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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267229Conicor. Lib. VI. ad L S eſt vt quadratum D Z ad quadratum Z F ; igitur P G ad G R ean-
dem proportionem habet, quàm Z L ad L S, & propterea figuræ ſectionem
11ex 12.
huius. erunt ſimiles; ĳs autẽ figuris æqualia oſtenſa ſunt quadrata dupliciũ O Y, & K
Z, quæ ſuppoſitæ fuerunt æquales; igitur figuræ P G R, & Z L S ſimiles, &
æquales ſunt inter ſe, atque diametri æquæ inclinatæ ſunt ad ordinatim ad eas
applicatas H I, M N; igitur ſectiones H G I, M L N æquales ſunt inter ſe,
22Prop. 10.
huius. ſimiles, & congruentes, quarum figuræ æquales ſunt quadratis duplicium inter-
ceptarum O Y, & K Z, quod erat propoſitum.

LEMMA IX.

S I in duobus conis A B C, D E F, baſes ſint in eodem plano, &
duo triangula per axes A B C, D E F fuerint ſimilia, & ſimi-
liter poſita, & in eodem plano exiſtentia, erunt coni ſimiles inter ſe.

314[Figure 314]

Ducantur à verticibus A, & D duæ rectæ A G, & D H perpendiculares ad
baſes conorũ, & à terminis axium A Y, & D Z coniungantur rectæ lineæ Y G,
& Z H. Quoniã planum, in quo exiſtunt duo triangula A B C, D E F ſecat
planum, in quo baſes conorum iacent in vna recta linea, quæ baſis eſt vtriuſque
trianguli per axes conorum ducti; ideoque B C, & E F in directum conſtitutæ
erunt, & circa angulos æquales B, & E latera A B ad B C, atque D E ad E
F ſunt proportionalia ( propter triangulorum A B C, & D E F ſimilitudinem)
erunt quoque ad conſequẽtium ſemiſſes proportionales, ſcilicet A B ad B Y erit,
vt D E ad E Z circa angulos æquales, & propterea triangula A B Y, & D E
Z ſimilia erunt: & ideò duo anguli B Y A, & E Z D, externus interno, æqua-
les erunt inter ſe; igitur Y A, & Z D in eodem plano exiſtentes, parallelæ
erunt inter ſe; ſunt quoque A G, D H inter ſe parallelæ ( cum ſint perpendicu-
lares ad idem planum baſium ) ergo duo anguli Y A G, & Z D H æquales ſunt
inter ſe; atquè anguli G, & H æquales ſunt, nempe recti; igitur in triangu-
lis A Y G, & D Z H, duo poſtremi anguli A Y G, & D Z H æquales

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