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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13294Apollonij Pergæi

117[Figure 117] concur ſu E non exiſtente ſuper axim rectum minorem ellipſis A B C ducatur ad
ſectionem A B vnicus ramus vtrumque axim ſecans, cuius portio G I inter ſe-
ctionem, & axim maiorem A C intercepta ſit linea breuiſsima; vel ducatur præ-
ter E G alius ramus breuiſecans, menſuram tantummodo abſcindens; vtique,
ramorum ſecantium, ex illo concurſu egredientium, maximus erit ille, qui axim
rectum ſectionis diuidit, & c.

Erigamus itaque ſuper D perpendicularem, & c. Scilicet ex centro ſectio-
11b nis D eleuetur D B perpendicularis ad axim maiorem A C, occurrens ſectioni
in B, & ipſi E G in L, & propterea D B erit ſemiſsis recti axis, & punctum
E in axi B D non exiſtit ex hypotheſi, & c.

Quoniam non egreditur ex E niſi vnus breuiſecans, ergo lineæ breuiſsi-
22c mæ egredientes ab extremitatibus reliquorum ramorum, abſcindunt ab axi
cum A C, L A lineam maiorem, quàm ſecent illorum rami (51. 52. ex
5.) & iam patet, quod ſi ita ſe res habet L E C eſt acutus; quia E C
breuiſsima eſt linearum egredientium ex E ad quadrantem A B, & pro-
pinquior illi, minor eſt remotiore, & c. Sic legendum puto; Luia præter E
G, vtrumque axim ſecantem nullus alius breuiſecans duci poſſe à concurſu E ad
ſectionem ſupponitur, ergo lineæ breniſsimæ egredientes ab axtremitatibus reli-
quorum ramorum in quadrante C B abſcindunt ab axi A C cum vertice C li-
neas maiores, quàm ſecent rami (51 52. ex 5.) pariterque conſtat, quod an-
gulus E C F ſit acutus, atque ramus E C eſt minimus egredientium ex E ad qua-
3364. 65,
huius. drantem C B, & propinquior minimæ, minor eſt remotiore. Demonſtrandum,
modo eſt, quod K E maior quoque eſt, quàm E B, & c.

Producamus itaque M B, M K tangentes; ergo M B E eſt obtuſus, &
44d M K E eſt acutus (29. ex 5.) quia breuiſsima egrediens ex K abſcindit A
lineam minorem, quàm A E (57. ex 5.) eo quod K eſt inter duo ſegmen-
ta L B, L G: & iungamus M E; ergo duo quadrata M B, B E minora,
ſunt, quàm quadratum M E, quæ minora ſunt duobus quadratis M K,
K E, & c. Ideſt: ex punctis B, K ducantur duæ tangentes ſectionem M B, K

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