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Apollonii Pergaei quae graece exstant cum ... - Wilbourhall.org

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CONICORUM LIBER IV. 63<br />

hyperbolam ABF ne <strong>cum</strong> E quidem opposita concurrit.<br />

ergo ne E quidem <strong>cum</strong> Z concurret.<br />

XLII.<br />

Si hyperbola <strong>cum</strong> utraque opposita concurrit, sectio<br />

ei opposita <strong>cum</strong> neutra oppositarum in duobus<br />

punctis<br />

concurret.<br />

sint oppositae A^ B, et hyperbola AFB <strong>cum</strong> utraque<br />

opposita Aj B concurrat. dico, sectionem hyperbolae<br />

AFB opposi-<br />

7B tam <strong>cum</strong> sectionibus<br />

Aj B in duobus punctis<br />

non concurrere.<br />

nam si fieri potest,<br />

concurrat in A^<br />

E, et ducta AE producatur.<br />

proptersectionem<br />

AE igitur recta AE <strong>cum</strong> sectione AB non<br />

concurret [II, 33], propter AEA autem <strong>cum</strong> B non<br />

concurret; nam per tria illa loca [II, 33] ueniet; quod<br />

fieri non potest. eodem modo demonstrabimus, eam ne<br />

<strong>cum</strong> B quidem sectione in duobus punctis concurrere.<br />

iam eadem de causa ne continget quidem utramque<br />

sectionem. ducta^) enim ®E utramque sectionem<br />

continget; quare propter sectionem AE <strong>cum</strong> AF non<br />

coDCurret, propter AE autem <strong>cum</strong> B non concurrit<br />

[II, 33]. ergo ne AF quidem <strong>cum</strong> B concurrit; quod<br />

contra hypothesim est.<br />

1) Anacolutliia foeda et (isv superfluum lin. 19 significant,<br />

aliquid turbatum esse.

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