Apollonii Pergaei quae graece exstant cum ... - Wilbourhall.org
Apollonii Pergaei quae graece exstant cum ... - Wilbourhall.org Apollonii Pergaei quae graece exstant cum ... - Wilbourhall.org
268 COMMENTARIA ANTIQUA. dvvarai ds ra rijg TtQordaecog d6L7cvv0^ai xal eTtl dvriKSLiievcov. Elg to ^5'. Tovro rb d^scoQTj^a TtrojasLg s%sl TclsLOvg, ag dsL^o- 6 ^sv 7tQo6s%ovrsg ratg 7trc60s0L rov /Lt/3'. vTtodsLy^arog ds %dqLV^ sav rb Z STtl rb B TtLTtroLro^ rb B^A laov iarl np ©B^M^ avrod^sv iQov^sv sitsl zoLvbv d(pr]Qri6d^o rb NM^B' koLTtbv ccQa rb ANM rc5 N@B idrLv taov, 10 iitl dl rrjg loLTtfjg iQOv^sv iTtSLdr} ro AE/i rc5 @BJM iarLv lcov. rovrsCrL ra KHziMxal rco HZE. rovrsan tc5 ZKN xal rc3 NE^M, tcolvov d(pr]Qr]0d^c3 ro NEJM' xal loLnov ccQa ro ANM ra KZN i'6ov. Elg rb ^t,'. 15 Tovro ro d^scoQrj^a inl ^sv rrjg v7tSQ^okr]g nrcoCSLg sxsL^ o6ag ro TtQo avrov ijtl rrjg TtaQafiolrjg si%sv, rdg 4. aff] addidi, om. Wp. dst^ofisv Ss Halley cum Comm. 5. nTmasaLv W. 6. jrtTrrotro] p, corr. ex nCmsixo W. 7. ^QOvyLSv'] iQOv ^. insQ ^Trt' Wp, corr. Comm. B^A] BdA Wp, corr. Comm. saTiv W. tc5] to Wp, corr. Comm. (9BZ/M] OBzTikTWp, corr. Comm. ' 8. NM^B] NMJAB Wp, corr. Comm. 10. fjrt'] -t in ras. W. ds] -s in ras. W. AEJ] z/ 8 corr. p. 11. tovtsaTLV W. 12. tovxsativ W. 13. xat] p, v.aX at W, om. Comm. Xoinov] -6- e corr. W. «9«! addidi cum Comm., om. Wp. ANM] ANM Wp, corr. Comm. KZN] N ins. m. 1 W, KZH p.
potest. EUTOCII COMMENTARIA IN CONICA. 269 propositio autem etiam de oppositis demonstrari Ad prop XLVI. Haec propositio complures habet casus, quos demonstrabimus ad casus propositionis XLII animaduertentes. exempli autem gratia, si Z in 5 cadit, statim dicemus: quoniam est [prop. XLII] B^A = &BJMj auferatur, quod commune est, NMzlB\ itaque, qui relinquitur, triangulus ANM = N®B, in reliqua autem figura dicemus: quoniam AE^ = ®BJM [prop. XLII] = KHJM + HZE = ZKN + NE^M, auferatur, quod communeest, NE/^M\ erit igitur etiam, qui relinquitur, triangulus ANM = KZN Ad prop. XLYIL Haec propositio in hyperbola totidem habet casus, quot praecedens in parabola habuit, demonstrationes autem eorum efficiemus ad casus propositionis XLIII animaduertentes, et in ellipsi quoque demonstrationes In Fig. 1 om. A W, pro N hab. H W. In Fig. 3 pro A hab. A, pro E hab. O, O et N om. W.
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268 COMMENTARIA ANTIQUA.<br />
dvvarai ds ra rijg TtQordaecog d6L7cvv0^ai xal eTtl<br />
dvriKSLiievcov.<br />
Elg to<br />
^5'.<br />
Tovro rb d^scoQTj^a TtrojasLg s%sl TclsLOvg, ag dsL^o-<br />
6 ^sv 7tQo6s%ovrsg ratg 7trc60s0L rov /Lt/3'.<br />
vTtodsLy^arog ds %dqLV^ sav rb Z STtl rb B TtLTtroLro^<br />
rb B^A laov iarl np ©B^M^<br />
avrod^sv iQov^sv sitsl<br />
zoLvbv d(pr]Qri6d^o rb NM^B' koLTtbv ccQa rb ANM<br />
rc5 N@B idrLv taov,<br />
10 iitl dl rrjg loLTtfjg iQOv^sv iTtSLdr} ro AE/i rc5<br />
@BJM iarLv lcov. rovrsCrL ra KHziMxal rco HZE.<br />
rovrsan tc5 ZKN xal rc3 NE^M, tcolvov d(pr]Qr]0d^c3<br />
ro NEJM' xal loLnov ccQa ro ANM ra KZN i'6ov.<br />
Elg rb ^t,'.<br />
15 Tovro ro d^scoQrj^a inl ^sv rrjg v7tSQ^okr]g nrcoCSLg<br />
sxsL^ o6ag ro TtQo avrov ijtl rrjg TtaQafiolrjg si%sv, rdg<br />
4. aff] addidi, om. Wp. dst^ofisv Ss Halley <strong>cum</strong> Comm.<br />
5. nTmasaLv W. 6. jrtTrrotro] p, corr. ex nCmsixo W. 7.<br />
^QOvyLSv'] iQOv ^. insQ ^Trt' Wp, corr. Comm. B^A] BdA<br />
Wp, corr. Comm. saTiv W. tc5] to Wp, corr. Comm.<br />
(9BZ/M] OBzTikTWp, corr. Comm. ' 8. NM^B] NMJAB<br />
Wp, corr. Comm. 10. fjrt'] -t in ras. W. ds] -s in ras. W.<br />
AEJ] z/ 8 corr. p. 11. tovtsaTLV W. 12. tovxsativ W.<br />
13. xat] p, v.aX at W, om. Comm. Xoinov] -6- e corr. W.<br />
«9«! addidi <strong>cum</strong> Comm., om. Wp. ANM] ANM Wp,<br />
corr. Comm. KZN] N ins. m. 1 W, KZH p.