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. 45 XXVII. 1) Si quae lineamm, quas antea diximus, in duobus punctis inter se contingunt, in alio puncto inter se non concurrunt. nam ex lineis, quas diximus, duae inter se in duobus punctis contingant A, B. dico, eas in alio puncto inter se non concurrere. nam si fieri potest, etiam in F concurrant, et F prius extra puncta contactus ^, B positum sit, ducanturque ab ^, 5 contingentes; contingent igitur utramque lineam. contingant et concurrant in A, ut in prima figura, ducaturque FA] ea igitur altera sectione [III, 37] FA : autem FA : utramque sectionem secabit. secet in H, M, et ducatur ANB. itaque erit in AH= FN: NH, in altera AM = FN: NM] quod absurdum est. XXVIII. Sin FH rectis in A, B contingentibus parallela est, ut A in ellipsi in secunda figura, ducta^5 concludemus, eam diametrum esse sectionum [II, 27]. quare utraque JTif, FM in N in binas partes aequales secabitur [I def. 4] quod absurdum est. ergo m lineae in nullo alio puncto concurrent, sed in solis A, B. B 1) Hanc propositionem in tres diuisi, ut numerus XLIII S apud Eutocium suae responderet propositioni; nam ne prok
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