Apollonius <Pergaeus>, Apollonii Pergaei Conicorvm Lib. V. VI. VII. paraphraste Abalphato Asphahanensi : nunc primum editi ; additvs in calce Archimedis assvmptorvm liber, ex codibvs arabicis mss Abrahamus Ecchellensis Maronita latinos reddidit, Jo. Alfonsvs Borellvs curam in geometricis versione contulit & [et] notas vberiores in vniuersum opus adiecit

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406367Conicor. Lib. VII.
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-
479[Figure 479] iorem proportionem habebit, quàm H E ad eandem H D, &
comparando ante-
cedentes ad terminorum ſummas H M ad M D maiorem proportionem habebit,
11Lem. 17.
huius.
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.
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.
Notæ in Propoſit. XXXXXI.
IN qualibet ellypſi ſit diameter a b æqualis eius erecto a c, eius latus erit C
22ex Lem.
18. huius.
D, &
diametri I L, & P Q cadant inter A C, & a b, earum

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