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

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CONICORUM LIBER 11. 227<br />

A contingens ducatur EZ productaque <strong>cum</strong> TX in T<br />

concurrat, et ducatur EX producaturque ad S*, et per<br />

X rectae EZ parallela ducatur Xif, per TL autem<br />

sectionem contingens ducatur @if.<br />

dico, esse 0if rectae<br />

XE parallelam et i/O, E% coniugatas esse diametros.<br />

ducantur<br />

enim ordinate KE, HAy TPn, parametri<br />

autem sint AM^ TN. iam quoniam est<br />

BA:AM=NT'.TA [I, 56],<br />

et BA'.AM=XKxKZ:KE^,<br />

NT:TA = HA^ :XAxA& [l, 37],<br />

erit etiam XK X KZ : EK^ = HA^ : XA<br />

uerum XKxKZ: KE^ = {XK : KE)<br />

et HA^ :<br />

itaque<br />

XA<br />

X A@.<br />

X (ZK : KE)<br />

X A& = (HA:AX)x(HA:A@),<br />

(XK : KE) X {ZK : KE) = (HA :AX)x {HA :<br />

[Eucl. 1, 29;<br />

A@).<br />

quarum rationum est ZK:KE = HA : AX<br />

YI, 4]; nam singulae EK, KZ, ZE singulis XA, AH,<br />

HX parallelae sunt [I def. 6]. itaque<br />

XK:KE=HA: A&.<br />

15*

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