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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141103Conicor. Lib. V. non ergo perpendicularis C F æqualis erit Trutinæ K, ſed priùs, neque maior
illa erat; igitur perpendicularis C F neceſſario minor erit Trutina K; quod
erat oſtendendum.

Iiſdem poſitis, ſi in productione breuiſsimæ A I ſumatur quodlibet
11PROP. 8.
Addit. punctum C citra terminum D perpendicularis D E, à puncto C duci
poterit alter ramus breuiſecans ſupra C A incedens; & ſi punctum C
ſumatur vltra punctum D poterit ex C duci alter ramus breuiſecans
infra ipſum C A.

126[Figure 126]

Quoniam quælibet recta C F parallela perpendiculari D E interpoſita inter
productionem breuiſsimæ A I, & axim minor eſt Trutina K nouæ menſuræ B
F (ex præcedenti propoſ.) propterea ramus principalis C O cadit ſupra ipſum
C A, quando B F minor eſt, quàm B E, & tunc quidem duci poteſt hyperbola
ex puncto A circa aſymptotos (vt in propoſitione 51. & 52. factum eſt) quæ pro-
ducta occurret ſectioni B A inter B, & O, vt in P, & coniuncto radio C P,
2251. 52. 53.
huius. erunt duo rami C A, & C P breuiſecantes, quorum infimus eſt C A. Si vero
punctum C ſumatur vltra punctum D, tunc quidem menſura B F maior erit,
quàm B E, & propterea abſciſſa N B maior, quàm H B, & ideo principalis
ramus C O cadet infra ramum C A; & denuo facta eadem conſtructione propo-
ſit. 51. & 52. huius, erunt duo rami C P, & C A breuiſecantes, quorũ ſupre-
mus verſus B erit C A, quod erat probandum.

Sit coniſectio, vel ellipſis portio quadrantis B A G, cuius axis B
33PROP. 9.
Addit. E, perpendicularis E D, euiuſque Trutina L ſit minor perpendiculari
D E, & centro D, interuallo cuiuslibet rami ſecantis D A circulus Z
A γ deſcribatur, & ex puncto A ducatur recta A x contingens

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