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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CMDNICORUM LIBER IV. 69 XLV. Si hyperbola cum altera oppositarum in duobus punctis concurrit concaua ad easdem partes babens, cum altera autem in uno, sectio ei opposita cum neutra oppositarum concurret. sint oppositae AB^ F, et hyperbola AFB cum AB in A, B concurrat, cum F autem in uno jT, sitque sectioni AFB opposita z/. dico, z/ cum neutra oppositarum ABy r concurrere. ducantur enim AF, BV et producantur. itaque AFj BF cum sectione z/ non concurrent [II, 33]. uerum ne cum F quidem sectione in alio puncto con- ^ currunt, cum opposita AB non concurrent [11, 33]; ^. current ac r. nam si in alio quoque puncto con- at supposuimus, eas cum illa concurrere. itaque rectae AFj BF cum sectione F in uno puncto F concurrunt, cum z/ autem sectione prorsus non concurrunt. quare z/ in angulo EFZ posita est. ergo sectio z/ cum ABy r non concurret. XLYL Si hyperbola cum altera oppositarum in tribus punctis concurrit, sectio ei opposita cum altera op- • positarum non concurret nisi in uno puncto. sint oppositae ABF, ^EZ, et hyperbola AMBF cum ABF in tribus punctis Ay B, F concurrat, sit autem sectioni AMF opposita JEK. dico, AEK cum ^EZ non concurrere in pluribus punctis quam in uno. nam si fieri potest, concurrat in z/, Ej ducanturque AB, AE.
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