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

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CONICORUM LIBER IV. 21<br />

EZ et <strong>cum</strong> sectione opposita concurrere, et rectas a<br />

punctis concursus ad /1 ductas sectiones contingere.<br />

opposita<br />

igitur<br />

sit Mj et a<br />

zl<br />

sectiones contingentes<br />

ducantur<br />

z/ik/, ^E,<br />

ductaque MH, si<br />

fieri potest, per<br />

iC, A ne cadat,<br />

sed aut per alterutrum<br />

aut per<br />

neutrum eorum.<br />

prius per K cadat et rectam ZH m X secet. itaque<br />

[III, 37] Zz/ : JH=XZ<br />

:<br />

est; supposuimus enim, esse<br />

ZJ'.^H=ZA:AH<br />

XH, quod absurdum<br />

sin per neutrum punctorum K, A cadit MZy in<br />

utraque E/l, AZ absurdum euenit.<br />

XIIL<br />

lisdem positis si punctum A in alterutra asymptotarum<br />

positum est, et reliqua eadem supponuntur,<br />

recta per puncta diuisionis ducta parallela erit asymptotae,<br />

in qua punctum positum est, et producta <strong>cum</strong><br />

sectione concurret, et recta a puncto concursus ad<br />

punctum ducta sectionem<br />

sit<br />

continget.<br />

enim hyperbola asymptotaeque, et in alterutra<br />

asymptotarum sumatur A, producanturque rectae et<br />

diuidantur, sicut dictum est, a A autem sectionem

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