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

341. Notæ in Propoſit. XXXXX.

SI hyperbole axis A C minor fuerit eius erecto A F, quia H M maior eſt,
quàm H E, & punctum H cadit inter D, & A, ergo H M ad H D ma-
iorem proportionem habebit, quàm H E ad eandem H D, & comparando ante-
cedentes ad terminorum ſummas H M ad M D maiorem proportionem habebit,
quàm H E ad E D, quare differentia quadratorum ex P Q, & ex P R minor
erit, quàm differentta quadratorum ex I L, & ex I K, ſeu minor quàm dif-
ferentia quadratorum ex A C, & ex A F.

341.1.

0405-01
Lem. 17.
huius.

Poſtea, quia vt in precedenti nota dictũ eſt, differentia quadrati A C à rectan-
gulo C A F ad ſemidifferentiã quadratorũ ex I L, & ex I K eandem proportionẽ
habet, quàm rectangulum E H G ad rectangulum ſub E D, & ſub G H, eſt-
que illud rectangulum minus rectangulo iſto æquè alto, (cum illius baſis E H
minor ſit, quàm E D), igitur differentia quadrati A C à rectangulo C A F
minor eſt, quàm ſemidifferentia quadratorum ex I L, & ex I K.

342. Notæ in Propoſit. XXXXXI.

IN qualibet ellypſi ſit diameter a b æqualis eius erecto a c, eius latus erit C
D, & diametri I L, & P Q cadant inter A C, & a b, earum laterum

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