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 |< < (73) of 458 > >|
11173Conicor. Lib. V.
Notæ in Propoſit. XXIX. XXX.
& XXXI.
A Lioquin producatur perpendicularis C E, & c. Exiſtente C A lineæ
11a breuiſsima, & A D tangente, ſi C A non eſt perpendicularis ad tangen-
tem ducatur ex origine C recta C E perpendicularis ad tangentem A D, ſecans
eam in E, & ſectionem in F, erit in triangulo A C E angulus C A E acutus,
& minor angulo recto E, & propterea C A ſubtendens maiorem angulum re-
ctum, maior erit quàm C E, quæ acutum ſubtendit: cumque punctum E tan-
gentis cadat extra ſectionem, erit C F minor, quàm C E; ideoque C A multo
maior eſt, quàm C F, quapropter C A non erit breuiſsima, quod eſt contra,
hypotheſin.
Si vero fuerit D A C rectus, & c. Quia C A ſupponitur breuiſsima,
22b3333. 34.
lib. 2.& angulus D A C rectus, erit A D tangens; nam ſi hoc verum non eſt,
ducatur ex puncto A recta linea A G, contingens ſectionem in
A; ſecabit vtique tangens A G ipſam D A, & erit an-
gulus C A G rectus nimirum contentus à breuiſsima
C A, & tangente A G, ex proxime demon-
ſtrata propoſitione; ergo duo anguli recti
C A D, & C A G æquales ſunt
inter ſe, pars, & totum, quod
eſt abſurdum.
93[Figure 93]

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