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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6527Conicor. Lib. V.

Educamus itaque E A, & c. Lego: Educamus itaq; E A perpendicularem, &
11b æqualem A D.

Et perducamus ex G, H perpendiculares, & c. Et perducamus ex G, H
22c perpendiculares ad D A, & ſint H L N, & G I M, quæ ſecent F D in Q, & D
E in M, & N, atque à punctis Q, M educantur M P, Q O, parallelæ D A,
quæ ſecent rectum axem B D in O, P. Addidi hæc poſtrema verba, vt conſtru-
ctio completa ſit.

Eo quod I D eſt æqualis I M, & c. Quoniam ſicuti in triangulo D A E
33d ſimili triangulo D I M (propter angulum D communem, & rectos angulos ad I,
& A) latus D A æquale erat E A, ita latus D I æquale eſt I M.

Nempe M I ad I Q, & è contra, & c. Lego: Nempe M I ad I Q, & per
44e conuerſionem rationis.

Cumque B D ſit dimidium axis recti erit perpendicularis ad A D men-
55f ſuram, & c. Hæc verba poſtrema pariter expungi debent, niſi fortè corollarium
propoſitionis exponunt, & tunc textus ſic reſtitui deberet. Ex dictis conſtat, li-
neam breuiſsimam è centro ellipſis ad ſectionem ductam, perpendicularem eße
ad axim eius maiorem.

Manifeſtum eſt ex centro ellipſis ad ſectionem duci non poſſe plures, quàm
quatuor ramos inter ſe æquales, neque pauciores duobus; tres autem nequaquam;
nam duæ medietates cuiuslibet axis æquales ſunt inter ſe, & quatuor rami ad
extremitates duarum applicatarum ad axim æqualiter è centro diſtantium ducti
æquales ſunt inter ſe.

SECTIO SEXTA

Continens Propoſit. XIII. XIV. XV. Apollonij.

OStendamus modò cõ-
uerſum harum pro-

40[Figure 40] poſitionum; & eſt, quod li-
nea breuiſſima B F continet
cum ſua menſura A F angu-
lum acutum, vt B F A in
omnibus ſectionibus, & el-
lipſi (ſi tamen non egre-
diatur ex eius centro) eiuſ-
que potentialis abſcindet
menſuram (13) in parabola æqualem comparatæ (14) & in
66a hyperbola (15) & ellipſi lineam, ad quam inuerſa eſt, vt pro-
portio figuræ.

SIt centrum D, & dimidium erecti A C. Quia B F eſt linea breuiſſima,
erit A F maior quàm A C, eo quòd ſi eſſet æqualis (4. 6. ex

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