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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9759Conicor. Lib. V. mum E C nullus alius ramus breuiſecans ex concurſu E ad ſectionem duci poteſt,
qui cadat in eodem quadrante B L, quem breuiſecans interſecat.

Nam ſi producantur E H, E G, & c. Ducantur quilibet rami E H, E G ad
11h vtraſque partes breuiſecantis E C intra quadrantem B L, qui ſecent D B in K,
& I, & producatur per centrum D recta M D L perpendicularis ad axim B A,
quæ ſecet ſectionem in L, & ramum E C in M.

Et quia iam productæ ſunt ex concurſu M duæ breuiſecantes, & c.
22i Quia C M breuiſsima ex hypotheſi occurrit ſemiaxi minori recto L D breuiſsi-
mæ pariter (ex 11. huius) in M, ſequitur (non quidem ex 51. 52. huius, ſed
ex lemmate 8. præmiſſo) quod linea recta ex M ad H coniuncta cadat infra
breuiſsimam ex puncto H ad axim B A ductam, & coniuncta recta M G cadit
ſupra breuiſsimam ex puncto G ad axim ductam.

Sed E H, & E G efficiunt abſciſsas oppoſito modo, & c. Quia ab eodem
33k puncto H ſectionis ducuntur tres rectæ lineæ. H E, H M, & breuiſsima ex H ad
axim B A ducta, quarum intermedia eſt H M, eo quod breuiſsima ex H ad
axim A B cadit ſupra H M ad partes B, vt dictum eſt, & H E cadit
44Lem 8. infra H M ad partes A; ergo H E cadit infra breuiſsimam ex
H ad A B ductam, & propterea E H nan erit breuiſecans:
Similiter breuiſsimaex G ad A B extenſa cadit infra
G M ad partes A, vt dictum eſt; at E G cadit
551 bidem. ſupra G M ad partes B; ergo E G cadit
ſupra breuiſsimam ex G ad axim
A B ductam, quare E G non
eſt breuiſecans.

74[Figure 74]

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