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

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CONICORUM LIBER III. 359<br />

est autem AZZ= ^ZT [prop. IV] et [prop. YII]<br />

nOAI = KPlElA', quare etiam<br />

AZ'^ :ATZ = HAXAI: P^AK.<br />

est autem ATZ:Z^^ = Pl^AK :<br />

MA<br />

X A^. ergo<br />

etiam ex aequo [Eucl. V^ 22^]<br />

AZ^:ZA^ = HAXAI:MAXAB.<br />

XX.<br />

Si duae rectae oppositas contingentes concurrunt,<br />

et per punctum concursus recta ducitur rectae puncta<br />

contactus coniungenti parallela <strong>cum</strong> utraque sectione<br />

concurrens, et alia quoque recta eidem parallela ducitur<br />

et sectiones et contingentes secans, erit, ut<br />

rectangulum rectis<br />

a puncto concursus ad sectiones adcidentibus<br />

comprehensum ad quadratum contingentis, ita<br />

rectangulum comprehensum rectis inter sectiones<br />

ducatur BZS, et<br />

contingentemque<br />

positis ad quadratum<br />

rectae ad punctum<br />

contactus<br />

abscisae.<br />

sint oppositae AB, Fzf,<br />

& quarum centrum sit E^ contingentes<br />

autem AZ, FZ,<br />

ducaturque AF et EZ, AE<br />

et producantur, per Z autem<br />

rectae AF parallela<br />

sumatur quoduis punctum K, et per<br />

id rectae AF parallela ducatur KAUMN^, dico,<br />

esse BZXZ^ :<br />

ZA^<br />

= KAxA^:A 4\<br />

ducantur enim a. K, B rectae AZ parallelae KH^<br />

BP. iam quoniam est<br />

In fig. pro K (Yp) posuerunt H Memus aliique.

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