Apollonii Pergaei quae graece exstant cum ... - Wilbourhall.org
Apollonii Pergaei quae graece exstant cum ... - Wilbourhall.org Apollonii Pergaei quae graece exstant cum ... - Wilbourhall.org
242 COMMENTARIA ANTIQUA. eig t6 avro. tstQaTtkEVQOv ovtog tov AA/iH tJx^cj tfi AA TtaQakkriXog rj FKB aTtote^voviSa to FHK tQiycovov tS AA/IH tstQaTtkavQCi i6ov] tovto de 5 TtOLTJeo^ev ovtcog' iav yccQ, oSg ev totg 6toi%eCoLg i^dd^o^ev, tS dod-evti evd^vyQa^^c) ta AAAH tetQa- TtXevQO) i0ov Tcal akkco t(p dod-evti ta AE^ tQiycovo ofioiov tb avtb 6v6tri(5(D[iie%^a tb 2JTT, C36te ouoXoyov elvai trjv ZIT trj A^, aai (XTtokd^cj^ev tfj ^ev 2JT 10 fariv trjv HK, tfj de TT l'6r}v trjv HT, xal ijti^ev- ^cj^ev t^v FK, e6tai tb ^rjtov^evov. eTtel yccQ r] TtQog ta T ycavia l'6r} iatl tfj z/, tovte6ti tfj H, did tovto l'6ov zal ofioiov tb FHK ta Z!TT. xal l'6rj rj r yiovCa tfj E, xaC ei6iv ivaXXd^' jtaQalXrjlog ccQa 15 i6tlv rj FK tfj AE. (paveQOV drj, oti, otav rj AB a^cav i6tCv, rj MA icpdjttetai trjg to^rjg, otav 8e }ir} ai^av, te^vei, ei ^Qog oQd^dg dyetai jtdvtcjg tfj dia^itQC). Eig tb xrj\ 20 '''Oti, xav r} F^ tifivrj trjv vneQ^oXrjv , td avtd 6vii^rJ6eTai, a6neQ inl rot» OTitcoxaidexdtov. Elg tb X'. Kal dtg aQa iitl ^ev trjg ikXeCipeog ^vvd^evti, inl d\ tc3v dvtiicei^ivcov dvdTtakiv xal dva- 5. aroix^ioLs] w, azvxioig e corr. W, axoUoLg p. 6. rc5 (pr.)] iv To5 Wp, corr. Comm. 7. A@j ^. 8. t6 avro] x(o avzm Wp, corr. Halley. avaxriaco^sQ^a'] scripsi, avatriaoiiB^a Wp. 9. ETp. r^ (alt.)] rrjV Wp, corr. Comm. ^ ETp. 10. xriv] ry Wp, corr. Comm. Post HK del. rr^v ds ¥v
EUTOCII COMMENTARIA IN CONICA. 243 Ad eandem. Cum AA/IH quadrilaterum sit, ducatur rectae AA parallela FKB triangulum FHK abscindens quadrilatero AAAH aequalem p. 238, 21— 24] hoc uero ita efficiemus. si enim, ut in Elementis [YI, 25] didicimus, datae figurae rectilineae, quadrilatero AAAH^ aequalem et alii figurae datae, triangulo AEAy similem eandem figuram construxerimus ZTVy ita ut ZT lateri A/1 respondeat, et posuerimus HK= ET^ HF == TT, et duxerimus FKy effectum erit, quod quaerimus. quoniam enim LT=^=:H, erit FHK^ETT [Eucl. I, 4]. et l_ r=E, et alterni sunt; itaque [Eucl. I, 27] TKj AE parallelae sunt. manifestum igitur, si AB axis sit, rectam MA sectionem contingere, sin non axis, secare, si quidem semper ad diametrum perpendicularis ducitur. Ad prop. XXVIII. Etiamsi Iz/ hyperbolam secat, eadem adcident, sicut in prop. XVIII [u. supra p. 230, 19]. Ad prop. XXX. Quare etiam, in ellipsi componendo, in oppositis autem e contrario et conuertendo 1'arjv xriv tij rpi p. ttjI zi^v Wp, corr. Halley. ti^vl W, T^ p. 12, Tc5] p, corr. ex to W S6tiv W. tovr- SGTLV W. 14. r] AF Wp, corr. Comm. 16. dr/] ds Halley cum Comm. 17. bI] scripsi, om. Wp. 23. iXXCTpscoq W, 16*
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242 COMMENTARIA ANTIQUA.<br />
eig t6<br />
avro.<br />
tstQaTtkEVQOv ovtog tov AA/iH tJx^cj tfi AA<br />
TtaQakkriXog rj FKB aTtote^voviSa to FHK tQiycovov<br />
tS AA/IH tstQaTtkavQCi i6ov] tovto de<br />
5 TtOLTJeo^ev ovtcog' iav yccQ, oSg ev totg 6toi%eCoLg i^dd^o^ev,<br />
tS dod-evti evd^vyQa^^c) ta AAAH tetQa-<br />
TtXevQO) i0ov Tcal akkco t(p dod-evti ta AE^ tQiycovo<br />
ofioiov tb avtb 6v6tri(5(D[iie%^a tb 2JTT, C36te ouoXoyov<br />
elvai trjv ZIT trj A^, aai (XTtokd^cj^ev tfj ^ev 2JT<br />
10 fariv trjv HK, tfj de TT l'6r}v trjv HT, xal ijti^ev-<br />
^cj^ev t^v FK, e6tai tb ^rjtov^evov. eTtel yccQ r]<br />
TtQog ta T ycavia l'6r} iatl tfj z/, tovte6ti tfj H, did<br />
tovto l'6ov zal ofioiov tb FHK ta Z!TT. xal l'6rj<br />
rj r yiovCa tfj E, xaC ei6iv ivaXXd^' jtaQalXrjlog ccQa<br />
15 i6tlv rj FK tfj AE.<br />
(paveQOV drj, oti, otav rj AB a^cav i6tCv, rj MA<br />
icpdjttetai trjg to^rjg, otav 8e }ir} ai^av, te^vei, ei<br />
^Qog oQd^dg dyetai jtdvtcjg tfj dia^itQC).<br />
Eig tb xrj\<br />
20 '''Oti, xav r} F^ tifivrj trjv vneQ^oXrjv , td avtd<br />
6vii^rJ6eTai, a6neQ inl rot» OTitcoxaidexdtov.<br />
Elg tb X'.<br />
Kal dtg aQa iitl ^ev trjg ikXeCipeog ^vvd^evti,<br />
inl d\ tc3v dvtiicei^ivcov dvdTtakiv xal dva-<br />
5. aroix^ioLs] w, azvxioig e corr. W, axoUoLg p. 6. rc5 (pr.)]<br />
iv To5 Wp, corr. Comm. 7. A@j ^. 8. t6 avro] x(o<br />
avzm Wp, corr. Halley. avaxriaco^sQ^a'] scripsi, avatriaoiiB^a<br />
Wp. 9. ETp. r^ (alt.)] rrjV Wp, corr. Comm. ^<br />
ETp.<br />
10. xriv] ry Wp, corr. Comm. Post HK del. rr^v ds ¥v