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

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CONICORUM LIBER III. 321<br />

iam quoniam AZ ordinate ducta est, et AT contingit,<br />

erit ZHxHr^^BH^ [I, 37]. itaque<br />

7r ZH:HB = BH:Hr<br />

J<br />

[Eucl. VI, 17]; quare etiam<br />

ZH:Hr=:ZH^:HB^<br />

[Eucl. V def. 9].<br />

est autem<br />

ZH^:HB^= AHZ:^HB<br />

[Eucl. VI, 19],<br />

et<br />

ZH:Hr^AHZ:AHr<br />

[Eucl. VI, 1].<br />

quare etiam<br />

AHZ:AHr=AHZ:^HB.<br />

itaque AHF = AHB [Eucl. V, 9]. auferatur, quod<br />

commune est, AHFE] reliquum igiiur AE^ = FEB.<br />

II.<br />

lisdem suppositis si in sectione uel ambitu circuli<br />

punctum aliquod sumitur, et per id rectae contingentibus<br />

parallelae ducuntur usque ad diametros, quadrangulus<br />

ad alteram contingentium alteramque diametrorum<br />

ortus aequalis erit triangulo ad eandem contingentem<br />

alteramque diametrum orto.<br />

sit enim AB coni sectio uel ambitus circuli contingentesque<br />

AEF^ BEA^ diametri autem ^^, BFy<br />

Apollonius, ed. Heiberg^ 21

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