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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353314Apollonij Pergæi
SECTIO SEXTA
Continens Propoſit. XXXIII. XXXIV.
XXXV. & XXXVI.
PROPOSITIO XXXIII.
A Xis inclinatus ſi non fuerit minor dimidio ſui erecti, vti-
que eius erectus minor eſt erecto cæterarum diametrorum
inclinatarum eiuſdem ſectionis, &
axi proximioris inclinati ere-
ctus minor eſt, quàm erectus remotioris.
XXXV. Et ſi ſuerit axis inclinatus minor dimidio erecti, vti-
que ad vtraſque eius partes cadent duæ inclinatæ, quarum quæ-
libet æqualis eſt ſemiſſi erecti ipſius, atque eius erectus minor
eſt erecto cuiuslibet inclinati ad vtraſque partes eius poſitæ, &

erectus proximioris minor eſt erecto remotioris.
In hyperbole A B N ſint A C,
418[Figure 418] I L, P Q, S T diametri inclinatæ,
&
A F ſit erectus ipſius A C, I
K ipſius I L, P R ipſius P Q, &

S Z ipſius S T:
ſitquè axis A C
non minor medietate ipſius A F.
Dico, quod A F minor eſt, quàm
I K, &
I K minor quàm P R, &
P R minor quàm S Z.
Educantur
C B parallela I L, &
C N ipſi P
Q &
C X ipſi S T: & ducantur
B E, N M, X V perpendiculares
ad axim C A E.
Quoniam ſi A C
æqualis eſt ipſi A F, etiam I L æ-
qualis eſt ipſi I K (21.
ex 7.) &
P Q ipſi P R;
eſtque A C minor
11ex 38
lib. 5.
quam I L, &
I L, quàm P Q;

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