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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278240Apollonij Pergæi

323[Figure 323] ad Z b, & ad Z a eſt eadem; & propterea Z b æqualis eſt Z a, quod eſt
abſurdum.

Ponamus iam quadratum F G ad G H in G I maiorem proportionem
habere, quàm D B ad B E. Dico in cono H F I exhiberi non poſſe ſe-
ctionem æqualem hyperbolæ A B. Si enim exhiberi poſſet illius axi ali-
qua parallela reperiretur vt F N: & quadratum F N ad I N in N H ma-
iorem proportionem habens, quàm quadratum F G ad quadratum G H,
erit vt D B ad B E; quæ minor eſt proportione quadrati F G ad qua-
dratum G H: quod eſt abſurdum. Non ergo reperitur in cono H F I ſe-
ctio æqualis hyperbolæ A B. Et hoc erat oſtendendum.

PROPOSITIO XXVIII.

SIt iam ſectio elliptica A B, cuius axis tranſuerſus B D, &
erectus illius B E, & circa coni triangulum H F I deſcri-
11a

324[Figure 324]

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