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

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itaque<br />

2Nxnp=;e;nx nz [EucI. v, 9].<br />

CONICORUM LIBER I. 47<br />

et<br />

itaque<br />

est<br />

JK:KB = ZH:HB = ZN: NP [ib.].<br />

autem<br />

SZ:ZA = {&N: NU) X {ZN:NP).<br />

(®N:N2:) X (ZN: NP) = &NxNZ: UNx NP.<br />

quare<br />

®N X NZ :<br />

UN X NP = ®Z :<br />

ZA = @N :NS [ib.].<br />

ZN est<br />

sumpta autem communi altitudine<br />

®N : N^ = ®N X NZ : ZN X NS.<br />

quare<br />

etiam<br />

&NXNZ: 2JN X NP= @N X NZ :<br />

IHJNX NZ,<br />

demonstrauimus autem,<br />

itaque<br />

uerum<br />

etiam<br />

esse<br />

MN^^^UNXNP.<br />

MN^ = SNX NZ.<br />

;s;nxnz = ;s!z.<br />

ergo MN quadrata aequalis est rectangulo SZ, quod<br />

rectae ZA adplicatum est latitudinem habens ZN et<br />

excedens spatio AlHj simili rectangulo SZA. uocetur<br />

autem talis sectio hyperbola, AZ autem parametrus<br />

rectarum Sid ZH ordinate ductarum; uocetur autem<br />

eadem latus rectum, transuersum uero Z@.

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