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 |< < (191) of 458 > >|
229191Conicor. Lib. VI. ad A M eandem
257[Figure 257] proportionem ha-
bebit, quàm X O
C ad quadratum
O C, ſeu eandẽ,
quàm habet X O
ad C O, & com-
parando conſequẽ
tes ad differẽtias
terminorum M A
ad A T eandem
proportionem ha-
bebit, quàm O C
ad C X: erat autẽ
prius T A ad A
E, vt X C ad C F; igitur ex æquali M A ad A E erit, vt O C ad C F, & fue-
runt oſtenſi anguli E, & F æquales. Quod erat oſtendendum.
SECTIO SEPTIMA
Continens Propoſit. XVIII. & XIX.
CViuslibet ſectionis A B C duo ſegmenta C F, A E ca-
dentia inter duas ordinationes A C, E F ad vtraſque par-
tes axis B V ſunt inter ſe ſimilia, & ſimiliter poſita, nec ſunt
ſimilia alteri ſegmento (niſi
258[Figure 258] in ellipſi, in qua quatuor ſeg
menta memorata in propo-
ſitione 8. ſunt æqualia, ſimi-
lia, & ſimiliter poſita, quæ al-
teri ſegmẽto ſimilia nõ ſunt.
Quoniam vnumquodque eo-
11a rum alteri congruit, nec non cõ-
gruunt duo ſegmenta GI, K H
in ellipſi (7. 8. ex 6.) at non ſunt
ſimilia alteri ſegmento: ſi enim
hoc fieri poteſt, ſit ſegmentum
L M ſimile ſegmento F C. Et
quia F C congruit A E. Ergo
duo ſegmenta L M, A E ſunt
ſimilia, producamus A E, L M
quouſque occurrant axi in N,
22b O, erit angulus N æqualis O (vti
demonſtrauimus in 16. & 17.

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