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170 COMMENTARIA ANTlQUA. ^sv ra oQ%-oycovtG) trjv vvv yMlovîvriv TtaQaôlriv^ iv ds rc5 a^^lvyavCc) trjv vjtEQôki^v^ iv ds tc5 ojuyovLC) tr]v eXksitlîv' xal s6tt %aQ avtotg svqelv oi^rog vvoâôîvag tag to^dg. c307Ceq ovv tcjv aQxaLmv 5 ijtl Evog EKaGtov aldovg tQLycovov dÊOQrjadvtcov tdg dvo OQ^dg TCQotEQOv iv ta L0O7tlEVQC(i Kal ndXtv iv rc3 looOHsXst aal vOtSQOv iv tcj exalrjva oC ÊtayEviotEQOL xaôXLKOv dÊcoQrjâ ditidELâv toLovto' jtavtbg tQiycovov aC ivtog tQstg yovLat dv6lv OQdâtg l'6ai, 10 siGLV' ovtog xal iTtl rcov roi5 xcoi/ou roficov* rryv lihv yaQ kEyoîvrjv oQd-oyovtov ;«aii/ou to^rjv iv OQd-oyovCo ôvov 7COVO id-EcoQovv tE^voîvo iTCLTcido 6q%ô TtQog [iLav TtlEVQav roi) kovov, tr]v de rot> d^^kvyovLOV XC3V0V toîr^v iv d^^Xvyovco yLvoîvrjv xcovo 15 ditEdELOCvvOav , tr^v ds tov o^vyovLOV iv o^vyovLO, oÔLog ijtl Tcdvtov tc5v xcdvov dyovtsg td iTCLTtEda oQ^d TCQog fLoav TcXsvQav rov tcovov drjXot ds xal avtd td aQiata ovoâta tov yjQa^ôv. v6t£Qov ds 'ATCoXXovLog IlEQyatog xad-oXov tc id-EcoQrjOEv, otv 20 iv TCavtl xcovo xal 6q%o xal CKaXrjvo JtdaaL aC toâC eIol xatd 8Ld(pOQOV tov ijtLTtidov JtQog tbv xovov TtQoCôlriV ov xal %av^d6avtEg oC ^co^r' avtbv ysvo- ÊVOL dtd tb âviidCLOV rc5v vtc avtov dEdsLyîvov xovLXOv %EOQrj^dtov fiiyav ysoîtQrjv ixdkovv. tavta 25 îEv ovv b Fs^tvog iv r« fxrco (pr]al rijg rc5i; âdî^- ^dtov dÊOQCag. o ds kiysL^ aacpsg TCOLiâoÊv iicl rc5v VTCoxELîvov xatayQacpov. iato ro did tov dôvog rov xovov tQCyovov tb 2, h Ss — v7i£Q§oli]v'] p, mg. W^ 3. IWtv W. 7. OKttXrjva] a corr. ex X m. 1 W. 8. dnsdsLâv] p, W^ navx6g] n corr. ex v m. 1 W. 10. ovxoa p. 13. 8b] supra
EUTOCII COMMENTARIA IN CONICA. 171 parabolam uocant, in obtusiangulo hyperbolam, in acutiangulo ellipsim; et sectiones illas apud eos ita denominatas inuenias. sicut igitur, cum ueteres propositionem de angulis duobus rectis aequalibus in singulis generibus trianguli inuestigassent, primum in aequilatero, postea in aequicrurio, deinde uero in scaleno, recentiores propositionem uniuersalem demonstrauerunt talem: cuiusuis trianguli tres anguli interiores duobus rectis aequales sunt [Eucl. I, 32], ita etiam in coni sectionibus factum est; sectionem enim rectanguli coni quae uocatur in solo cono rectangulo perscrutabantur secto plano ad latus coni perpendiculari, sectionem autem coni obtusianguli in cono obtusiangulo, sectionem autem acutianguli in acutiangulo oriri demonstrabant in omnibus conis similiter planis ad latus coni perpendicularibus ductis; id quod ipsa nomina linearum illarum autiqua docent. postea uero Apollonius Pergaeus uniuersaliter inuestigauit, in quouis cono et recto et scaleno omnes sectiones illas oriri secundum uariam plani ad conum positionem; quem admirati aequales ob admiranda theoremata conica ab eo demonstrata magnum geometram adpellabant. haec igitur Geminus iu libro sexto de scientia mathematica; et quae dicit, nos in figuris infra descriptis illustrabimus. sit ABF triangulus per axem coni positus, et a
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(D s APOLLONIl PERGAEI QUAE GEAECE
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PEAEFATIO. Praeter librum lY Conico
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AB PRAEFATIO. V 3. cod. Paris. Gr.
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PRAEFATIO. VII II p. 306, 2 A, B] A
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; PRAEFATIO. IX pro nACGON, p. 202,
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PROLEGOMENA. Cap. I. De codieibus C
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PROLEGOMENA. XIII Apollonii Conic.
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PROLEGOMENA. XV codicum illorum XXV
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