Apollonii Pergaei quae graece exstant cum ... - Wilbourhall.org
Apollonii Pergaei quae graece exstant cum ... - Wilbourhall.org Apollonii Pergaei quae graece exstant cum ... - Wilbourhall.org
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CONICORUM LIBER IV. 83 LL Si hyperbola utramque oppositam contingit, sectio ei opposita cum neutra oppositarum concurret. sint oppositae Aj By et hyperbola AB m Aj B utramque contingat, ei autem opposita sit E. dico, E cum neutra sectionum Ay B concurrere. ^ nam si fieri potest, cum A \n A concurrat, et ab Aj B rectae ducantur sectiones contingentes ; eae igitur intra asymptotas sectiouis AB inter se concurrent [11,25]. concurrant in Fy ducaturque Tz/; FA igitur in spatio inter AFj FB posito erit. uerum eadem inter BFj FZ^) cadet; quod absurdum est. ergo E cum A^ B non concurret. LIL Si utraque opposita utramque oppositam in singulis punctis contingit ad easdem partes concaua habens, in alio puncto non concurret. tnam oppositae in punctis A, A inter se concurant. dico, eas in nullo alio puncto concurrere. nam si fieri potest, concurrant in E. quoniam ^itur hyperbola alteram oppositarum in A contingens um ea in E concurrit, AB cum AF in pluribus lunctis non concurrit quam in uno [prop. XLIX]. ab 1) Quia ex II, 33 recta FB cum sectione Ad non concurrit, h. e. extra z/r, quae cum AJ concurrit, cadit. 6*
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SL yaQ dvvarov, 0v^7tL7irsrcj rrj A xard ro z/,<br />
10 Tial rii^co6av dito rcjv A, B s
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