute/rou to/nw| e)pitaqe/ntos, o(/per e)sti\n e)po/gdoon, gi/gnetai sis': tou/tou pa/lin to/nw| a)/llw| e)pitaqe/ntos, gi/gnetai smg': tau=ta me\n ga\r u(pere/xei tw=n sis' toi=s kz', ta\ de\ sis' tw=n e(kato\n e)nenh/konta du/o toi=s ei)/kosi kai\ te/ssarsin w(=n ta\ me\n kz' tw=n sis' o)/gdoa/ e)sti, ta\ de\ kz' tw=n e(kato\n e)nenh/konta du/o. dio\ gi/gnetai tw=n triw=n tou/twn a)riqmw=n o(/ te me/gistos e)po/gdoos tou= me/sou kai\ o( me/sos tou= e)laxi/stou: to\ d' a)po\ tou= e)laxi/stou dia/sthma me/xri tou= megi/stou, toute/sti to\ a)po\ tw=n e(kato\n e)nenh/konta du/o me/xri tw=n smg', di/tonon e)k duei=n sumplhrou/menon e)pogdo/wn a)fairoume/nou de\ tou/tou, peri/esti tou= o(/lou dia/sthma loipo\n to\ metacu\ tw=n smg' kai\ tw=n sns', ta\ triskai/deka dio\ kai\ lei=mma tou=ton to\n a)riqmo\n w)no/mazon. e)gw\ me\n ou)=n eu)shmo/tata dhlou=sqai th\n *pla/twnos oi)=mai gnw/mhn e)n tou/tois toi=s a)riqmoi=s.

e(/teroi de\ tou= dia\ tessa/rwn o(/rous qe/menoi, to\n me\n o)cu\n e)n toi=s sph' to\n de\ baru\n e)n toi=s sis', a)nalo/gws h)/dh toi=s e(ch=s perai/nousin: plh\n o(/ti to\ lei=mma tw=n duei=n to/nwn metacu\ lamba/nousi tou= ga\r barute/rou to/nw| e)pitaqe/ntos, gi/gnetai smg': tou= d' o)cute/rou to/nw| a)neqe/ntos, gi/gnetai sns': e)/sti ga\r e)po/gdoa ta\ me\n smg' tw=n sis' ta\ de\ sph' tw=n sns': w(/ste toniai=on ei)=nai tw=n diasthma/twn e(ka/teron, lei/pesqai de\ to\ metacu\ tw=n smg' kai\ tw=n sns', o(/per ou)k e)/stin h(mito/nion a)ll' e)/latton ta\ me\n ga\r sph' tw=n sns' u(pere/xei toi=s kz' kai\ dusi/, ta\ de\ smg' tw=n sis' u(pere/xei toi=s kz', ta\ de\ sns' tw=n smg' u(pere/xei toi=s ig': tau=ta de\ tw=n u(peroxw=n a)mfote/rwn e)la/ttw h)\ h(mi/sea/ e)sti. dio\ duei=n to/nwn kai\ lei/mmatos, ou) duei=n kai\ h(mi/seos, eu(/rhtai to\ dia\ tessa/rwn. kai\ tau=ta me\n e)/xei toiau/thn a)po/deicin. e)kei=no d' ou) pa/nu xalepo\n e)k tw=n proeirhme/nwn sunidei=n, ti/ dh/pote fh/sas o( *pla/twn h(mioli/ous kai\ e)pitri/tous kai\ e)pogdo/ois gi/gnesqai diasta/seis e)n tw=| sumplhrou=sqai ta\s e)pitri/tous tai=s e)pogdo/ois, ou)k e)mnh/sqh tw=n h(mioli/wn a)lla\ pare/lipe. to\ ga\r h(mio/lion, tou= e)pitri/tou tw=| e)pogdo/w| tw=| e)pitri/tw| prostiqeme/nou, sumplhrou=sqai kai\ to\ h(mio/lion.

*(upodedeigme/nwn de\ tou/twn, to\ me\n sumplhrou=n ta\ diasth/mata kai\ parenta/ttein ta\s meso/thtas, ei) kai\ mhdei\s e)tu/gxane pe\poihkw\s pro/teron, u(mi=n a)\n au)toi=s e(/neka gumnasi/as parh=ka nu=n de\ polloi=s ka)gaqoi=s a)ndra/sin e)ceirgasme/nou tou/tou, ma/lista de\ *kra/ntori kai\ *klea/rxw| kai\ *qeodw/rw| toi=s *soleu=si, mikra\ peri\ th=s tou/twn diafora=s ei)pei=n ou)k a)/xrhsto/n e)stin. o( ga\r *qeo/dwros ou)x w(s e)kei=noi du/o sti/xous poiw=n, a)ll' e)pi\ mia=s eu)qei/as e)fech=s tou/s te diplasi/ous e)kta/ttwn kai\ tou\s triplasi/ous, prw=ton me\n i)sxuri/zetai th=| legome/nh| kata\ mh=kos sxi/sei th=s ou)si/as, du/o poiou/sh| moi/ras w(s e)k mia=s ou) te/ssaras e)k duei=n e)/peita/ fhsi ta\s tw=n mesoth/twn parenta/ceis ou(/tw lamba/nein prosh/kein xw/ran: ei) de\ mh/, taraxh\n kai\ su/gxusin e)/sesqai kai\ metasta/seis ei)s to\ prw=ton eu)qu\s tripla/sion e)k tou= prw/tou diplasi/ou tw=n sumplhrou=n e(ka/teron o)feilo/ntwn. toi=s de\ peri\ to\n *kra/ntora bohqou=sin ai(/ te qe/seis tw=n a)riqmw=n, e)pipe/dwn e)pipe/dois kai\ tetragw/nwn tetragw/nois kai\ ku/bwn ku/bois a)ntiqe/tws suzugou/ntwn, th=| te mh\ kata\ ta/cin au)tw=n lh/yei, a)ll' e)nalla\c a)rti/wn kai\ 30b perittw=n. th\n ga\r mona/da koinh\n ou)=san a)mfoi=n prota/cas lamba/nei ta\ o)ktw\ kai\ e)fech=s ta\ kz' mononouxi\ deiknu/wn h(mi=n, h(\n e(kate/rw| ge/nei xw/ran a)podi/dwsi. tau=ta me\n ou)=n e(te/rois prosh/kei ma=llon e)cakribou=n, to\ d' a)poleipo/menon oi)kei=o/n e)sti th=s u(pokeime/nhs h(mi=n pragmatei/as.

ou) ga\r e)pi/deicin o( *pla/twn qewri/as maqhmatikh=s poiou/menos ei)s fusikh\n u(po/qesin mh\ deome/nhn meso/thtas a)riqmhtika\s kai\ a(rmonika\s pareish/gagen, a)lla\ w(s ma/lista dh\ th=| susta/sei th=s yuxh=s tou= lo/gou tou/tou prosh/kontos. kai/toi tine\s me\n e)n toi=s ta/xesi tw=n planwme/nwn sfairw=n tine\s de\ ma=llon e)n toi=s a)posth/masin e)/nioi d' e)n toi=s mege/qesi tw=n a)ste/rwn, oi( d' a)/gan a)kribou=n dokou=ntes e)n tai=s tw=n e)piku/klwn diame/trois zhtou=si ta\s ei)rhme/nas a)nalogi/as, w(s th\n yuxh\n e(/neka tou/twn tou= dhmiourgou= toi=s ou)rani/ois e)narmo/santos, ei)s e(pta\ moi/ras nenemhme/nhn. polloi\ de\ kai\ ta\ *puqagorika\ deu=ro metafe/rousin, a)po\ tou= me/sou ta\s tw=n swma/twn a)posta/seis triplasia/zontes: gi/gnetai de\ tou=to kata\ me\n to\ pu=r mona/dos tiqeme/nhs, kata\ d' a)nti/xqona triw=n, kata\ de\ gh=n e)nne/a kai\ kata\ selh/nhn ei)kosiepta/, kai\ kata\ to\n *(ermou= mia=s kai\ o)gdoh/konta, kata\ de\ *fwsfo/ron triw=n kai\ m' kai\ s', kat' au)to\n de\ to\n h(/lion q' kai\ k' kai\ y', o(/stis a(/ma tetra/gwno/s te kai\ ku/bos e)sti/ dio\ kai\ to\n h(/lion e)/stin o(/te tetra/gwnon kai\ ku/bon prosagoreu/ousin. ou(/tw kai\ tou\s a)/llous e)pana/gousi toi=s triplasiasmoi=s, polu\ tou= kata\ lo/gon ou(=toi/ ge parapai/ontes, ei)/ ti tw=n gewmetrikw=n o)/felo/s e)stin a)podei/cewn, kai\ makrw=| piqanwte/rous parabalei=n au)toi=s a)podeiknu/ontes tou\s o(rmwme/nous e)kei=qen, ou)d' au)tou\s panta/pasin e)cakribou=ntas a)ll' w(s e)/ggista le/gontas, o(/ti th=s me\n h(li/ou diame/trou pro\s th\n dia/metron th=s gh=s lo/gos e)sti\ dwdekapla/sios, th=s de\ gh=s au)= pa/lin diame/trou pro\s th\n selh/nhs dia/metron tripla/sios, o( de\ faino/menos e)la/xistos tw=n a)planw=n a)ste/rwn ou)k e)la/ttona th=s diame/trou th=s gh=s h)\ trithmo/rion e)/xei th\n dia/metron th=| d' o(/lh| sfai/ra| th=s gh=s pro\s th\n o(/lhn sfai=ran th=s selh/nhs w(s e(pta\ kai\ ei)/kosi pro\s e(/n e)sti *fwsfo/rou de\ kai\ gh=s ai( me\n dia/metroi, to\n dipla/sion ai( de\ sfai=rai to\n o)ktapla/sion e)/xousi lo/gon, to\ de\ dia/sthma th=s e)kleiptikh=s skia=s th=s diame/trou th=s selh/nhs tripla/sion o(\ d' e)ktre/petai pla/tos h( selh/nh th=s diame/trou tw=n zw|di/wn e)f' e(ka/tera dwdeka/moiron. ai( de\ pro\s h(/lion sxe/seis au)th=s e)n trigw/nois kai\ tetragw/nois a)posth/masi dixoto/mous kai\ a)mfiku/rtous sxhmatismou\s lamba/nousin e(\c de\ zw/|dia dielqou=sa th\n panse/lhnon w(/sper tina\ sumfwni/an e)n e(cato/nw| dia\ pasw=n a)podi/dwsi. tou= d' h(li/ou peri\ ta\s tropa\s e)la/xista kai\ me/gista peri\ th\n i)shmeri/an e)/xontos kinh/mata, di' w(=n a)fairei= th=s h(me/ras kai\ th=| nukti\ prosti/qhsin h)\ tou)nanti/on, ou(=tos o( lo/gos e)sti/n: e)n ga\r tai=s prw/tais h(me/rais l' meta\ ta\s xeimerina\s tropa\s th=| h(me/ra| prosti/qhsi to\ e(/kton th=s u(peroxh=s, h(\n h( megi/sth nu\c pro\s th\n braxuta/thn h(me/ran e)mpoiei=, tai=s d' e)fech=s tria/konta to\ tri/ton, to\ d' h(\misu tai=s loipai=s a)/xri th=s i)shmeri/as, e)n e(caplasi/ois kai\ triplasi/ois diasth/masi tou= xro/nou th\n a)nwmali/an e)panisou=ntos. *xaldai=oi de\ le/gousi to\ e)/ar e)n tw=| dia\ tetta/rwn gi/gnesqai pro\s to\ meto/pwron, e)n de\ tw=| dia\ pe/nte pro\s to\n xeimw=na, pro\s de\ to\ qe/ros e)n tw=| dia\ pasw=n. ei) d' o)rqw=s o( *eu)ripi/dhs diori/zetai qe/rous te/ssaras mh=nas kai\ xeimw=nos i)/sous fi/lhs t' o)pw/ras diptu/xous h)=ro/s t' i)/sous e)n tw=| dia\ pasw=n ai( w(=rai metaba/llousin. e)/nioi de\ gh=| me\n th\n tou= proslambanome/nou xw/ran a)podido/ntes selh/nh| de\ th\n u(pa/thn *sti/lbwna de\ kai\ *fwsfo/ron e)n diato/nois kai\ parupa/tais kai\ lixanoi=s kinou=ntes, au)to\n to\n h(/lion w(s me/shn sune/xein to\ dia\ pasw=n a)ciou=sin, a)pe/xonta th=s me\n gh=s to\ dia\ pe/nte th=s de\ tw=n a)planw=n to\ dia\ tessa/rwn.

a)ll' ou)/te tou/twn to\ komyo\n a(/ptetai/ tinos a)lhqei/as ou)/t' e)kei=noi panta/pasi tou= a)kribou=s e)/xontai. oi(=s d' ou)=n ou) dokei= tau=ta th=s tou= *pla/twnos a)phrth=sqai dianoi/as, e)kei=na komidh=| fanei=tai tw=n mousikw=n lo/gwn e)/xesqai, to\ e' tetraxo/rdwn o)/ntwn tw=n u(pa/twn kai\ me/swn kai\ sunhmme/nwn kai\ diezeugme/nwn kai\ u(perbolai/wn e)n pe/nte diasth/masi teta/xqai tou\s pla/nhtas: w(=n to\ me/n e)sti to\ a)po\ selh/nhs e)f' h(/lion kai\ tou\s o(modro/mous h(li/w|, *sti/lbwna kai\ *fwsfo/ron: e(/teron to\ a)po\ tou/twn e)pi\ to\n *)/areos *puro/enta: tri/ton de\ to\ metacu\ tou/tou kai\ *fae/qontos: ei)=q' e(ch=s to\ e)pi\ *fai/nwna kai\ pe/mpton h)/dh to\ a)po\ tou/tou pro\s th\n a)planh= sfai=ran: w(/ste tou\s o(ri/zontas fqo/ggous ta\ tetra/xorda to\n tw=n planwme/nwn lo/gon e)/xein a)ste/rwn. e)/ti toi/nun tou\s palaiou\s i)/smen u(pa/tas me\n du/o trei=s de\ nh/tas mi/an de\ me/shn kai\ mi/an parame/shn tiqeme/nous, w(/ste toi=s pla/nhsin i)sari/qmous. ei)=nai tou\s e(stw=tas. oi( de\ new/teroi to\n proslambano/menon, to/nw| diafe/ronta th=s u(pa/ths, e)pi\ to\ baru\ ta/cantes to\ me\n o(/lon su/sthma di\s dia\ pasw=n e)poi/hsan, tw=n de\ sumfwniw=n th\n kata\ fu/sin ou)k e)th/rhsan ta/cin: to\ ga\r dia\ pe/nte pro/teron gi/gnetai tou= dia\ tessa/rwn, e)pi\ to\ baru\ th=| u(pa/th| tou= to/nou proslhfqe/ntos. o( de\ *pla/twn dh=lo/s e)stin e)pi\ to\ o)cu\ proslamba/nwn: le/gei ga\r e)n th=| *politei/a| tw=n o)ktw\ sfairw=n e(ka/sthn perife/rein ei)=t' e)p' au)th=| *seirh=na bebhkui=an a)/|dein de\ pa/sas e(/na to/non i(ei/sas, e)k de\ pasw=n kera/nnusqai mi/an a(rmoni/an au(=tai d' a)nie/menai ta\ qei=a ei)/rousi kai\ kata/|dousi th=s i(era=s perio/dou kai\ xorei/as o)kta/xordon e)mme/leian o)ktw\ ga\r h)=san kai\ oi( prw=toi tw=n diplasi/wn kai\ triplasi/wn o(/roi lo/gwn, e(kate/ra| prosariqmoume/nhs meri/di th=s mona/dos. oi( de\ presbu/teroi *mou/sas pare/dwkan kai\ h(mi=n e)nne/a, ta\s me\n o)ktw\ kaqa/per o( *pla/twn peri\ ta\ ou)ra/nia, th\n d' e)na/thn ta\ peri/geia khlei=n a)nakaloume/nhn kai\ kaqista=san e)k pla/nhs kai\ diafora=s a)nwmali/an kai\ taraxh\n e)xou/shs.

skopei=te de\ mh\ to\n me\n ou)rano\n a)/gei kai\ ta\ ou)ra/nia tai=s peri\ au)th\n e)mmelei/ais kai\ kinh/sesin h( yuxh\ fronimwta/th kai\ dikaiota/th gegonui=a: ge/gone de\ toiau/th toi=s kaq' a(rmoni/an lo/gois, w(=n ei)ko/nes me\n u(pa/rxousin ei)s ta\ a)sw/mata e)n toi=s o(ratoi=s kai\ o(rwme/nois me/resi tou= ko/smou kai\ sw/masin h( de\ prw/th kai\ kuriwta/th du/namis o(ratw=s e)gke/kratai th=| yuxh=| kai\ pare/xei su/mfwnon e(auth\n kai\ peiqh/nion, a)ei\ tw=| krati/stw| kai\ qeiota/tw| me/rei tw=n a)/llwn a(pa/ntwn o(monoou/ntwn. paralabw\n ga\r o( dhmiourgo\s a)taci/an kai\ plhmme/leian e)n tai=s kinh/sesi th=s a)narmo/stou kai\ a)noh/tou yuxh=s diaferome/nhs pro\s e(auth\n ta\ me\n diw/rise kai\ die/sthse ta\ de\ sunh/gage pro\s a)/llhla kai\ sune/tacen, a(rmoni/ais kai\ a)riqmoi=s xrhsa/menos: oi(=s kai\ ta\ kwfo/tata sw/mata, li/qoi kai\ cu/la kai\ floioi\ futw=n kai\ qhri/wn o)sta= kai\ puti/ai, sugkerannu/mena kai\ sunarmotto/mena qaumasta\s me\n a)galma/twn o)/yeis, qaumasta\s de\ pare/xei farma/kwn kai\ o)rga/nwn duna/meis h(=| kai\ *zh/nwn o( *kitieu\s e)pi\ qe/an au)lhtw=n pareka/lei ta\ meira/kia katamanqa/nein, oi(/an ke/rata kai\ cu/la kai\ ka/lamoi kai\ o)sta=, lo/gou mete/xonta kai\ sumfwni/as, fwnh\n a)fi/hsi. to\ me\n ga\r a)riqmw=| pa/nta e)peoike/nai kata\ th\n *puqagorikh\n a)po/fansin lo/gou dei=tai: to\ de\ pa=sin, oi(=s e)k diafora=s kai\ a)nomoio/thtos e)gge/gone koinwni/a tis pro\s a)/llhla kai\ sumfwni/a, tau/ths ai)ti/an ei)=nai metrio/thta kai\ ta/cin, a)riqmou= kai\ a(rmoni/as metasxou=sin, ou)de\ tou\s poihta\s le/lhqen a)/rqmia me\n ta\ fi/la kai\ proshnh= kalou=ntas a)narsi/ous de\ tou\s e)xqrou\s kai\ tou\s polemi/ous, w(s a)narmosti/an th\n diafora\n ou)=san. o( de\ tw=| *pinda/rw| poih/sas to\ e)pikh/deion a)/rmenos h)=n cei/noisin a)nh\r o(/de kai\ fi/los a)stoi=s eu)armosti/an dh=lo/s e)sti th\n a)reth\n h(gou/menos: w(/s pou kai\ au)to\s o( *pi/ndaros tou= qeou= fhsin e)pa kou=sai mousika\n o)rqa\n e)pideiknume/nou to\n *ka/dmon oi(/ te pa/lai qeolo/goi, presbu/tatoi filoso/fwn o)/ntes, o)/rgana mousika\ qew=n e)nexei/rizon a)ga/lmasin: ou)x w(s lu/ran pou kai\ au)lou=sin, a)ll' ou)de\n e)/rgon oi)o/menoi qew=n oi(=on a(rmoni/an ei)=nai kai\ sumfwni/an. w(/sper ou)=n o( tou\s e)pitri/tous kai\ h(mioli/ous kai\ diplasi/ous lo/gous zhtw=n e)n tw=| zugw=| th=s lu/ras kai\ th=| xelw/nh| kai\ toi=s kolla/bois geloi=o/s e)sti dei= me\n ga\r a)me/lei kai\ tau=ta summe/trws gegone/nai pro\s a)/llhla mh/kesi kai\ pa/xesi, th\n d' a(rmoni/an e)kei/nhn e)pi\ tw=n fqo/ggwn qewrei=n ou(/tws ei)ko\s me/n e)sti kai\ ta\ sw/mata tw=n a)ste/rwn kai\ ta\ diasth/mata tw=n ku/klwn kai\ ta\ ta/xh tw=n periforw=n, w(/sper o)/rgana e)n tetagme/nois lo/gois e)/xein e)mme/trws pro\s a)/llhla kai\ pro\s to\ o(/lon, ei) kai\ to\ poso\n h(ma=s tou= metri/ou diape/feuge: tw=n me/ntoi lo/gwn e)kei/nwn, oi(=s o( dhmiourgo\s e)xrh/sato, kai\ tw=n a)riqmw=n e)/rgon h(gei=sqai th\n au)th=s th=s yuxh=s e)mme/leian kai\ a(rmoni/an pro\s au(th/n, u(f' h(=s kai\ to\n ou)rano\n e)ggenome/nh muri/wn a)gaqw=n e)mpe/plhke, kai\ ta\ peri\ gh=n w(/rais kai\ metabolai=s me/tron e)xou/sais a)/rista kai\ ka/llista pro/s te ge/nesin kai\ swthri/an tw=n gignome/nwn diakeko/smhken.