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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[31.] PROPOS. II.
Page: 43 (5)
[32.] PROPOS. III.
Page: 44 (6)
[33.] Notæ in Propoſitionem primam.
Page: 44 (6)
[34.] Notæ in Propoſitionem ſecundam.
Page: 45 (7)
[35.] Notæ in Propoſitionem tertiam.
Page: 45 (7)
[36.] SECTIO SECVNDA Continens propoſitiones IV. V. VI. Apollonij.
Page: 45 (7)
[37.] PROPOSITIO IV.
Page: 46 (8)
[38.] PROPOSITIO V. & VI.
Page: 46 (8)
[39.] Notæ in pro poſitionem quartam.
Page: 47 (9)
[40.] Notæ in propoſitionem quintam.
Page: 48 (10)
[41.] MONITVM.
Page: 50 (12)
[42.] LEMMA I.
Page: 51 (13)
[43.] LEMMA II.
Page: 52 (14)
[44.] LEMMA III.
Page: 53 (15)
[45.] LEMMA IV.
Page: 53 (15)
[46.] SECTIO TERTIA Continens VIII. IX. X. Propoſ. Apollonij.
Page: 54 (16)
[47.] PROPOSITIO IX. & X.
Page: 56 (18)
[48.] Notæ in Propoſitionem VIII.
Page: 57 (19)
[49.] Notæ in Propoſitionem IX. & X.
Page: 59 (21)
[50.] SECTIO IV. Continens Propoſit. VII. & XII. Apollonij.
Page: 62 (24)
[51.] NOTÆ.
Page: 63 (25)
[52.] SECTIO QVINTA Continens XI. Propoſit. Apollonij.
Page: 64 (26)
[53.] NOTÆ.
Page: 64 (26)
[54.] SECTIO SEXTA Continens Propoſit. XIII. XIV. XV. Apollonij.
Page: 65 (27)
[55.] NOTÆ.
Page: 66 (28)
[56.] SECTIO SEPTIMA Continens XXVI. XXVII. XXVIII. Propoſ. Apollonij. PROPOSITIO XXVI. & XXVII.
Page: 67 (29)
[57.] PROPOSITIO XXVIII.
Page: 67 (29)
[58.] NOTÆ.
Page: 68 (30)
[59.] LEMMA V.
Page: 68 (30)
[60.] LEMMA. VI.
Page: 69 (31)
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page |< < (70) of 458 > >|
10870Apollonij Pergæi
SECTIO VNDECIMA
Continens Propoſ. LXVIII. LXIX. LXX.
& LXXI. Apollonij.
PROPOSITIO LXVIII. LXIX.
SI occurrant duæ tangentes alicui ſectioni A B C, vt ſunt A
11a F, E F, vtique quod abſcinditur ex tangente proximiori
vertici ſectionis, qui eſt B minus eſt ſegmento abſciſſo ex alia,
nempe E F minor eſt, quàm A F.
Iuncta enim A E,
22b88[Figure 88]& in parabola ex F
producta linea F I
parallela axi B D e-
rit illa diameter, bi-
fariam ſecans E A in
G (34. ex 2.) Simi-
3330. lib. 2. liter ex centro H pro-
ducamus H F G, quæ
eſt quoque diameter
(34. ex 2.) bifariam
44Ibidem. ſecans E A in G, &
ducamus A D in pa-
rabola, & hyperbola perpendicularem ſuper axim D B. Ergo angulus
A I G in parabola eſt rectus, & in hyperbola obtuſus; ergo F G A erit
obtuſus in illis omnibus; quare maior eſt, quàm angulus F G E, & A
G æqualis eſt ipſi G E, & F G communis; igitur E F minor eſt, quàm
F A.
89[Figure 89]

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