Full text: Pergaeus, Apollonius: Apollonii Pergaei Conicorvm Lib. V. VI. VII. paraphraste Abalphato Asphahanensi

Quia C G ad A G, nempe quadratum A C ad ſuam figuram in ma-
iori, & in figura ſecunda ellipſi in minori proportione, & c. Ideſt. In,
prima, & ſecunda figura hyperboles,
& in prima figura ellipſis habet C G ad
G A maiorem proportionem, quàm ad
G E, eo quod G E maior eſt, quàm G
A: at in ſecunda figura ellipſis propor-
tio minor eſt; quia G E minor eſt, quã
A G. Propoſitum verò aliter oſtendetur
hac ratione.

296.1.

c
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Quoniam ex demonſtratis in nota
propoſit. 27. in hyperbola, atquè ex
propoſitione 11. libri quinti in ellipſi
erit axis minor, & rectus Q R minor
diametro recta N O, & N O minor
remotiore V X, ideoquè quadratum Q
R minus erit quadrato N O, & qua-
dratum N O minus quàm quadratum
V X : eſt verò figura, ſeu rectangulum
C A F ſub extremis contentum ęquale
quadrato Q R ex media proportionali
inter illas deſcriptum: pariterquè re-
ctangulum L I K ęquale eſt quadrato
diametri ei coniugatę N O, nec non,
rectangulum T S Z ęquale erit qua-
drato V X, ergo rectangulum C A F
minus eſt rectangulo L I K, atque rectangulum L I K minus eſt rectangulo T
S Z. E contra in ellipſi ſecunda. Quia. Q R maior eſt, quàm N O, & hęc
maior, quàm V X ; ergo rectangulum C A F maius eſt rectangulo L I K, & hoc maius erit rectangulo T S Z.

296.1.

15. lib. 1.
0347-02

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