Full text: Pergaeus, Apollonius: Apollonii Pergaei Conicorvm Lib. V. VI. VII. paraphraste Abalphato Asphahanensi

Apollonij Pergæi D N ſupra, & infra breuiſe-
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
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.

123.1.

0144-01
72. huius.

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
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.

123.1.

72. huius.

Si ad coniſectionem,
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 cir-

Note to user

Dear user,

In response to current developments in the web technology used by the Goobi viewer, the software no longer supports your browser.

Please use one of the following browsers to display this page correctly.

Thank you.

powered by Goobi viewer