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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334295Conicor. Lib. VII.
Notæ in Propoſit. XXIX.
QVoniam in hyperbola differentia quadratorum ex axi A C, & ex axi Q
1112. huius. R æqualis eſt differentiæ inter quadratum I L à quadrato eius coniugatæ
N O; eſtque Q R media proportionalis inter ſiguræ latera A C, &
2216. lib. 1. A F; ergo rectangulum C A F ſub extremis contentum æquale eſt quadrato in-
termediæ Q R: Et propterea differentia inter quadratum A C, & rectangu-
lum C A F æqualis erit differentiæ inter quadratum A C à quadrato Q R.
386[Figure 386] pari ratione erit differentia quadrati I L à rectangulo L I P æqualis differen-
tiæ quadrati I L à quadrato N O; & propterea in hyperbole differentia qua-
drati axis A C à rectangulo ſub figuræ lateribus contentum C A F æqualis
eſt differentiæ quadrati diametri I L à rectangulo L I P ſub lateribus figuræ
eius.
Notæ in Propoſit. XXX.
QVoniam in ellipſi quadratorum ex A C, & ex Q R ſumma æqualis eſt
33Prop. 13.
huius.
ex 15.
lib. 1. ſummæ quadratorum ex I L, & ex N O: eſtque rectangulum C A F
æquale quadrato Q R, & rectangulum L I P æquale quadrato N O
(vt in præcedenti nota dictum eſt) igitur in ellipſi quadratum axis A C, &
rectangulum C A F ſub eius lateribus cõtentum ſimul ſumpta æqualia ſunt qua-
drato ex I L cum rectangulo figuræ eius L I P.

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