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. 47 XXIX. lam uero F inter puncta contactus positum sit, in tertia figura. manifestum est, lineas in F inter se non contingere; nam suppositum est, eas in duobus solis contingere. secent igitur in JT, ducanturque sh Ay B contingentes Aji, AB, et ducatur AB seceturque in Z in duas partes aequales; itaque recta ah A a.d ut Z ducta diametrus erit [II, 29]. iam per F non ueniet; nam si ueniet, recta per F rectae AB parallela ducta utramque sectionem continget [II, 5— 6]; hoc autem fieri non potest. ducatur igitur a F rectae AB parallela FKHM] erit igitur [I def. 4] in altera sectione FK = KH, in altera autem KM == KR quare etiam KM = KH] quod fieri non potest. similiter autem etiam, si rectae contingentes parallelae sunt, eodem modo, quo supra, demonstrabimus fieri non posse. XXX. Parabola parabolam non continget in pluribus punctis quam in uno. nam si fieri potest, parabolae AHB^ AMB in Aj B contingant, ducanturque contingentes AA, AB\ eae igitur utramque sectionem contingent et in A concurrent. ducatur AB et in Z in duas partes aequales secetur, ducaturque AZ, quoniam igitur duae lineae AHBf AMB inter se contingunt in duobus punctis positiones XXV et XXVI in binas diuidamus, 7tQ0ELQ7i[i£va} piop. XXVI p. 44, 2. obstat uocabulum
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