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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143105Conicor. Lib. V.

COROLLARIVM.

HInc conſtat, ſupremam circuli peripheriam A Z cadere in locum à tan-
gente X A, & coniſectionem B A contentum, infimam vero circuferen-
tiam A γ cadere ne dum infra tangentem, ſed etiam infra coniſectionem A G;
eoquod recta A X cadit extra circuli peripheriam A Z, quàm contingit in A,
& eadem circumferentia A Z cadit extra ſectionem A B, quàm ſecat in A, vt
dictum eſt.

Mirabile quidem hoc videri poterit aliquibus, qui contingentiæ angulos, quos
vocant, verè angulos eſſe cenſent; nam hic duæ circumſerentiæ curuæ, conica
nimirum B A G, & circularis Z A γ ſe mutuo ſecant in A, & tamen ambo
tanguntur ab eadẽ recta linea A X in eodem puncto A, in quo illæ ſe mutuò ſecant.
Vnde colligent etiam, quod anguli contingentiæ facti à coniſectione B A G, &
recta linea X A non ſunt æquales inter ſe, quando punctum A in vertice axis
non exiſtit; nam duo anguli contingentiæ circumſerentiæ circularis, & rectæ
tangentis X A æquales ſunt inter ſe: at angulus contingentiæ ſectionis conicæ ſu-
premus reſpiciens verticem B maior eſt angulo contingentiæ circularis, vt dictũ
eſt: infimus vero angulus contingentiæ à ſectione conica, & eadem tangente
contentus minor eſt eodem angulo contingentiæ circularis, & propterea ſupremus
angnlus contingentiæ ſectionis conicæ maior erit inferiori.

129[Figure 129]

Sit perpendicularis D E
11PROP.
II.
Addit.
Ex 51. 52.
53. huius. minor trutina L, ſintque D
A, & D C duo illi rami,
qui tantummodo breuiſecantes
eſſe poſſunt omnium ramorum
ex concurſu D ad ſectionem
B C cadentium; atque cen-
tro D, interuallo D A deſcri-
batur circulus Z A γ; pari-
terque centro D, interuallo D
C deſcribatur circulus O C Q;
ducanturque rectæ X P, M
P contingentes coniſectionem
in A, & C. Dico, circulũ
Z A γ contingere coniſectio-
nem in A, & extra ipſam
cadere, at circulum O C Q contingere eandem coniſectionem in C, &
intra ipſam cadere.

Ducantur quilibet rami D F, D G ſupra, & infra breuiſecantem D A, ſe-
cantes circulum Z A γ in Z, & γ; pariterque ducantur quilibet rami D

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