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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6628Apollonij Pergæi aut minor illa (7. ex quinto) eſ-
ſet linea breuiſſima A F, aut pars

41[Figure 41] illius, quod eſt falſum, igitur
maior eſt, quàm A C; & pro-
pterea A D ad A C maiorem
proportionem habet, quàm ad
A F; ponamus ergo, vt A D ad
A C, ita D G ad G F in hyper-
bola, & ellipſi; at in parabola
11b ponamus G F æqualem A C, &
ducatur ex G perpendicularis ad
ſectionem. Dico, quod ei oc-
curret ad B. Nam ſi occurrat
ſectioni ad aliud punctum, vt H co-

42[Figure 42] niuncta H F erit H F breuiſſima (8. 9.
10. ex quinto) ſed ſuppoſuimus B F eſſe
breuiſſimam, quod eſt abſurdum, ergo
perpendicularis occurrit ſectioni in B.
Et quia angulus B G F eſt rectus, erit
angulus B F G acutus, quod erat oſten-
dendum.

NOTÆ.

ET eius potentialis ſecet menſuram
in parabola, & c. Ideſt, & eius po-
22a

43[Figure 43] tentialis abſcindet ex menſura vſque ad originem,
in parabola quidem ſegmentum æquale compara-
tæ, & in hyperbola, & ellipſi lineam, ad quam
inuerſa eandem proporportionem habet, quam la-
tus tranſuerſum ad rectum.

Et ducatur ex G perpendicularis ad ſectio-
33b nem, & c. Et ducatur ex G recta linea perpendi-
cularis ad axim, & producatur vſque ad ſectio-
nem.

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