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-
22a43[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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