11.01.2015 Views

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

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

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

SHOW MORE
SHOW LESS

You also want an ePaper? Increase the reach of your titles

YUMPU automatically turns print PDFs into web optimized ePapers that Google loves.

CONICORUM LIBER IV. 79<br />

tes aequales diuidens sectiones in S^ O secet, sectionesque<br />

contingentes ab S, O ducantur SII, OP. erit<br />

igitur [II, 5; Eucl. VI, 4] AU^ : nS'<br />

= ^P'' : PO',<br />

quare [III, 19]<br />

^NX NTiENxNZ = BNxNr-.ENxNZ.<br />

ergo ^NxNr= BNxNr [Eucl. V, 9]; quod<br />

fieri<br />

non potest.<br />

L.<br />

Si hyperbola alteram oppositarum in uno puncto<br />

contingit^), sectio ei opposita <strong>cum</strong> altera oppositarum<br />

in pluribus punctis non concurret quam in duobus.<br />

sint oppositae ABj EzlHj et hyperbola ^T sectionem<br />

AB m A contingat, sitque sectioni AF op-<br />

1) Sc. ad easdem partes concaua habens; cf. prop. LIV.

Hooray! Your file is uploaded and ready to be published.

Saved successfully!

Ooh no, something went wrong!