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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229191Conicor. Lib. VI. ad A M eandem

257[Figure 257] proportionem ha-
bebit, quàm X O
C ad quadratum
O C, ſeu eandẽ,
quàm habet X O
ad C O, & com-
parando conſequẽ
tes ad differẽtias
terminorum M A
ad A T eandem
proportionem ha-
bebit, quàm O C
ad C X: erat autẽ
prius T A ad A
E, vt X C ad C F; igitur ex æquali M A ad A E erit, vt O C ad C F, & fue-
runt oſtenſi anguli E, & F æquales. Quod erat oſtendendum.

SECTIO SEPTIMA

Continens Propoſit. XVIII. & XIX.

CViuslibet ſectionis A B C duo ſegmenta C F, A E ca-
dentia inter duas ordinationes A C, E F ad vtraſque par-
tes axis B V ſunt inter ſe ſimilia, & ſimiliter poſita, nec ſunt
ſimilia alteri ſegmento (niſi

258[Figure 258] in ellipſi, in qua quatuor ſeg
menta memorata in propo-
ſitione 8. ſunt æqualia, ſimi-
lia, & ſimiliter poſita, quæ al-
teri ſegmẽto ſimilia nõ ſunt.

Quoniam vnumquodque eo-
11a rum alteri congruit, nec non cõ-
gruunt duo ſegmenta GI, K H
in ellipſi (7. 8. ex 6.) at non ſunt
ſimilia alteri ſegmento: ſi enim
hoc fieri poteſt, ſit ſegmentum
L M ſimile ſegmento F C. Et
quia F C congruit A E. Ergo
duo ſegmenta L M, A E ſunt
ſimilia, producamus A E, L M
quouſque occurrant axi in N,
22b O, erit angulus N æqualis O (vti
demonſtrauimus in 16. & 17.

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