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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343304Apollonij Pergæi. libet caſu maior erit differentia I L, eiuſque erecti. Pari modo oſtende-
tur quod differentia ipſius I L, & eius erecti maior ſit differentia ipſius S
T, eiuſque erecti. Et hoc erat oſtendendum.

PROPOSITIO XXXVII.

In hyperbole differentia la-
terum figuræ axis inclinati
maior eſt differentia laterũ figu-
rę ſui homologi eiuſdẽ ſectionis:
& differẽtia laterum figuræ in-

399[Figure 399] clinati proximioris axi maior
eſt differentia laterum figuræ
inclinati ab illo remotioris.

In hyperbole A B P ſit axis C
A, & I L, S T ſit duæ aliæ dia-
metri, & centrum D; atque ere-
ctus ipſius A C ſit A F, & ipſius
I L ſit I K, atque ipſius S T ſit S
Z: & educamus C B, C P, pa-
rallelas duabus homologis diame-
tris I L, S T, & duas ad axim
perpendiculares B E, P M, ſece-
muſque duas interceptas C H, A
G, & ſit inclinatus A C in prima
figura maior, quàm A F, in ſecũ-
da verò minor. Et quoniam A C
ad A F ſupponitur vt H A ad A G

400[Figure 400]

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