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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9153Conicor. Lib. V.

68[Figure 68] ponendo eadem K G
ad G R minorẽ pro-
portionem habebit,
quãad K M, & pro-
pterea G R maior e-
rit, quàm K M, vnde
E I ad G R, ſeu I T
ad G B (propter ſi-
militudinem trian-
gulorum E I T, R G
B) minorem propor-
tionem habet, quàm
E I ad K M, ſeu I C
ad C S; & ideo com-
parando homologarũ
ſummas in ellipſi, &
11Lem. 4. eorundem differen-
tias in hyperbola C
T ad O B, ſiue C H
ad H O (propter ſi-
militudinem trian-
gulorũ) habebit mi-
norẽ proportionem,
quàm I C ad C S,
vel C D ad D F, &
diuidendo in hyper-
bola, & componendo in ellipſi C O ad O H habebit minorem proportionem, quàm
22Ex 9. 10.
huius. C F ad F D, ſiue quàm latus tranſuerſum habet ad rectum; ergo breuiſsima ex
B ad axim ducta eum ſecat ſupra punctum H, & abſcindit lineam minorem,
quàm A H.

Rurſus ĳſdem poſitis, oſtendendum eſt, ramum E p cadentem ſupra ramum
E V verſus verticem, velinfra infimum breuiſecantem E V non eße breuiſecan-
tem, & abſcindere ex axi minorem lineam, quàm abſcindit breuiſsima ex pun-
cto p ad axim ducta. Ducatur ex p recta linea p x perpendicularis ad axim,
eum ſecans in x, & ſecans S M in r, & hyperbolen V o in t, pariterque ramus
E p ſecet S M in z, & A F in q, atque I C in f. Quoniam hyperbole V o ſe-
cat coniſectionem A B in V, & p ponitur ſupra V ad partes A; ergo t cadit
extra ſectionem A B, & propterea t r maior erit, quàm p r; vnde rectangulum
p r M minus erit rectangulo t r M; ſed propter aſymptotos S M, M F eſt rectan-
3312. lib.2. gulum t r M æquale rectangulo o G M, ſeu rectangulo E M, vt dictum eſt; ergo
rectangulum p r M minus eſt rectangulo E K M, & propterea E K ad p r, ſeu
44Lem. 5. K z ad z r (propter ſimilitudinem triangulorum) maiorem proportionem habet,
quàm r M ad M K, & componendo, eadé K r ad r z maioré proportioné habet,
quàm ad M K; ergo r z minor eſt, quàm M K; ideoque E I ad r z, ſeu I f ad
r p (propter ſimilitudinem triangulorum E I ſ, & r p z) maiorem proportionem
habet, quàm E I ad M K, ſeu I C ad C S, vel ad r x; ergo comparando homo-
55Lem. 4. logorum ſummas in ellipſi, & eorundem differentias in hyperbola C ſ ad x

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