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

EDucamus itaque duas perpendiculares, & c. Educamus itaque ex pun-
11a ctis B, G duas G L, B I perpendiculares ad axim ei occurrentes in L, I.
Et LG maior eſt, quàm B I, & c. Subiungo: Eo quod potentialis G L ma-
22b gis recedit à vertice, quàm B I; ſi iam ducatur B M parallela axi in parabola,
& ex centro educta in reliquis ſectionibus, ſecans G L in M, coniungaturque H
M, erit in parabola M L minor quàm G L, & æqualis B I, & ideo angulus M
H L minor erit angulo G H L, & æqualis angulo F, & propterea angulus F mi-
nor eſt, quàm G H L.

45[Figure 45]

Si verò ſectio fuerit hyperbole, aut ellipſis, & c. Addo: Manifeſtum eſt
3331. lib. I.44C rectam B D ex centro ductam ſectionem ſecare in B, & propterea occurrere po-
tentiali G L à vertice remotiori, quàm B I inter puncta G, & L, & erit F I,
& cætera.

Erit ID ad LD, nempe B I ad M L, & c. Addo (propter parallelas B I,
55d M L, & ſimilitudincm triangulorum D B I, & D M L.)

Quia angulus A F B minor eſt, quàm angulus A H G, & c. Addo: Et
66e ſumpto communi angulo F H N erunt A F B, ſeu H F N, & F H N ſimul ſumpti
minores duobus angulis G H A, F H N, qui duobus rectis æquales ſunt; quare
B F, G H, concurrunt ad partes F, & H, vt in N.

Pro intelligentia ſequentium propoſitionum hæc præmitti debent.

LEMMA V.

Habeat A ad B maiorem proportionem, quàm C ad D. Dico, re-
ctangulum ſub extremis A, D contentum maius eſſe eo, quod ſub me-
dijs B, C continetur, & è conuerſo.

Flat vt C ad D, ita E ad B; patet ex elementis, A excedere ipſam E; qua-
re rectangulum A D maius erit rectangulo E D: eſt verò rectangulum

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