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

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CONICORUM LIBER IV.<br />

11.<br />

Haec quidem communiter in omnibus sectionibus<br />

lemonstrantur, in hyperbola autem sola hocce:<br />

si z/5 contingit, ^F autem in duobus punctis E, F<br />

et puncta Ej F punctum contactus B continent, et<br />

iecat,<br />

mnctum zJ intra angulum ab asymptotis comprehenjum<br />

positum est, demonstratio similiter conficietur;<br />

nam fieri potest, ut a z/ puncto aliam rectam contingentem<br />

zlA ducamus et<br />

similiter<br />

conficiamus.<br />

IIL<br />

reliquam demonstrationem<br />

lisdem positis puncta Ej T punctum contactus B<br />

IV.<br />

inter se ne contineant,<br />

punctum autem z/ intra<br />

angulum ab asymptotis<br />

comprebensum positum<br />

sit. itaque fieri potest,<br />

ut a z/ aliam contingentem<br />

ducamus ^A et<br />

reliqua similiter demonstremus.<br />

lisdem positis si puncta concursus E, F punctum<br />

contactus B continent, zJ autem punctum in angulo<br />

positum est, qui angulo ab asymptotis comprelienso<br />

deinceps positus est, recta a puncto contactus ad<br />

punctum diuisionis ducta <strong>cum</strong> sectione opposita concurret,<br />

et recta a puncto concursus ducta oppositam<br />

continget.

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