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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181143Conicor. Lib. VI.

184[Figure 184] æqualia ſunt inter ſe: ſunt verò rectangula N K, & L I æqualia quoque (cum
latera circa angulos rectos æqualia habeant, ſingula ſingulis) ergo duo rectangu-
la A P, & D R æqualia ſunt inter ſe.

Quia, ſi non cadit ſuper illum, eſſent ſectioni hyperbolicæ duo axes,
11C& in ellipſi tres axes, & c. Quoniam æquales ſectiones B A, E D ſibi mutuò
congruunt, & vertices A, & D coincidunt, ſiquidem axis A L non cadit ſuper
axim D N (cum ambo tamen axes ſint) haberet vnica ſectio, ſcilicet duæ ſe-
ctiones congruentes, duos axes A L, & D N conuenientes in eodem puncto ver-

185[Figure 185] ticis, quod in hyperbola eſt im-
2248. lib. 2. poſſibile; in ellipſi verò, in qua
ſemper duo axes reperiuntur ſe
ſe ſecantes in centro ad angulos
rectos, reperietur tertius axis,
ille nimirum, qui ab eodem ver-
tice A ducitur in eadem ſectione
A B, & non coincidit cum axi
A L.

Ideoque B L æqualis eſt N
33d E, & poterunt A P, D R, ap-
plicata ad A L, D N æqualia
& c. Quia quadrata æqualium.
B L, E N æqualia ſunt rectangulis A P, D R; erunt illa æqualia, & corum
latera A L, D N facta ſunt æqualia; igitur reliqua duo latera L P, N R æ-
qualia quoque ſunt. Simili modo oſtendetur, quod M Q æqualis eſt O S, ſeù L
T æqualis eſt N V, & L M, ſeu T Q æqualis eſt N O, ſeu V S; erant autem.
prius L P, N R æquales; igitur reſiduæ P T, & R V æquales erunt, ſed quia
T Q, & G L ſunt parallelæ pariterque V S, & H N; ergo vt T P ad P L ita
eſt Q T ad L G, ſimili modo vt V R ad R N ita eſt S V ad N H; habent ve-
rò duæ æquales T P, & V R ad duas æquales P L, & R N eandem proportio-
nem, igitur duæ æquales Q T, & S V eandem proportionem habent ad L G, &
N H, & propterea hæ erunt æquales, & ablatis æqualibus A L, D N, erunt reliquæ
A G, & D H inter ſe æquales, & habet G A ad A I eandem proportionẽ, quàm
Q T ad T P, ſeu quàm S V ad V R; pariterq; H D ad D K eſt vt S V ad V R
(propter parallelas & ſimilitudinẽ triangulorũ) igitur vt G A ad A I itaerit H

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