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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320282Apollonij Pergæi ſecet axim in M, & I S ad axim perpendicularem, ſeu ordinatim applica-
tam, eum ſecans in S. Et quia trianguli A C B duo latera A C, A B ſecan-
tur proportionaliter, ſcilicet bifariam in D, & K; ergo I D parallela eſt baſi
C B: eſtquè tangens I M parallela ipſi B A, cum ambo ad diametrum I L ſint
11Prop. 5.
lib. 2. ordinatim applicatæ; pariterquè I S parallela eſt B E ( cum ſint ad axim per-
pendiculares ) igitur triangula M I S, A B E ſimilia erunt; pariterquè trian-
gula D I S, C B E erunt ſimilia: & ideo M S ad S I erit vt A E ad E B, &
S I ad S D erit, vt B E ad E C: quarè ex æquali ordinata M S ad S D ean-
dem proportionem habebit, quàm A E ad E C: eſtquè quadratum I M ad qua-
dratum N D, vt M S ad S D; ergo quadratum I M ad quadratum N D eſt,
22Prop. 4.
huius. vt A E ad E C, & c.
372[Figure 372]
SECTIO TERTIA
Continens Propoſit. Apollonij VIII. IX. X.
XI. XV. XIX. XVI. XVIII.
XVII. & XX.
VIII. IN hyperbola, vel ellipſi quadratum axis inclinati, ſiue
tranſuerſi ad quadratum ſummæ duarum diametrorum
coniugatarum eiuſdem ſectionis habebit eandem proportionem,
quàm productum præſectæ axis in ſuam interceptam compara-
tam ad quadratum ſummæ ſuæ interceptæ, & potentis compa-
ratarum.

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