Apollonii Pergaei quae graece exstant cum ... - Wilbourhall.org
Apollonii Pergaei quae graece exstant cum ... - Wilbourhall.org Apollonii Pergaei quae graece exstant cum ... - Wilbourhall.org
252 COMMENTARIA ANTIQUA. rsQct tov /i ioxiv ri i%\ xov z/ ij avcoxeQco tov z/, xcil dLCi tovto to ® b^oCcog avta XQstg €%sl toTtovg, xal 7tQo6sxtsov, ort, sl'ts aaxcJXSQCJ 7Cs0r] xb Z xov z/, Kal tb @ tov r s6tav natcotsQCj^ shs tb Z snl tb z/, 5 Kal tb ® s%l tb JT, sits dvcotsQco tb Z rov z/, zal xb rov r s0tai dvatsQco. Eig tb ^a'. Tb d^scoQfj^a tovto sscl iisv tijg vTCSQ^okrjg 7ttco6iv ovx ^xsc, STcl ds tijg iXXsc^scog, idv rj Katayo^svrj ijcl 10 ro xsvtQOv TCLJCtrj^ td ds XoiTcd ysvrjtaL td avtd, tb djcb xrjg xaxrjy^svrjg sldog l'6ov sCxac xa ditb trig ix tov xsvtQOv sfdsL, s6tco ydg sllsLtpcg, rjg dLa^stQog rj AB^ ksvxqov xb z/, xal xatriid-co xsxay^svcog rj Pzf, zal dvays- 15 yQd(p^co d%b xs trjg JTz/ xal trjg AJ sfdrj laoycovLa td AZ, AH, ixstco ds rj z/P %Qbg FH tbv 6vyxsLlisvov loyov sx ts tov. ov s%sl r\ A^ %Qbg z/Z xa\ rot; ov sxsL rj CQ^Ca %Qbg trjv %XayCav. Xsyco, otL tb AZ l'6ov i6t\ ta /IH. 20 i%s\ ydQ iv tc5 Qrjxci dsdsLXxaL, (Dg xb d%b AA %Qbg tb AZ^ ovtcog tb v%b AAB %Qbg tb zJH, (pi^uC, oxL xa\ ivaXXd^, G)g xb d%b Azi %Qbg xb v%b AAB^ ovxcog xb AZ %Qbg tb z/i/. l0ov ds tb d%b A/d t(p v%b A^B' l'6ov aQa xa\ tb AZ ta zlH 25 ECg ro fip\ Tb d^scoQrj^a tovto s^sl %xco6SLg Td, ^Cav fisv, sl i6coxsQco kaii^dvoLXO xb z/ rot» F" drjXov yaQ, oxl xa\ 6. dvcotsQco] corr. ex avoTsgco W. 10, ninxTi^ ra] in ras. W. 13. diaftfT^og] corr. ex didfistQov W, comp. p. KSVTQOV de Halley. 16. JH, AZ Comm. 18. ov] in
EUTOCII COMMENTARIA IN CONICA. 253 et animaduertendum est, siue Z infra z/ cadat, etiam ® infra F positum esse, siue in z/ cadat Z, etiam in JT, siue Z supra Zl, etiam supra F positum esse.^) Ad prop. XLI. Haec propositio in hyperbola casum non habet, in ellipsi autem, si recta ordinate ducta in centrum cadit, reliqua autem eadem fiunt, figura in recta ordinate ducta descripta aequalis erit figurae in radio descriptae. sit enim ellipsis, cuius diametrus sit AB, centrum z7, et ordinate ducatur Fz/, describanturque et in r^ et in AJ figurae dico, esse AZ = JH, aequiangulae AZ, AH, habeat autem ziriFH rationem compositam ex ratione AA: z/Z et ea, quam babetlatus rectum adtransuersum. nam quoniam in uerbis Apollonii [I p. 126, 7 — 8] demonstratum est, dico, etiam permutando esse esse A^^:AZ = AJxJB:zlHy AA^ :AAXAB = AZ: AH. uerum AA'^ = AA X AB\ ergo etiam AZ = AH Ad prop. XLII. Haec propositio XI casus habet, unum, si A intra T sumitur; manifestum enim, etiam parallelas intra 1) Quia ZH : Hr= Hr: H@ et HT = HJ. ras. W. 19. lartV W. 21. ovtoj p. 23. ovtco p. t6 JH. i'aov 8s] bis W. 24. AZ'] JZ Wp, corr. Comm.
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252 COMMENTARIA ANTIQUA.<br />
rsQct tov /i ioxiv ri i%\ xov z/ ij avcoxeQco tov z/,<br />
xcil dLCi tovto to ® b^oCcog avta XQstg €%sl toTtovg,<br />
xal 7tQo6sxtsov, ort, sl'ts aaxcJXSQCJ 7Cs0r] xb Z xov z/,<br />
Kal tb @ tov r s6tav natcotsQCj^ shs tb Z snl tb z/,<br />
5 Kal tb ® s%l tb JT, sits dvcotsQco tb Z rov z/, zal<br />
xb rov r s0tai dvatsQco.<br />
Eig tb ^a'.<br />
Tb d^scoQfj^a tovto sscl iisv tijg vTCSQ^okrjg 7ttco6iv<br />
ovx ^xsc, STcl ds tijg iXXsc^scog, idv rj Katayo^svrj ijcl<br />
10 ro xsvtQOv TCLJCtrj^ td ds XoiTcd ysvrjtaL td avtd, tb<br />
djcb xrjg xaxrjy^svrjg sldog l'6ov sCxac xa ditb trig ix<br />
tov xsvtQOv sfdsL,<br />
s6tco ydg sllsLtpcg, rjg dLa^stQog rj AB^ ksvxqov<br />
xb z/, xal xatriid-co xsxay^svcog rj Pzf, zal dvays-<br />
15 yQd(p^co d%b xs trjg JTz/ xal trjg AJ sfdrj laoycovLa<br />
td AZ, AH, ixstco ds rj z/P %Qbg FH tbv 6vyxsLlisvov<br />
loyov sx ts tov. ov s%sl r\ A^ %Qbg z/Z xa\<br />
rot; ov sxsL rj CQ^Ca %Qbg trjv %XayCav.<br />
Xsyco, otL tb AZ l'6ov i6t\ ta /IH.<br />
20 i%s\ ydQ iv tc5 Qrjxci dsdsLXxaL, (Dg xb d%b AA<br />
%Qbg tb AZ^ ovtcog tb v%b AAB %Qbg tb zJH, (pi^uC,<br />
oxL xa\ ivaXXd^, G)g xb d%b Azi %Qbg xb v%b AAB^<br />
ovxcog xb AZ %Qbg tb z/i/. l0ov ds tb d%b A/d t(p<br />
v%b A^B' l'6ov aQa xa\ tb AZ ta zlH<br />
25 ECg ro fip\<br />
Tb d^scoQrj^a tovto s^sl %xco6SLg Td, ^Cav fisv, sl<br />
i6coxsQco kaii^dvoLXO xb z/ rot» F" drjXov yaQ, oxl xa\<br />
6. dvcotsQco] corr. ex avoTsgco W. 10, ninxTi^ ra] in<br />
ras. W. 13. diaftfT^og] corr. ex didfistQov W, comp. p.<br />
KSVTQOV de Halley. 16. JH, AZ Comm. 18. ov] in
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