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

Page concordance

< >
Scan Original
431 392
432 393
433 394
434 395
435 396
436 397
437 398
438 399
439 400
440 401
441 402
442 403
443 404
444 405
445 406
446 407
447 408
448 409
449 410
450 411
451 412
452 413
453 414
454 415
455
456
457
< >
page |< < (282) of 458 > >|
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.

Text layer

  • Dictionary

Text normalization

  • Original

Search


  • Exact
  • All forms
  • Fulltext index
  • Morphological index
Impressum