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320 COMMENTARIA ANTIQUA. jtXrjv orr, si ^sv rrig fiiccg tcov to^i^v dvo evd^stai icpditrovxai^ r} dccc rrjg av^7ercD0€og a^rcov xal rov xevrQOv rj itXayia dcd^szQog i6ri rcov dvrLxeL^svcov, al ds sxarsQag (lia i&rlv icpaTtro^svrj, rj did rfjg Cv^- 5 7trco(Ssog avrciv koI roi5 xsvrQOv rj oQd^ia dLa^stQog iativ. Elg t6 s. ^ETtSLdr] daacpsg i0tL to s' d^sojQTj^a, XsKtsov inl ^sv trjg xatayQacp^g trjg i%ov0rig trjv ^Cav oQ^^Cav did(istQOv' i%sl SsdsLXtaL to H®M tov FAS ^st^ov to F^Z, 10 l'6ov dv strj tb H@M to r0A xal tc5 T^Z* m6ts xal to Kjd® ^std tov ZAK. ro aQa HM0 tov K^® dLacpsQSL ta KAZ. xolvov dcpaiQOv^svov tov ®JK loLTtov to KAZ l0ov rc5 KJMH. iitl ds trjg ixov^rjg trjv jtXayCav dcd^stQOV 16 . iitSLdrj TtQodsdsLXtat to FA® tov M®H ^st^ov rc5 FjdZ^ L0OV aQa ietl tb r®A rc5 ®HM pLStd roi} r^Z, xoLvbv dcprjQriad-G) tb FJKA' loLnbv aQa tb K®J l'6ov iatl rc5 ®HM ^std roi) KAZ. hL xOLvbv dq^i^Qi^ad^co tb M®H' lotJtbv aQa tb KZA ta 20 JMHK i'0ov. 7ttc36SLg dh sxsL TtoXXdg, alg dst i(pL
EUTOCn COMMENTARIA IN CONICA. 321 figura; nisi quod, si utraque recta alteram sectionem contingit, recta per punctum concursus earum centrumque ducta diametrus transuersa oppositarum erit, sin singulas una contingit, recta per punctum concursus earum centrumque ducta diametrus recta est. Ad prop. V. Qupniam propositio V obscurior est, in figura, quae unam diametrum rectam habet, dicendum: quoniam demonstratum est [I, 45], esse H@M maiorem quam rA@ triangulo FzIZj erit H@M = r®A + Tz/Z = K^0 + ZAK. itaque HM® sl K^® difFert triangulo KAZ. ablato, qui communis est, triangulo ®zlK erit reliquus KAZ = K^MH. in figura autem, quae diametrum transuersamhabet: quoniam antea demonstratum est [I, 45], FA® maiorem esse quam M®H triangulo JTz/Z, erit r®A = @HM + FziZ. auferatur, quod commune est, FAKA] itaque reliquus K@J == 0HM ^ KAZ. fursus auferatur, qui communis est, M®H] itaque reliquus KZA = JMHK. casus autem multos habet, qui inueniendi sunt per ea, quae in propp. XLIV et XLV libri I demonstrata sunt. cum dicimus autem aut auferatur aut adiiciatur quadrilaterum triangulusue, auferri aut adiici secundum proprietatem castium • oportet. corr. W. 15. M& H] ]ji^ ri Wp, corr. Comm. 16. rd] Tc5 Wp, corr. Comm. 17. lomov — 19. M@ H] bis p (multa euan., sicut etiam in sqq.). 18. iGtCv W. 20. iGov] om. Wp, corr. Comm. 25. itQOGQ^sGsig] corr. ex nQOGQ^EGTi^; m. 1 W. ApoUonius, ed. Heiberg. II. 21
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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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p. 74, 15 AHT] ABF PROLEGOMENA. LII
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1B4 FRAGMENTA. Cfr. p. 124, 17 sq.:
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138 FRAGMENTA. XBVtQOv avtov tr^v t
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I COMMENTARIA ANTIQUA.
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144 COMMENTARIA ANTIQUA. [Eucl. III
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2. ccficporEQcc] Bv.dxsQOv Hultsch.
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IV. EUTOCII COMMENTAKIA IN CONICA.
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