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

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EUTOCII COMMENTARIA IN CONICA. 339<br />

est auteni etiam AUA : AA^ HK^<br />

VI, 22^]'^ itaque etiam ex aequo<br />

EA^ : AA^ = K®'- : HK\<br />

EA^ :<br />

= HKM :<br />

h. e.<br />

AA^ = ®KXKT: HK X KO.<br />

[Eucl.<br />

lisdem suppositis, si @KII siue recta rectae EA<br />

parallela ducta per K centrum cadit, HO autem non<br />

per centrum, dico, sic quoque esse<br />

EA^<br />

: AA^<br />

EA^ :<br />

= @^ X ^77 : ifS X ^O.<br />

EAT==<br />

HK^ :<br />

ducantur enim per O, IJ<br />

contingentibus parallelae OP^<br />

nU.<br />

quoniam igitur<br />

MOP = MNK + AKT<br />

et<br />

KZn=AKT [III, 15],<br />

erit<br />

MOP = MNK + KZU',<br />

quare reliquum^) quadrilaterum<br />

^P = IHIU.<br />

et quoniam<br />

est<br />

KZH<br />

= KlHl^ : KlHjN<br />

[Eucl. VI, 22], erit [Eucl. V, 19]<br />

EA^ :EAT=®;s!xSn:;slP [Eucl. II, 5].<br />

et A0A = EAT [III, 4], SP= ^2:; itaque<br />

EA^ : AA0 = 0^ X ^77 : ^2;.<br />

In fig. litt. J, H, & om. W, pro N hab. H.<br />

1) Ablatis triangulis MKN + KN iSl.<br />

oportuit. 17. iGtLv W. EA2 p 20. t6 (pr.)] ra Wp,<br />

corr. Halley <strong>cum</strong> Comm. x6 (sec.)] xa. Wp, corr. Halley<br />

<strong>cum</strong> Comm. >^2;] ElEl p.<br />

22*

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