Apollonii Pergaei quae graece exstant cum ... - Wilbourhall.org
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Apollonii Pergaei quae graece exstant cum ... - Wilbourhall.org

Apollonii Pergaei quae graece exstant cum ... - Wilbourhall.org Apollonii Pergaei quae graece exstant cum ... - Wilbourhall.org

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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.

EUTOCII COMMENTARIA IN CONICA. 213<br />

rectae NK parallela ducatur PU, esse P2J > ^71<br />

et ideo PU > HK, sin inter if , IHI punctum sumatur<br />

uelut r, et per id parallela ducatur TT, esse<br />

TT < Sn et rr < KH. et quoniam est<br />

/. SHK > ASn,<br />

et /. OUK = OH^, erit etiam L OHS > HlSlO. itaque<br />

SO > OH [Eucl. I, 19] et ideo etiam KO > 077.<br />

et si quando altera diametrorum in duas partes<br />

aequales diuisa erit, reliqua in partes inaequales secabitur.<br />

Ad prop. VI.<br />

Animaduertere oportet, non sine causa in propositione<br />

adiici [I p. 20, 12 sq.], rectam a puncto in<br />

superficie posito parallelam ductam rectae alicui iu<br />

basi positae omnino rectae ad basim trianguli per<br />

axem positi perpendiculari parallelam duci oportere;<br />

nam si hoc non ita est, fieri non potest, ut a triangulo<br />

per axem posito in duas partes aequales secetur;<br />

quod in figura in uerbis <strong>Apollonii</strong> posita adparet.<br />

nam si MN, cui parallela est ^ZH, ad rectam BF<br />

perpendicularis non est, adparet, ne KA quidem in<br />

duas partes aequales secari. et eadem ratione concludimus,<br />

esse K®:@A = AZ : ZH [I p. 22, 20 sq.].<br />

ergo etiam z/H in Z in partes inaequales secabitur.<br />

fieri<br />

autem potest, ut et infra circulum et in superficie<br />

ad uerticem posita idem demonstretur.<br />

corr. Comm. 9. HSO] NSO p. 10. KO] SIO Halley<br />

<strong>cum</strong> Comm. 15. iv] i Wp. 20. sotlv W. 28. dsL- e<br />

corr. p.

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