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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144106Apollonij Pergæi D N ſupra, & infra breuiſe-

130[Figure 130] cantem D C, ſecantes circulum
O C Q, in O, & Q, dummo-
do D G non ducatur infra D C
in primo caſu, nec ſupra D A
in ſecundo. Quoniam ramus D
A ſupremus duorum breuiſecan-
tium maximus eſt omnium ra-
morum cadentium ad periphe-
riam B A C; igitur D A maior
1172. huius. erit, quàm D F, & quàm D G;
ſunt verò D Z, & D γ æqua-
les eidem D A (cum ſint radĳ
eiuſdem circuli) ergo D Z ma-
ior eſt, quàm D F; pariterque
D γ maior eſt quàm D G: &
propterea duo quælibet puncta
Z, γ eiuſdem circuli Z A γ ca-
dunt extra coniſectionem B A
G; & ideo circulus Z A γ tan-
tummodo in puncto A coniſectio-
nem extrinſecus tangit.

Poſtea quia ramus D C infimus breuiſecantium eſt minimus omnium ramo-
rum cadentium ex D ad peripheriam A C N, ergo ramus D C minor eſt, quàm
2272. huius. D G, & quàm D N: ſunt vero D O, D Q æquales eidem D C (cum ſint radĳ
eiuſdem circuli) igitur D O minor eſt, quàm D G: pariterque D Q minor eſt,
quàm D N: quare quælibet duo puncta O, Q circuli O C Q hinc inde à puncto
C cadunt intra coniſectionem B C N, & ideo circulus O C Q intrinſecus con-
tingit coniſectionem in C, quod erat oſtendendum.

Si ad coniſectionem,
33PROP.
12.
Addit.

131[Figure 131] vel ad portionem qua-
drantis ellipſis B A C,
ex concurſu D duci non
poſsit, niſi vnicus tan-
tum breuiſecans D A,
atque centro D, interual-
lo D A circulus Z A γ
deſcribatur; Dico, om-
nium circulorum tangen-
tium eandem rectam li-
neam X A P (quàm
cõtingit quoque coniſectio
in A) vnicum eſſe

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