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270 COMMENTARIA ANTIQUA. dh ccTtodeL^SLg avtojv Ttotrjaoêdâ 7tQoCB%ovt£g rcctg %X(Q0e0i tov ^y' d^scoQT^âtog, xal inl rijg iXXsLipsag de tag aTtodecêtg ix tcov 7tt(66sa)v tov ^y', olov inl trjg VTtoKecusvrjg xatayQacprjg tov H 6rjêL0v ixtog 5 eiXrj^^svov, iTtSLdrj l'0ov i6tl tb AAF tQLyavov totg &HSI, ^TM, tovtsatL totg O&T, OHM tQLycovoLg, rc3 ds AAF L'0ov s6tl to ts Slir tQLycovov xal ro AAHS tstQccTtXsvQOv , tovts(3tL to N®n tQLycavov 6lcc ta dsdsLy^sva iv ta ^y' dscoQijâtL, xal ta Snr, 10 N®n ccQa tQLycjva l'0a iatl totg 0®r, OMH tQLycavoig. tcolvov acpyQiâdâ) ro 0Or tQLycovov XoLitbv ccQa 'ro SON rc5 HOM l'6ov iatCv. y,al TtaQaXXrjlog rj NS tfi MH l'(jr} ccQa ^ NO tfj OH Eig tb fiYj'. 15 Kal tovtov at TitcoasLg Sâvtcog s%ov0l totg JtQOSLQrj- ÊvoLg inl tov iit,' xata trjv trjg vTtSQPoXrjg xatayQacpTJv, Elg tb fid''. AoLTtbv ccQa tb KAN tQLycovov t^ Z/AUr 20 TtaQaXXrjkoyQa^^c) i6tlv l'6ov. Kal l'0rj i0tlv rj vTtb AAH ycovCa tfj vTtb KAN ycovCa* dLTtXdaLOv ccQa ietl tb VTtb KAN tov vTtb AAF] iKxsCad^co yccQ x^Q^S T^b KAN tQCycovov xal ro AAUr TtaQaX- 2. nzCOGBGlV W. 5. EGxlv W. 6. XOVtSGXlV W. 7. Tc5] scripsi, x6 Wp. • ds'] yccQ Wp, corr. Halley. sgxCv W. ro] W, rc5 p. ZUr p. xgCyaivov] scripsi, rîycovo) Wp. ro] W, Tc5 p. 8. xEXQu.nXEVQOv] W, comp. p. xovtiGxiv W. 10. EGxCvW. OMH] OM W, OÂ p, corr. Comm. 12. HOM] HOMWv, corr. Halley, mog Comm. 13. OH] 0H Wp, corr. Comm. 15. %ov(Jtv W. 22. iaxiv W. 23. JAUr] JAUT Wp, corr. Comm.
» EUTOCII COMMENTARIA IN CONICA. 271 efficiemus e casibus propositionis XLIII^ uelut in figura infra descripta puncto H extra E sumpto, quoniam est efc [prop. XLTII] AAF = ©HSl + £irM =0®r-\- OHM, Snr + AAHS = AAr= Snr-\- N&U propter ea, <strong>quae</strong> in prop. XLIII demonstrata sunt [u. supra p. 258, 2], erit etiam ^nr + N®n = Oer+ OMH auferatur, qui communis est, triangulus BOF] erit igitur, qui relinquitur, triangulus ÔN == HOM, et NS, MH parallelae suntj ergo NO == OH Ad prop. XLVIIL Huius quoque propositionis casus eodem modo se habent atque ii, quos in prop. XLVII in figura hyperbolae explicauimus. Ad prop. XLIX. Erit igitur KAN = JAUr. est autem L AAH = LKAN] itaque erit KAxAN=2A^XAr I p. 148, 3-6] seorsum enim describantur triangulus KAN et parallelogrammum AAUr. €i quoniam est KAN = Û, per j„ N rectae AK parallela ducatur NP, per K autem rectae AN parallelaXP; parallelogrammum igitur est AP et = 2 KAN [EucL I, 34]; quare etiam AP=2An. iam AT, AH ad 2, T producantur, et ponatur FZ = AF, Figura est codicis W, nisi qiiod ibi ducta est ^P; pro JT liab. X; K corr. m. rec. ex M.
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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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: PROLEGOMENA. XVH in Galliam cum c
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PROLEGOMENA. XIX i-n — om., ov 8i
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p. 74, 15 AHT] ABF PROLEGOMENA. LII
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