Apollonii Pergaei quae graece exstant cum ... - Wilbourhall.org
Apollonii Pergaei quae graece exstant cum ... - Wilbourhall.org Apollonii Pergaei quae graece exstant cum ... - Wilbourhall.org
184 COMMENTARIA ANTIQUA. 7t8Qi(p8Q£Lav tou xvkXov KXcj^svai, rbv avtov E%ov6ai Xoyov ratg JT, z/. Xsyco drj, ort TtQog ciXXc) ^rj^sio) ^rj ovn enl r^g 7t8Qi(peQeCag ov yCvErau Xoyog rcav aito rcjv A^ B cri- 5 ^eCcov 8% avro ijtL^svyvv^Evcov svd^siSv 6 avrog ra5 rrig F itQog z/. 81 yaQ dvvarov, ysyovsrco TtQog tw M ixrog xrjg TtsQicpSQsCag' Tial yccQ st ivrbg XrjcpdsCrj, rb avrb aro- Ttov 6v^Prj0sraL Tcad'' irsQav rcov VTtod^sOscov ' xal 10 i7t8t,8v%^Gi6av aC MJ^ MB, MZ, xal vTtoxsCad-cj, a)g ri r JtQog z/, ovrog r^ AM TtQbg MB, sortv ccQa, ag ri Ez] TtQbg z/, ovrcag rb aitb E/i itQbg rb ccjtb F xal rb aitb AM JtQbg rb anb MB. aAA' d}g rj EA TtQbg z/, ovrcog vTtoKSLrat rj AZ TtQbg ZB' xal cog 15 ccQa rj AZ TtQbg ZB, rb dnb AM TtQbg rb ditb MB. xal dia rd 7tQodsL%xt8vra^ idv dnb rov B rrj AM naQaXXrjlov dydyco^sv, dsL^d^riCsraL, (bg rj AZ n^bg ZB, rb dnb AZ n^bg rb dnb ZM, idsCxd-rj ds xaC, cog rj AZ nQog ZB, rb dnh AZ n^hg rh dnh Z®, 20 tcri (XQa r] Z® rfi ZM' onsQ ddvvarov. rcnoL ovv inCnsdoL XsyovraL rd roiavra' oC ds Xsyo^svoL 6rsQ8ol ronoL rijv nQo^covv^Cav i6%rixa6Lv dnh rov rdg yQa^^dg, dt' dov yQacpovraL rd xar avrovg nQO^lrnLara, ix rrjg ro^rjg rdov (Stsqscov tr^v 25 yivs(5LV s%8LV, olaC sI^lv al rov xcovov ro^al xal srsQaL nlsCovg. siel ds xal dXXoL ronoL n^bg im^pdvsLav ksyo^svoL^ oC rr^v incovv^Cav s%ov0lv dnh rrjg nsQl avrovg CdLorrjrog. 2. r] A Wp, corr. U. 3. aXXa)] corr. ex aUo m. 1 W. 4. tcov Al scripsi, ^ Wp. 9. fTf^av] scr. e^arsQav.
EUTOCII COMMENTARIA IN CONICA. 185 ambitum circuli fractas eandem rationem habere quam r:z/. iam dico, ad nullum aliud punctum^ quod in ambitu non sit, rationem rectarum a punctis A, B ad id ductarum eandeni fieri quam F : z/. nam si fieri potest, fiat ad M extra ambitum positum; nam etiam si intra eum sumitur, idem absurdum eaenit per utramque suppositionem; ducanturque MAy MB, MZ, et supponatur F: ^ = AM: MB. itaque E+ Zf: A = {E+ AY:r^=-AM^:MB^ [p. 183 not. 1]. supposuimus autem E+ z/:z/ = ^Z: Z5; quare etiam AZ:ZB = AM^ :MB^, et eodem modo, quo supra demonstratum est [p. 182, 11 sq.], si a 5 rectae AM parallelam duxerimus, demonstrabimus, esse AZ : ZB = AZ^:ZM^. demonstrauimus autem, esse etiam AZ : ZB = AZ^ : Z®^ [p. 182, 13 sq.]. ergo Z@ = ZM*, quod fieri non potest. plana igitur loca talia uocantur, solida uero quae uocantur loca nomen inde acceperunt, quod lineae, per quas problemata ad ea pertinentia soluuntur, e sectione solidorum originem ducunt, quales sunt coni sectiones aliaeque complures. sunt autem et alia loca ad superficiem quae uocantur a proprietate sua ita denominata. 10. MB] M e coir. p. 12. ovtco p. 14. —cog vnov.. — 17. 7] AZ] in ras. m. 1 p. 21. ds] addidi; om. Wp. 22. nQoaovvfiiav W. 26. sxsiv'] i%si Wp, corr. U. 26. bIgCv W. 27. l-ncovviiiav] co corr. ex o m. 1 p, ETtovv^Lav W. 28. sldiozrjtos W.
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184 COMMENTARIA ANTIQUA.<br />
7t8Qi(p8Q£Lav tou xvkXov KXcj^svai, rbv avtov E%ov6ai<br />
Xoyov ratg JT, z/.<br />
Xsyco drj, ort TtQog ciXXc) ^rj^sio) ^rj ovn enl r^g<br />
7t8Qi(peQeCag ov yCvErau Xoyog rcav aito rcjv A^ B cri-<br />
5 ^eCcov 8% avro ijtL^svyvv^Evcov svd^siSv 6 avrog ra5<br />
rrig F itQog z/.<br />
81 yaQ dvvarov, ysyovsrco TtQog tw M ixrog xrjg<br />
TtsQicpSQsCag' Tial yccQ st ivrbg XrjcpdsCrj, rb avrb aro-<br />
Ttov 6v^Prj0sraL Tcad'' irsQav rcov VTtod^sOscov ' xal<br />
10 i7t8t,8v%^Gi6av aC MJ^ MB, MZ, xal vTtoxsCad-cj, a)g<br />
ri r JtQog z/, ovrog r^ AM TtQbg MB, sortv ccQa, ag<br />
ri Ez] TtQbg z/, ovrcag rb aitb E/i itQbg rb ccjtb F<br />
xal rb aitb AM JtQbg rb anb MB. aAA' d}g rj EA<br />
TtQbg z/, ovrcog vTtoKSLrat rj AZ TtQbg ZB' xal cog<br />
15 ccQa rj AZ TtQbg ZB, rb dnb AM TtQbg rb ditb MB.<br />
xal dia rd 7tQodsL%xt8vra^ idv dnb rov B rrj AM<br />
naQaXXrjlov dydyco^sv, dsL^d^riCsraL, (bg rj AZ n^bg<br />
ZB, rb dnb AZ n^bg rb dnb ZM, idsCxd-rj ds xaC,<br />
cog rj AZ nQog ZB, rb dnh AZ n^hg rh dnh Z®,<br />
20 tcri (XQa r] Z® rfi ZM' onsQ ddvvarov.<br />
rcnoL ovv inCnsdoL XsyovraL rd roiavra' oC ds<br />
Xsyo^svoL 6rsQ8ol ronoL rijv nQo^covv^Cav i6%rixa6Lv<br />
dnh rov rdg yQa^^dg, dt' dov yQacpovraL rd xar<br />
avrovg nQO^lrnLara, ix rrjg ro^rjg rdov (Stsqscov tr^v<br />
25 yivs(5LV s%8LV, olaC sI^lv al rov xcovov ro^al xal<br />
srsQaL nlsCovg. siel ds xal dXXoL ronoL n^bg im^pdvsLav<br />
ksyo^svoL^ oC rr^v incovv^Cav s%ov0lv dnh rrjg<br />
nsQl<br />
avrovg CdLorrjrog.<br />
2. r] A Wp, corr. U. 3. aXXa)] corr. ex aUo m. 1 W.<br />
4. tcov Al scripsi, ^ Wp. 9. fTf^av] scr. e^arsQav.
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