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

Table of contents

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[311.] PROPOSITIO XXXIX.
Page: 363 (324)
[312.] PROPOSITIO XXXX.
Page: 364 (325)
[313.] In Sectionem VII. Propoſit: XXXVIII. XXXIX. & XXXX. LEMMA VI.
Page: 366 (327)
[314.] LEMMA VII.
Page: 366 (327)
[315.] LEMMA VIII.
Page: 367 (328)
[316.] LEMMA IX.
Page: 367 (328)
[317.] Notæ in Propoſit. XXXVIII. XXXIX.
Page: 369 (330)
[318.] Notæ in Propoſit. XXXX.
Page: 369 (330)
[319.] SECTIO OCTAVA Continens Propoſit. XXXXIIII. XXXXV. & XXXXVI.
Page: 372 (333)
[320.] PROPOSITIO XXXXVI.
Page: 374 (335)
[321.] In Sectionem VIII. Propoſit. XXXXIIII. XXXXV. & XXXXVI. LEMM A.X.
Page: 375 (336)
[322.] LEMM A XI.
Page: 375 (336)
[323.] LEMM A XII.
Page: 376 (337)
[324.] Notæ in Propoſit. XXXXIV. & XXXXV.
Page: 378 (339)
[325.] Notæ in Propoſit. XXXXVI.
Page: 378 (339)
[326.] SECTIO NONA Continens Propoſit. XXXXI. XXXXVII. & XXXXVIII.
Page: 380 (341)
[327.] PROPOSITIO XXXXI.
Page: 382 (343)
[328.] PROPOSITIO XXXXVII.
Page: 383 (344)
[329.] PROPOSITIO XXXXVIII.
Page: 386 (347)
[330.] In Sectionem IX. Propoſit. XXXXI. XXXXVII. & XXXXVIII. LEMMA. XIII.
Page: 388 (349)
[331.] LEMMA XIV.
Page: 389 (350)
[332.] LEMMA XV.
Page: 389 (350)
[333.] Notæ in Propoſit. XXXXI.
Page: 392 (353)
[334.] Notæ in Propoſit. XXXXVII.
Page: 393 (354)
[335.] Notæ in Propoſit. XXXXVIII.
Page: 394 (355)
[336.] SECTIO DECIMA Continens Propoſit. XXXXIX. XXXXX. & XXXXXI.
Page: 397 (358)
[337.] In Sectionem X. Propoſit. XXXXIX. XXXXX. & XXXXXI. LEMMA XVI.
Page: 400 (361)
[338.] LEMMA XVII.
Page: 400 (361)
[339.] LEMMA XVIII.
Page: 403 (364)
[340.] Notæ in Propoſit. XXXXIX.
Page: 404 (365)
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page |< < (413) of 458 > >|
452413Aſſumpt. Liber. tũ O B, ſiue X S in parabola
526[Figure 526]11Prop. 11.
lib. 1. æquale eſt rectangulo S FN,
ergo AO ad A C eſt vt qua-
dratum E B ad quadratum
O B, & propterea parallele-
pipedum, cuius baſis quadra-
tum O B, altitudo O A æ-
quale erit parallelepipedo ba-
ſe quadrato E B, altitudine
A C contento, quod erat
propoſitum.
Ex hiſce propoſitionibus de-
ducit inſuper Eutocius aliqua,
quæ non omnino firma, & cer-
ta mihi videntur, nam ex eo
quod recta linea vt I X tangit
vtramq; coniſectionem (hyper-
bolen ſcilicet B X, & parabo-
len F X) in eodem puncto X
concludit hyperbolen interius
contingere parabolen quàm de-
inceps non ſecat ad eaſdem par-
tes axis illius. Hoc autem omnino
neceſſarium nõ eſt ex demonſtra-
tis à me in prop. 20. 21. &
22. Adàit. lib. 6. Apoll. fieri
enim poteſt vt Parabole exte-
rius hyperbolen tangat in X, &
poſtea hinc inde eam ſecet. Poteſt inſuper hyperbole ſecare eandem parabolam
in eodem puncto X, licet ambo in eodem puncto tangantur ab aliqua recta li-
nea, vt eſt I X; quod quidem adnotaſſe fuit operepretium.
FINIS.

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