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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170132Apollonij Pergæi angulo D B E; cadit verò F E infra rectam B E, quam ſecat in E, propter
curuitatem ſectionis F E B; igitur angulus D E F obtuſus quoque erit, & an-
gulus D F E acutus; & propterea recta linea D E minor erit, quàm D F; ea-
dem ratione oſtendetur D F minor, quàm D A.

Notæ in Propoſit. XXXIX.

ALioquin ſecet illam, & ſecemus ex,

168[Figure 168]& D G intra ſectionem, & c. Si e-
nim recta F D non contingit ellipſim A B,
ſecet eam ſi fieri poteſt in D: quare F D pro-
ducta in directum cadet intra ſectionem, &
in producta recta linea F D G ſumatur quod-
libet punctum G dummodo intra ſectionem
exiſtat, & per G ad concurſum C coniunga-
tur recta linea G C, quæ producta occurrat
ſectioni in B: & quia ex hypotheſi recta F
D G perpendicularis erat ad maximum ramum D C, ergo in triangulo D G C
rectangulo erit hypothenuſa G C maior quàm D C, & ideo B C multo maior
erit quàm D C; quod eſt abſurdum, ſuppoſita enim fuit D C omnium maxima
earum, quæ ex C ad ſectionem A B duci poſſunt.

Notæ in Propoſit. XXXXVIII.

ALioquin occurtant in O, quia iſtæ

169[Figure 169] lineæ ſunt maximæ, & c. Secant e-
nim lineæ maximæ ſemiaxim maiorem D A
in punctis M, N, & L: & ſiquidem tres li-
neæ maximæ conueniunt in vnico puncto O,
erunt ſegmenta inter axim maiorem, & ſe-
1132. buius. ctionem intercepta, nimirum M K, N H, L
F lineæ breuiſſimæ; quarum duæ quæquè L
F, N H educuntur ab eodem puncto concur-
ſus O: igitur (ex 54. 55. huius) tertius ra-
mus O K ab eodem concurſu O eductus non erit breuiſecans; quod eſt contra
hypotheſim.

LIBRI QVINTI FINIS.

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