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Colored diff for /texts/archimedes/xml/Attic/monan_mecha_01_la_1599.xml between version 1.48 and 1.49

version 1.48, 2003/07/31 15:57:04

version 1.49, 2003/08/03 13:34:32

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<s id="id.000239"><foreign lang="el">*a*r*i*s*t*o*t*e*l*o*u*s<lb/>*m*h*x*a*n*i*k*a</foreign>. <lb/>ARISTOTELIS <lb/>MECHANICA. </s>

<s id="id.000241"><foreign lang="el">Ti e)sti mhxanh\, kai=\ peri\ ku/klou, tw=n e)n toi=s mhxanikoi=s <lb/>qaumasi/wn ai)ti/an e)/xontos. <arrow.to.target n="marg1"/></foreign></s>

<s id="id.000241"><foreign lang="el">Ti/ e)sti mhxanh\, kai=\ peri\ ku/klou, tw=n e)n toi=s mhxanikoi=s <lb/>qaumasi/wn ai)ti/an e)/xontos. <arrow.to.target n="marg1"/></foreign></s>

<s id="id.000242"><margin.target id="marg1"/>Pro <foreign lang="el">mhxanh\,</foreign><lb/>lege <foreign lang="el">mhxani<lb/>kh/. </foreign></s>

<s id="id.000243"><emph type="italics"/>Quid e&longs;t Mechanice, & de circulo in quo admirabilium, <lb/>quæ &longs;unt in Mechanicis, cau&longs;a continetur. <emph.end type="italics"/></s>

<s id="id.000244"><foreign lang="el">*qauma/zetai tw=n me\n kata\ fu/sin sumbaino/ntwn, o(/swn <lb/>a)gnoei=tai to\ ai)/tion, tw=n de\ para\ fu/sin, o(/sa gi/netai dia\ <lb/>te/xnhn pro\s to\ sumfe/ron toi=s a)nqrw/pois.</foreign></s>

<s id="id.000244"><foreign lang="el">*q*a*u*m*a*z*e*t*a*i tw=n me\n kata\ fu/sin sumbaino/ntwn, o(/swn <lb/>a)gnoei=tai to\ ai)/tion, tw=n de\ para\ fu/sin, o(/sa gi/netai dia\ <lb/>te/xnhn pro\s to\ sumfe/ron toi=s a)nqrw/pois.</foreign></s>

<s id="id.000245">MIRA &longs;unt in his, quæ <lb/><expan abbr="&longs;ecund&utilde;">&longs;ecundum</expan> <expan abbr="naturã">naturam</expan> <expan abbr="eue-ni&utilde;t">eue<lb/>niunt</expan>, ea: <expan abbr="quor&utilde;">quorum</expan> cau&longs;a igno<lb/>ratur, & in his quæ præter <lb/>naturam, ea, <expan abbr="qu&ecedil;cunq;">qu&ecedil;cunque</expan> arte <lb/>facta hominibus <expan abbr="cõferunt">conferunt</expan>. </s>

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<s id="id.000312"><foreign lang="el">e)n polloi=s ga\r <lb/>h( fu/sis u(penanti/on pro\s to\ xrh/simon h(mi=n poiei=. </foreign></s>

<s id="g0110103"><foreign lang="el">h( me\n <lb/>ga\r fu/sis a)ei\ to\n au)to\n e)/xei tro/pon kai\ a(plw=s, to\ de\ <lb/>xrh/simon metaba/llei pollaxw=s.</foreign></s>

<s id="g0110201"><foreign lang="el">o(/tan ou)=n de/h| ti para\ <lb/>fu/sin pra=cai, dia\ to\ xalepo\n a)pori/an pare/xei kai\ dei=tai <lb/>te/xnhs.</foreign></s>

<s id="id.000313">In multis enim natura ab <lb/>vtilitate no&longs;tra di&longs;cedit. </s>

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<s id="id.000339">Re<lb/>nititur autem Natura &longs;ub&longs;tantia, numero, magnitudine, pondere, <lb/>figura, quæ omnia ars <expan abbr="immutãdo">immutando</expan>, addendo, detrahendo, <expan abbr="trã&longs;ponendo">tran&longs;ponendo</expan>, <lb/>poliendo, figurando corrigit, & ad v&longs;us humanos accommodat. <emph.end type="italics"/></s></subchap1><subchap1>

<s id="id.000340"><foreign lang="el">dio\ kai\ kalou=men th=s te/xnhs to\ pro\s ta\s toiau/tas <lb/>a)pori/as bohqou=n me/ros mhxanh/n.<arrow.to.target n="marg8"/></foreign></s>

<s id="id.000340"><foreign lang="el">dio\ kai\ kalou=men th=s te/xnhs, to\ pro\s ta\s toiau/tas <lb/>a)pori/as bohqou=n me/ros, mhxanh/n, <arrow.to.target n="marg8"/>kaqa/per ga\r e)poi/hsen <lb/>*)antifw=n o( poihth/s, ou(/tw kai\ e)/xei: te/xnh| ga\r kratou=men, <lb/>w(=n fu/sei nikw/meqa.</foreign></s>

<s id="g0110202"><foreign lang="el">kaqa/per ga\r e)poi/hsen <lb/>*)antifw=n o( poihth/s, ou(/tw kai\ e)/xei: te/xnh| ga\r kratou=men, <lb/>w(=n fu/sei nikw/meqa.</foreign></s>

<s id="g0110203"><foreign lang="el">toiau=ta de/ e)stin e)n oi(=s ta/ te e)la/ttona <lb/>kratei= tw=n meizo/nwn, kai\ ta\ r(oph\n e)/xonta mikra\n kinei= <lb/>ba/rh mega/la, kai\ pa/nta sxedo\n o(/sa tw=n problhma/twn <lb/>mhxanika\ prosagoreu/omen.</foreign></s><lb/>

<s id="id.000341"><margin.target id="marg8"/><foreign lang="el">mhxanikh\n. </foreign></s>

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<s id="id.000397"><emph type="italics"/>quales multæ apud Vegetium & Heronem mechanicum.) bom<lb/>bardas ingentes ad locum destinatum conuertimus. <emph.end type="italics"/></s></subchap1><subchap1>

<s id="id.000398"><foreign lang="el">e)/sti de\ tau=ta toi=s fusikoi=s <lb/>problh/masin ou)/te tau)ta\ pa/mpan ou)/te kexwrisme/na li/an, <lb/>a)lla\ koina\ tw=n te maqhmatikw=n qewrhma/twn kai\ tw=n <lb/>fusikw=n: to\ me\n ga\r w(\s dia\ tw=n maqhmatikw=n dh=lon, to\ <lb/>de\ peri\ o(\ dia\ tw=n fusikw=n.</foreign></s>

<s id="id.000398"><foreign lang="el">e)/sti de\ tau=ta toi=s fusikoi=s <lb/>problh/masin, ou)/te tau)ta\ pa/mpan, ou)/te kexwrisme/na li/an, <lb/>a)lla\ koina\ tw=n te maqhmatikw=n qewrhma/twn, kai\ tw=n <lb/>fusikw=n: to\ me\n ga\r w(\s dia\ tw=n maqhmatikw=n dh=lon, to\ <lb/>de\ peri\ o(\, dia\ tw=n fusikw=n.</foreign></s>

<s id="id.000399">Sunt vero hæc proble<lb/>matis Phy&longs;icis, nec omni<lb/>no <expan abbr="ead&etilde;">eadem</expan>, nec valdè di&longs;&longs;imi<lb/>lia: &longs;ed con&longs;entanea theo<lb/>tematis, tum mathemati<lb/>cis, tum Phy&longs;icis. </s>

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<s id="id.000412">Hæc enim &longs;i abunde &longs;uppetant, nec ma<lb/>teria omnino repugnet, nihil non fieri poterit. <emph.end type="italics"/></s></subchap1><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.053.jpg" pagenum="14"/><subchap1>

<s id="id.000413"><foreign lang="el">perie/xetai de\ tw=n a)poroume/nwn<lb/> e)n tw=| ge/nei tou/tw| ta\ peri\ to\n moxlo/n.</foreign></s>

<s id="g0120102"><foreign lang="el">a)/topon ga\r <lb/>ei)=nai dokei= to\ kinei=sqai me/ga ba/ros u(po\ mikra=s i)sxu/os, <lb/>kai\ tau=ta meta\ ba/rous plei/onos: o(\ ga\r a)/neu moxlou= kinei=n <lb/>ou) du/natai/ tis, tou=to tau)to\ ba/ros, proslabw\n e)/ti to\ <lb/>tou= moxlou= ba/ros, kinei= qa=tton.</foreign></s>

<s id="g0120102"><foreign lang="el">a)/topon ga\r <lb/>ei)=nai dokei= to\ kinei=sqai me/ga ba/ros u(po\ mikra=s i)sxu/os, <lb/>kai\ tau=ta meta\ ba/rous plei/onos: o(\ ga\r a)/neu moxlou= kinei=n <lb/>ou) du/natai/ tis, tou=to au)to\ to\ ba/ros proslabw\n e)/ti to\ <lb/>tou= moxlou= ba/ros, kinei= qa=tton.</foreign></s>

<s id="id.000414">Dubitantur <expan abbr="aut&etilde;">autem</expan> in hoc <lb/>genere ea, quæ de vecte di<lb/>cuntur. </s>

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<s id="id.000435"><emph type="italics"/>Ergo à circulo prodire id quod e&longs;t admirabile in vecte, mechani<lb/>ci&longs;que problematis non e&longs;t alienum. <emph.end type="italics"/></s></subchap1><subchap1>

<s id="id.000436"><foreign lang="el">qaumasiw/taton de\ to\ ta)nanti/a <lb/>gi/nesqai met' a)llh/lwn.</foreign></s>

<s id="id.000436"><foreign lang="el">qaumasiw/taton de\ to\ tou)nanti/a <lb/>gi/nesqai met' a)llh/lwn.</foreign></s>

<s id="g0120202"><foreign lang="el">o( de\ ku/klos sune/sthken e)k toiou/twn: </foreign></s>

<s id="g0120202"><foreign lang="el">o( de\ ku/klos sune/sthken e)k toiou/twn. </foreign></s>

<s id="g0120203"><foreign lang="el"><lb/>eu)qu\s ga\r e)k kinoume/nou te gege/nhtai kai\ me/nontos, w(=n h( <lb/>fu/sis e)sti\n u(penanti/a a)llh/lois. w(/st' e)ntau=qa e)/stin e)pible/yasin <lb/>h(=tton qauma/zein ta\s sumbainou/sas u(penantiw/seis <lb/>peri\ au)to/n.</foreign></s>

<s id="g0120203"><foreign lang="el"><lb/>eu)qu\s ga\r e)k kinoume/nou te gege/nhtai kai\ me/nontos, w(=n h( <lb/>fu/sis e)sti\n u(penanti/a a)llh/lois. </foreign></s>

<s id="g0120203a"><foreign lang="el">w(/st' e)ntau=qa e)/stin e)pible/yasin <lb/>h(=tton qauma/zein ta\s sumbainou/sas u(penantiw/seis <lb/>peri\ au)to/n.</foreign></s>

<s id="id.000437">Maximè verò mirabile <lb/>e&longs;t contraria sibi inuicem <lb/>&longs;imul fieri: Atqui circulus <lb/>ex iis con&longs;titutus e&longs;t. </s>

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<s id="id.000457">Idque beneficio puncti B cum tota <lb/>linea A B moti, atque puncti A quieti, vt hic vult Ari&longs;toteles. <emph.end type="italics"/></s></subchap1><subchap1>

<s id="id.000458"><foreign lang="el">prw=ton me\n ga\r th=| periexou/sh| grammh=| to\n <lb/>ku/klon, pla/tos ou)qe\n e)xou/sh|, ta)nanti/a pws prosemfai/netai, <lb/>to\ koi=lon kai\ to\ kurto/n.</foreign></s>

<s id="id.000458"><foreign lang="el">prw=ton me\n ga\r th=| periexou/sh| grammh=| to\n <lb/>ku/klon pla/tos ou)qe\n e)xou/sh|, ta)nanti/a pws prosemfai/netai, <lb/>to\ koi=lon kai\ to\ kurto/n.</foreign></s>

<s id="g0120204"><foreign lang="el">tau=ta de\ die/sthken a)llh/lwn <lb/>o(\n tro/pon to\ me/ga kai\ to\ mikro/n. </foreign></s>

<s id="g0120204"><foreign lang="el">tau=ta de\ die/sthken a)llh/lwn, <lb/>o(\n tro/pon to\ me/ga kai\ to\ mikro/n. </foreign></s>

<s><foreign lang="el">dio\ metaba/llonta ei)s <lb/>a)/llhla ta\ me\n a)nagkai=on i)/sa gene/sqai pro/teron h)\ tw=n<lb/> a)/krwn o(poteronou=n, th\n de\ grammh\n eu)qei=an, o(/tan e)k kurth=s <lb/>ei)s koi=lon h)\ pa/lin e)k tau/ths gi/nhtai kurth\ kai\ periferh/s. <lb/>e(\n me\n ou)=n tou=to tw=n a)to/pwn u(pa/rxei peri\ to\n ku/klon,</foreign></s>

<s id="g0120205a"><foreign lang="el">dio\ metaba/llonta ei)s <lb/>a)/llhla, ta\ me\n a)nagkai=a i)/sa gene/sqai pro/teron h)\ tw=n<lb/> a)/krwn o(poteronou=n, th\n de\ grammh\n eu)qei=an, o(/tan e)k kurth=s <lb/>ei)s koi=lon h)\ pa/lin e)k tau/ths gi/nhtai kurth\ kai\ periferh/s. <lb/></foreign></s>

<s id="id.000459">Primum &longs;iquidem lineæ <lb/>ip&longs;um circulum <expan abbr="compre-hend&etilde;ti">compre<lb/>hendenti</expan>, licet latitudinem <lb/>nullam habeat, contraria <lb/>quodammodo, cauum & <lb/>conuexum ine&longs;&longs;e <expan abbr="appar&etilde;t">apparent</expan>. <lb/></s>

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<s id="id.000487">Atque vnum hoc e&longs;t.] <foreign lang="el">to\ a)/topon. </foreign><emph type="italics"/>Hic vt & alibi &longs;æpius <lb/>pro<emph.end type="italics"/> <foreign lang="el">qauma/sion</foreign> <emph type="italics"/>&longs;umitur, id e&longs;t igitur e&longs;&longs;e conuexum & concauum <lb/>in linea vnum e&longs;t ex admirabilibus circuli. <emph.end type="italics"/></s></subchap1><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.059.jpg" pagenum="20"/><subchap1>

<s id="id.000488"><foreign lang="el">deu/teron de\ o(/ti a(/ma kinei=tai ta\s e)nanti/as kinh/seis: <lb/>a(/ma ga\r ei)s to\n e)/mprosqen kinei=tai to/pon kai\ to\n o)/pisqen.</foreign></s>

<s id="id.000488"><foreign lang="el">deu/teron de\ o(/ti a(/ma kinei=tai ta\s e)nanti/as kinh/seis: <lb/>a(/ma ga\r ei)s to\n e)/mprosqen kinei=tai to/pon kai\ to\n o)/pisqen: <lb/>h(/ te gra/fousa grammh\ to\n ku/klon w(sau/tws e)/xei. </foreign></s>

<s id="g0120302"><foreign lang="el"><lb/>h(/ te gra/fousa grammh\ to\n ku/klon w(sau/tws e)/xei: e)c <lb/>ou(= ga\r a)/rxetai to/pou to\ pe/ras au)th=s, ei)s to\n au)to\n tou=ton to/pon <lb/>e)/rxetai pa/lin: sunexw=s ga\r kinoume/nhs au)th=s to\ e)/sxaton <lb/>pa/lin a)ph=lqe prw=ton, w(/ste kai\ fanero\n o(/ti mete/balen <lb/>e)nteu=qen.</foreign></s>

<s id="g0120302a"><foreign lang="el">e)c <lb/>ou(= ga\r a)/rxetai to/pou to\ pe/ras au)th=s, ei)s to\n au)to\n tou=ton to/pon <lb/>e)/rxetai pa/lin: sunexw=s ga\r kinoume/nhs au)th=s to\ e)/sxaton <lb/>pa/lin a)ph=lqe prw=ton, w(/ste kai\ fanero\n o(/ti mete/balen <lb/>e)nteu=qen.</foreign></s>

<s id="g0120303"><foreign lang="el">dio/, kaqa/per ei)/rhtai pro/teron, ou)de\n a)/topon to\ <lb/>pa/ntwn ei)=nai tw=n qauma/twn au)to\n a)rxh/n.</foreign></s>

<s id="g0120303"><foreign lang="el">dio/, kaqa/per ei)/rhtai pro/teron, ou)de\n a)/topon, to\ <lb/>pa/ntwn ei)=nai tw=n qauma/twn au)to\n a)rxh/n.</foreign></s>

<s id="g0120401"><foreign lang="el">ta\ me\n ou)=n peri\ <lb/>to\n zugo\n gino/mena ei)s to\n ku/klon a)na/getai, ta\ de\ peri\ <lb/>to\n moxlo\n ei)s to\n zugo/n, ta\ d' a)/lla pa/nta sxedo\n ta\ <lb/>peri\ ta\s kinh/seis ta\s mhxanika\s ei)s to\n moxlo/n.</foreign></s>

<s id="g0120401"><foreign lang="el">ta\ me\n ou)=n peri\ <lb/>to\n zugo\n gino/mena, ei)s to\n ku/klon a)na/getai, ta\ de\ peri\ <lb/>to\n moxlo\n ei)s to\n zugo/n. </foreign></s>

<s id="g0120401a"><foreign lang="el">ta\ d' a)/lla pa/nta sxedo\n ta\ <lb/>peri\ ta\s kinh/seis ta\s mhxanika\s, ei)s to\n moxlo/n.</foreign></s>

<s id="id.000489">Secundum e&longs;t, quod con<lb/>trariis motionibus &longs;imul <lb/>moueatur. </s>

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<s id="id.000512">Propterea vt e&longs;t prius.] <emph type="italics"/>Conclu&longs;io generalis e&longs;t, huc, vt exi<lb/>&longs;timo, è fine primi huius capitis, vbi melius collocaretur, <expan abbr="trãspo&longs;ita">transpo&longs;ita</expan>, <lb/>quod amplius declarant ea, quæ &longs;ubijciuntur de vecte & libra, ad <lb/>quæ cum referat omnia Mechanica, & ip&longs;a vectis & libra referan<emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.061.jpg" pagenum="22"/><emph type="italics"/>tur ad circulum, &longs;equenti etiam capite, quod erat proximum, libræ <lb/>motiones explicat. <emph.end type="italics"/></s></subchap1><subchap1>

<s id="id.000513"><foreign lang="el">e)/ti de\ <lb/>dia\ to\ mia=s ou)/shs th=s e)k tou= ke/ntrou grammh=s mhqe\n e(/teron <lb/>e(te/rw| fe/resqai tw=n shmei/wn tw=n e)n au)th=| i)sotaxw=s, a)ll' a)ei\ <lb/>to\ tou= me/nontos pe/ratos porrw/teron o)\n qa=tton, polla\ tw=n qaumazome/nwn <lb/>sumbai/nei peri\ ta\s kinh/seis tw=n ku/klwn: peri\ <lb/>w(=n e)n toi=s e(pome/nois problh/masin e)/stai dh=lon.</foreign></s>

<s id="id.000513"><foreign lang="el">e)/ti de\ <lb/>dia\ to\ mia=s ou)/shs th=s e)k tou= ke/ntrou grammh=s mhqe\n e(/teron <lb/>e(te/rw| fe/resqai tw=n shmei/wn tw=n e)n au)th=| i)sotaxw=s, a)ll' a)ei\ <lb/>to\ tou= me/nontos pe/ratos porrw/teron o)\n qa=tton, polla\ tw=n qaumazome/nwn <lb/>sumbai/nei peri\ ta\s kinh/seis tw=n ku/klwn, peri\ <lb/>w(=n e)n toi=s e(pome/nois problh/masin e)/stai dh=lon.</foreign></s>

<s id="id.000514">Præterea etiam, quod, <lb/>cum vna &longs;it ea linea, quæ <lb/>ex centro, nullum eorum, <lb/>quæ in ea &longs;unt, <expan abbr="p&utilde;ctorum">punctorum</expan>, <lb/>æquè celeriter fertur: &longs;ed <lb/>hoc, quod longius e&longs;t ab <lb/>extremo eius immobili, <lb/>&longs;emper celerius: miranda <lb/>multa circa motiones cir<lb/>culi contingunt, vt in <expan abbr="&longs;e-qu&etilde;tibus">&longs;e<lb/>quentibus</expan> problematis fiet <lb/>manife&longs;tum. </s>

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<s id="id.000531">Et &longs;ic peripheria <lb/>remotioris puncti à centro maior e&longs;t peripheria puncti centro pro<lb/>pinquioris, quod fuit demon&longs;trandum. <emph.end type="italics"/></s></subchap1><subchap1>

<s id="id.000532"><foreign lang="el">dia\ de\ to\ <lb/>ta\s e)nanti/as kinh/seis a(/ma kinei=sqai to\n ku/klon, kai\ to\ <lb/>me\n e(/teron th=s diame/trou tw=n a)/krwn, e)f' ou(= to\ *a, ei)s tou)/mprosqen <lb/>kinei=sqai, qa/teron de/, e)f' ou(= to\ *b, ei)s tou)/pisqen, <lb/>kataskeua/zousi/ tines w(/st' a)po\ mia=s kinh/sews pollou\s u(penanti/ous <lb/>a(/ma kinei=sqai ku/klous, w(/sper ou(\s a)natiqe/asin e)n <lb/>toi=s i(eroi=s poih/santes troxi/skous xalkou=s te kai\ sidhrou=s.</foreign></s>

<s id="id.000532"><foreign lang="el">dia\ de\ to\ <lb/>ta\s e)nanti/as kinh/seis a(/ma kinei=sqai to\n ku/klon, kai\ to\ <lb/>me\n e(/teron th=s diame/trou tw=n a)/krwn, e)f' ou(= to\ a, ei)s tou)/mprosqen <lb/>kinei=sqai, qa/teron de/, e)f' ou(= to\ *b ei)s tou)/pisqen <lb/>kataskeua/zousi/ tines, w(/st' a)po\ mia=s kinh/sews pollou\s u(penanti/ous <lb/>a(/ma kinei=sqai ku/klous, w(/sper ou(\s a)natiqe/asin e)n <lb/>toi=s i(eroi=s; poih/santes troxi/skous xalkou=s te kai\ sidhrou=s.</foreign></s>

<s id="g0120502"><foreign lang="el"><lb/>ei) ga\r ei)/h tou= *a*b ku/klou a(pto/menos e(/teros ku/klos e)f' ou(= <lb/>*g*d, tou= ku/klou tou= e)f' ou(= *a*b kinoume/nhs th=s diame/trou <lb/>ei)s tou)/mprosqen, kinhqh/setai h( *g*d ei)s tou)/pisqen tou= ku/klou <lb/>tou= e)f' ou(= *a, kinoume/nhs th=s diame/trou peri\ to\ au)to/.</foreign></s>

<s id="g0120502"><foreign lang="el"><lb/>ei) ga\r ei)/h tou= *a*b ku/klou a(pto/menos e(/teros ku/klos e)f' ou(= <lb/>*g*d, tou= ku/klou, e)f' ou(= *a*b, kinoume/nhs th=s diame/trou <lb/>ei)s tou)/mprosqen, kinhqh/setai h( *g*d ei)s tou)/pisqen tou= ku/klou <lb/>tou= e)f' w(=| *a, kinoume/nhs th=s diame/trou peri\ to\ au)to/.</foreign></s>

<s id="g0120503"><foreign lang="el">ei)s <lb/>tou)nanti/on a)/ra kinhqh/setai o( e)f' ou(= *g*d ku/klos tw=| e)f' <lb/>ou(= to\ *a*b: kai\ pa/lin au)to\s to\n e)fech=s, e)f' ou(= *e*z, ei)s <lb/>tou)nanti/on au(tw=| kinh/sei dia\ th\n au)th\n ai)ti/an.</foreign></s>

<s id="g0120503"><foreign lang="el">ei)s <lb/>tou)nanti/on a)/ra kinhqh/setai o( e)f' ou(= *g*d ku/klos, tw=| e)f' <lb/>ou(= to\ *a*b: kai\ pa/lin au)to\s to\n e)fech=s, e)f' ou(= *e*z, ei)s <lb/>tou)nanti/on au(tw=| kinh/sei dia\ th\n au)th\n tau/thn ai)ti/an.</foreign></s>

<s id="g0120601"><foreign lang="el">to\n au)to\n de\ <lb/>tro/pon ka)\n plei/ous w)=si, tou=to poih/sousin e(no\s mo/nou kinhqe/ntos.</foreign></s>

<s id="g0120602"><foreign lang="el"><lb/>tau/thn ou)=n labo/ntes u(pa/rxousan e)n tw=| ku/klw| th\n <lb/>fu/sin oi( dhmiourgoi\ kataskeua/zousin o)/rganon kru/ptontes <lb/>th\n a)rxh/n, o(/pws h)=| tou= mhxanh/matos fanero\n mo/non to\ <lb/>qaumasto/n, to\ d' ai)/tion a)/dhlon. <lb/></foreign></s>

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<s id="id.000656">Agitur hîc autem de &longs;implicibus tantum, <lb/>quæ vno &longs;implici motu, vel &longs;i duobus, ijs &longs;imilibus creantur, & &longs;i<lb/>milares &longs;unt: quales cum duæ tantum &longs;int recta &longs;cilicet & circula<lb/>ris, inde bene inferetur è po&longs;ita &longs;implicè &longs;i recta non e&longs;t, e&longs;&longs;e cir<lb/>cularis. <emph.end type="italics"/></s></subchap1><subchap1>

<s id="id.000657"><foreign lang="el">o(/ti me\n toi/nun h( to\n ku/klon gra/fousa <lb/>fe/retai du/o fora\s a(/ma, fanero\n e)/k te tou/twn, <lb/>kai\ o(/ti to\ fero/menon kat' eu)qei=an e)pi\ th\n ka/qeton a)fi<lb/>knei=tai, w(/ste ei)=nai pa/lin au)th\n a)po\ tou= ke/ntrou ka/qeton.</foreign></s>

<s id="g0121001"><foreign lang="el"><lb/>e)/stw ku/klos o( *a*b*g, to\ d' a)/kron to\ e)f' ou(= *b fere/sqw <lb/>e)pi\ to\ *d. a)fiknei=tai de/ pote e)pi\ to\ *g.</foreign></s>

<s id="g0121002"><foreign lang="el">ei) me\n ou)=n e)n tw=| <lb/>lo/gw| e)fe/reto o(\n e)/xei h( *b*d pro\s th\n *d*g, e)fe/reto a)\n <lb/>th\n dia/metron th\n e)f' h(=| *b*g.</foreign></s>

<s id="g0121003"><foreign lang="el">nu=n de/, e)pei/per e)n ou)deni\ <lb/>lo/gw|, e)pi\ th\n perife/reian fe/retai th\n e)f' h(=| *b e *g.</foreign></s>

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<s id="id.000671">hoc enim e&longs;t quod an<lb/>tea e&longs;t demon&longs;tratum. <emph.end type="italics"/></s></subchap1><subchap1>

<s id="id.000672"><foreign lang="el">e)a\n <lb/>de\ duoi=n ferome/noin a)po\ th=s au)th=s i)sxu/os to\ me\n e)kkrou/oito <lb/>plei=on to\ de\ e)/latton, eu)/logon bradu/teron kinhqh=nai <lb/>to\ plei=on e)kkrouo/menon tou= e)/latton e)kkrouome/nou: o(\ dokei= <lb/>sumbai/nein e)pi\ th=s mei/zonos kai\ e)la/ttonos tw=n e)k tou= <lb/>ke/ntrou grafousw=n tou\s ku/klous.</foreign></s>

<s id="g0121102"><foreign lang="el">dia\ ga\r to\ e)ggu/teron <lb/>ei)=nai tou= me/nontos th=s e)la/ttonos to\ a)/kron h)\ to\ th=s mei/zonos, <lb/>w(/sper a)ntispw/menon ei)s tou)nanti/on, e)pi\ to\ me/son bradu/teron <lb/>fe/retai to\ th=s e)la/ttonos a)/kron.</foreign></s>

<s id="g0121201"><foreign lang="el">pa/sh| me\n ou)=n <lb/>ku/klon grafou/sh| tou=to sumbai/nei.</foreign></s>

<s id="id.000673">Si vero duorum eadem <lb/>vi latorum vnum plus re<lb/>pellitur, alterum minus: <lb/>æquum e&longs;t, plus repul&longs;um, <lb/>altero minus repul&longs;o tar<lb/>dius ferri. </s>

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