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

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CONICORUM LIBER III. 327<br />

V.<br />

Si duae rectae oppositas contingentes inter se<br />

concurrunt, et in utraque sectione punctum aliquod<br />

sumitur, ab eoque duae rectae ducuntur altera contingenti<br />

parallela, altera rectae puncta contactus<br />

coniungenti parallela, triangulus ab iis ad diametrum<br />

per punctum concursus ductam effectus a triangulo<br />

ad punctum concursus contingentium absciso differt<br />

triangulo ad contingentem diametrumque per punctum<br />

contactus<br />

ductam absciso.<br />

sint oppositae A^ 5, quarum centrum sit F, et<br />

contingentes EJ^ AZ va. J concurrant, ducaturque<br />

EZ et r*^, <strong>quae</strong> producatur, et ZF, ET ductae producantur,<br />

sumaturque in sectione punctum aliquod<br />

i/, et per id ducatur ®HKA rectae EZ parallela,<br />

HM autem rectae z/Z parallela. dico, esse<br />

H@M= K&A + KAZ.<br />

quoniam enim demonstrauimus [II, 39 et 38], Pz/<br />

diametrum esse oppositarum, et EZ ad eam ordinate<br />

ducta est, et H& rectae EZ parallela, MH autem<br />

rectae ^Z parallela, erit [I, 45]<br />

ergo<br />

MH® = rA& + FAZ.<br />

MH@ = K®A + KZA.<br />

et manifestum est, esse KZA = MHKA.

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