Apollonii Pergaei quae graece exstant cum ... - Wilbourhall.org
Apollonii Pergaei quae graece exstant cum ... - Wilbourhall.org Apollonii Pergaei quae graece exstant cum ... - Wilbourhall.org
' a 356 COMMENTARIA ANTIQUA. avdyvcDd-c ovv avtcc iTtL^slcjg^ koX sl' 6ol xatad^v^icog yevrjtac xal ta XoiTCa xata tovtov roi' tvTCov V7C £^ov iKtsd^rjvai, Tcal tovto d^sov rjyov^svov ysv7]6£tav. £QQCD0O. 5 ^'AXXciyg tb zd\ ''E6tco6av aC EABF^ ^ABF toiiat, (og SLQritaiy Kal dnqx^^co^ mg hv%£v^ ri ^EF, xal dca tov A tfj ^EF TtaQccXXrjXog ri%^o Ti A&. 10 £l ovv ivtog tmv to^cov 7tL7Ct£i, ri iv ta Qrjta dTCodst^Lg aQ^60£L* sl ds iq^dijjstaL xatd to A, d^cpotsQCOv iiCLt}javasL tSv to^cov, xal dLa tovto rj djto tov A dyo^svrj dLd^stQog trjg stsQag 15 tcov to^cov dLd^stQog s0taL %a\ tfjg XoLTC^g. dCxa ccQa ts^vsL Tiatd tb Z triv ts FJ xal trjv EF' otcsq ddvvatov. "AXlcog tb avto. "E(3tG}6av aC EABF, zlABF to^ac, ag slQrjtaL, 20 xal sikricpd^G) iicl tov ABF xolvov t^ri^atog avtcov ^rj^SLOv tL tb B, xal iitst.svjp^co r] AB xal ^Cya tst\jir\0^ca Katd to Z, xal d^d tov Z dLd^stQog r\ypGo r\ HZ®, Tcal dLa tov F itaQa trjv AB 7]xd-co rj FzJE. iTCsl ovv dLd^stQog ictLv r\ Z0 xal dCxa ts^vsL 26 rrjv AB, tszay^svcog aQa xatrJKtaL rj AB. naC iazL Fig. om. Wp. 1. dvdyvco&i^l p, dvccyvoad^si, W. Goi] in ras. m. 1 W. 2. yivrjTui] p, ysvoizai W. 6. EABF] E insert. m. 1 W. JABF] om. Wp, corr. Halley cum Comm. 7. xat (pr.)] iatcoa y.ui W (puncta add. m. rec, ^ ra. 1 sunt), fcroo ot«t p^ xat''w. 19. xoyiOii] om. p. 23. Ante HZ@ del. H@Z p. 24. Y.ui] om. Wp, corr. Halley; quae Comm. 25. sariv W.
EUTOCII COMMENTARIA IN CONICA. 357 itaque eos studiose legas uelim, et si concupiueris, reliquos etiam ad hanc formam a me exponi, hoc quoque deo duce fiet. uale. Aliter prop. XXIV. Sint EABFy /iABF sectiones, quales diximus, et ducatur quaelibet recta AEFy per A autem rectae /lEr parallela ducatur A&. ea igitur si intra sectiones cadit, demonstratio in uerbis Apollonii proposita apta erit; sin in A contingit, utramque sectionem continget, et ea de causa diametrus ab A ducta alterius sectionis etiam reliquae diametrus erit. ergo in Z et FJ et EF in binas partes secat [I def. 4]; quod fieri non potest. Aliter idem. Sint EABFj ^ABF sectiones, quales diximus, et in ^JSr* communi earum parte punctum aliquod sumatur 5, ducaturque AB et in Z in duas partes aequales secetur, per Z autem diametrus ducatur HZ®, et per r rectae AB parallela ducatur r^E. quoniam igitur diametrus est Z0 et rectam AB m duas partes aequales secat, AB ordinate ducta est ^ [I def. 4]. et ei parallela est F^E. itaque in in binas partes aequales secta est [I def. 4] in EABF sectione EF, in ^ABF autem z/T. ergo E@ = @^5 quod fieri non potest. Fig. om. Wp.
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' a<br />
356 COMMENTARIA ANTIQUA.<br />
avdyvcDd-c ovv avtcc iTtL^slcjg^ koX sl' 6ol xatad^v^icog<br />
yevrjtac xal ta XoiTCa xata tovtov roi' tvTCov<br />
V7C £^ov iKtsd^rjvai, Tcal tovto d^sov rjyov^svov ysv7]6£tav.<br />
£QQCD0O.<br />
5 ^'AXXciyg tb zd\<br />
''E6tco6av aC EABF^ ^ABF toiiat, (og SLQritaiy<br />
Kal dnqx^^co^ mg hv%£v^ ri ^EF, xal<br />
dca tov A tfj ^EF TtaQccXXrjXog ri%^o<br />
Ti<br />
A&.<br />
10 £l ovv ivtog tmv to^cov 7tL7Ct£i, ri<br />
iv ta Qrjta dTCodst^Lg aQ^60£L* sl ds<br />
iq^dijjstaL xatd to A, d^cpotsQCOv iiCLt}javasL<br />
tSv to^cov, xal dLa tovto rj<br />
djto tov A dyo^svrj dLd^stQog trjg stsQag<br />
15 tcov to^cov dLd^stQog s0taL %a\ tfjg XoLTC^g. dCxa ccQa<br />
ts^vsL Tiatd tb Z triv ts FJ xal trjv EF' otcsq ddvvatov.<br />
"AXlcog tb avto.<br />
"E(3tG}6av aC EABF, zlABF to^ac, ag slQrjtaL,<br />
20 xal sikricpd^G) iicl tov ABF xolvov t^ri^atog avtcov<br />
^rj^SLOv tL tb B, xal iitst.svjp^co r] AB xal ^Cya tst\jir\0^ca<br />
Katd to Z, xal d^d tov Z dLd^stQog r\ypGo r\<br />
HZ®, Tcal dLa tov F itaQa trjv AB 7]xd-co rj FzJE.<br />
iTCsl ovv dLd^stQog ictLv r\ Z0 xal dCxa ts^vsL<br />
26 rrjv AB, tszay^svcog aQa xatrJKtaL rj AB. naC iazL<br />
Fig.<br />
om. Wp.<br />
1. dvdyvco&i^l p, dvccyvoad^si, W. Goi] in ras. m. 1 W.<br />
2. yivrjTui] p, ysvoizai W. 6. EABF] E insert. m. 1 W.<br />
JABF] om. Wp, corr. Halley <strong>cum</strong> Comm. 7. xat (pr.)]<br />
iatcoa y.ui W (puncta add. m. rec,<br />
^<br />
ra. 1 sunt), fcroo ot«t p^<br />
xat''w. 19. xoyiOii] om. p. 23. Ante HZ@ del. H@Z p.<br />
24. Y.ui] om. Wp, corr. Halley; <strong>quae</strong> Comm. 25. sariv W.
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