Apollonii Pergaei quae graece exstant cum ... - Wilbourhall.org
Apollonii Pergaei quae graece exstant cum ... - Wilbourhall.org Apollonii Pergaei quae graece exstant cum ... - Wilbourhall.org
212 COMMENTARIA ANTIQUA. olrj tj HK TTi iBln. xal cpavsQov, ott, iccv ^sta^v tcov N, lEl Xrjq^d^rj ti arj^stov ms tb P, xal dca toi; P tij NK TtagaXXrjXog dx^^fj rj PU, ^sc^idv eatat trjg IHUI xal dva tovto xal trjg HK, iav ds ^sta^v tSv H, IS 5 Xrjg^d^rj ti arjnstov olov t6 T, zal dt' avtov Ttagdlkrikog dx%-ri rj TT, ikdttcov satai tijg ^H Tcal trjg KH. xal ijtsl rj vtco SHK yovCa ^sl^cov iatl trjg vito ASn, lari dl ri vTcb OHK trj vnb OHIS;, ^SLtcav aga xal rj v%b OHlSl trjg vnb HlElO. ri ^O dga trjg 10 OH ^st^cov xal dtd tovto xal r} KO tfjg OH. idv dd TCots rj stsQa avtc5v dcxcc diaLQsd^fj, rj XoLTtij sig dviaa t^rjd^ijastaL. Eig tb g\ HQoasxsLv XQV^ ort ov ^dtrjv TtQoaxsLtaL iv tfj 15 TtQotdasL to dstv trjv dyo^svrjv svd^stav dnb toij iv trj iTtifpavsCa arjfisCov TtaQdXkrjkov ^La tLVt tmv iv tij pdasL svd^SLCOv nQog oQd^dg ovar] Ttdvtcag tfj ^dasi tov dLa toi) d^ovog tQLycovov dysa^aL TtaQdXXrjXov tovtov yaQ iirj ovtog ov dvvatov iatLV avtr]v dCxa ts^i- 20 vsad^aL vjtb toij dcd rov d^ovog tQLyoovov OTtSQ iatl (pavsQov ix trjg iv tco Qrjta KatayQa(pijg. sl yaQ rj MN, xitLVL TCaQdkXrilog iatLv rj ziZH, [irj JtQog OQd^dg strj tfj 5Jr, drjkov^ otL ovds dC^a ti^vstaL ov8s rj KA. Ttal dLa rtov avt^v koycav avvdystaL, otL iatCv, 25 (og rj K& TCQog ®A, oijtcog rj z/Z jCQog ZH' xal rj ^H aQa slg dvLaa t^rj^rjastaL xatd ro Z. dvvatbv dh xatcDtsQG) tov xvxkov xal inl trjg xatd xoQvcprjv iTCLtpavsCag td avtd dsCxwad^aL. 7. SnX] n e corr. m. 1 W. iauv W. 8. OUK] O insert. m. 1 W. OH^] HIS p et ^a/ in ras. m. 1 W;
EUTOCII COMMENTARIA IN CONICA. 213 rectae NK parallela ducatur PU, esse P2J > ^71 et ideo PU > HK, sin inter if , IHI punctum sumatur uelut r, et per id parallela ducatur TT, esse TT < Sn et rr < KH. et quoniam est /. SHK > ASn, et /. OUK = OH^, erit etiam L OHS > HlSlO. itaque SO > OH [Eucl. I, 19] et ideo etiam KO > 077. et si quando altera diametrorum in duas partes aequales diuisa erit, reliqua in partes inaequales secabitur. Ad prop. VI. Animaduertere oportet, non sine causa in propositione adiici [I p. 20, 12 sq.], rectam a puncto in superficie posito parallelam ductam rectae alicui iu basi positae omnino rectae ad basim trianguli per axem positi perpendiculari parallelam duci oportere; nam si hoc non ita est, fieri non potest, ut a triangulo per axem posito in duas partes aequales secetur; quod in figura in uerbis Apollonii posita adparet. nam si MN, cui parallela est ^ZH, ad rectam BF perpendicularis non est, adparet, ne KA quidem in duas partes aequales secari. et eadem ratione concludimus, esse K®:@A = AZ : ZH [I p. 22, 20 sq.]. ergo etiam z/H in Z in partes inaequales secabitur. fieri autem potest, ut et infra circulum et in superficie ad uerticem posita idem demonstretur. corr. Comm. 9. HSO] NSO p. 10. KO] SIO Halley cum Comm. 15. iv] i Wp. 20. sotlv W. 28. dsL- e corr. p.
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212 COMMENTARIA ANTIQUA.<br />
olrj tj HK TTi iBln. xal cpavsQov, ott, iccv ^sta^v<br />
tcov N, lEl Xrjq^d^rj ti arj^stov ms tb P, xal dca toi; P<br />
tij NK TtagaXXrjXog dx^^fj<br />
rj PU, ^sc^idv eatat trjg IHUI<br />
xal dva tovto xal trjg HK, iav ds ^sta^v tSv H, IS<br />
5 Xrjg^d^rj ti arjnstov olov t6 T, zal dt' avtov Ttagdlkrikog<br />
dx%-ri rj TT, ikdttcov satai tijg ^H Tcal trjg KH.<br />
xal ijtsl rj vtco SHK yovCa ^sl^cov iatl trjg vito<br />
ASn, lari dl ri vTcb OHK trj vnb OHIS;, ^SLtcav<br />
aga xal rj v%b OHlSl trjg vnb HlElO. ri ^O dga trjg<br />
10 OH ^st^cov xal dtd tovto xal r} KO tfjg OH. idv<br />
dd TCots rj stsQa avtc5v dcxcc diaLQsd^fj, rj XoLTtij sig<br />
dviaa t^rjd^ijastaL.<br />
Eig tb g\<br />
HQoasxsLv XQV^ ort ov ^dtrjv TtQoaxsLtaL iv tfj<br />
15 TtQotdasL to dstv trjv dyo^svrjv svd^stav dnb toij iv<br />
trj iTtifpavsCa arjfisCov TtaQdXkrjkov ^La tLVt tmv iv tij<br />
pdasL svd^SLCOv nQog oQd^dg ovar] Ttdvtcag tfj ^dasi tov<br />
dLa toi) d^ovog tQLycovov dysa^aL TtaQdXXrjXov tovtov<br />
yaQ iirj ovtog ov dvvatov iatLV avtr]v dCxa ts^i-<br />
20 vsad^aL vjtb toij dcd rov d^ovog tQLyoovov OTtSQ iatl<br />
(pavsQov ix trjg iv tco Qrjta KatayQa(pijg. sl yaQ rj<br />
MN, xitLVL TCaQdkXrilog iatLv rj ziZH, [irj JtQog OQd^dg<br />
strj tfj 5Jr, drjkov^ otL ovds dC^a ti^vstaL ov8s rj<br />
KA. Ttal dLa rtov avt^v koycav avvdystaL, otL iatCv,<br />
25 (og rj K& TCQog ®A, oijtcog rj z/Z jCQog ZH' xal rj<br />
^H aQa slg dvLaa t^rj^rjastaL xatd ro Z.<br />
dvvatbv dh xatcDtsQG) tov xvxkov xal inl trjg<br />
xatd xoQvcprjv iTCLtpavsCag td avtd dsCxwad^aL.<br />
7. SnX] n e corr. m. 1 W. iauv W. 8. OUK]<br />
O insert. m. 1 W. OH^] HIS p et ^a/ in ras. m. 1 W;