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

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CONICORUM LIBER IV. 11<br />

sint oppositae B, & asymptotaeque KAj MSNj<br />

punctum autem z/ in angulo AI^N positum, ab eoque<br />

contingat JBy secet autem z/F, et puncta concursus<br />

Ej r punctum contactus B contineant, sit autem<br />

rZ:ZE = r^: /lE.<br />

demonstrandum, rectam a 5 ad Z ductam <strong>cum</strong><br />

sectione ® concurrere, rectamque a puncto concursus<br />

ad z/ ductam sectionem contingere.<br />

ducatur enim a ^ sectionem contingens z/0, et<br />

ducta SBj si fieri potest, per Z ne cadat, sed per H,<br />

itaque [III, 37] FA : ^E = rH: HE] quod absurdum<br />

est; supposuimus enim, esse FA : zIE = FZ : ZE.<br />

V.<br />

lisdem positis si z/ punctum in alterutra asymptotarum<br />

est,<br />

parallela<br />

erit.<br />

recta a 5 ad Z ducta eidem asymptotae<br />

supponantur enim eadem, et punctum z/ in alterutra<br />

asymptotarum MN sit. demonstrandum, rectam a B<br />

rectae MN parallelam ductam in Z cadere.

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