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. 63 hyperbolam ABF ne cum E quidem opposita concurrit. ergo ne E quidem cum Z concurret. XLII. Si hyperbola cum utraque opposita concurrit, sectio ei opposita cum neutra oppositarum in duobus punctis concurret. sint oppositae A^ B, et hyperbola AFB cum utraque opposita Aj B concurrat. dico, sectionem hyperbolae AFB opposi- 7B tam cum sectionibus Aj B in duobus punctis non concurrere. nam si fieri potest, concurrat in A^ E, et ducta AE producatur. proptersectionem AE igitur recta AE cum sectione AB non concurret [II, 33], propter AEA autem cum B non concurret; nam per tria illa loca [II, 33] ueniet; quod fieri non potest. eodem modo demonstrabimus, eam ne cum B quidem sectione in duobus punctis concurrere. iam eadem de causa ne continget quidem utramque sectionem. ducta^) enim ®E utramque sectionem continget; quare propter sectionem AE cum AF non coDCurret, propter AE autem cum B non concurrit [II, 33]. ergo ne AF quidem cum B concurrit; quod contra hypothesim est. 1) Anacolutliia foeda et (isv superfluum lin. 19 significant, aliquid turbatum esse.
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62 KSiNIKSiN d'.<br />
dia tr^v ABF vtcsq^oXtiv ovda rfj E avvLxeL^EVfj Cv^-<br />
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7Cs0straL Tcara dvo 0rj^sta.<br />
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