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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6224Apollonij Pergæi aggregato differentiali ab-
35[Figure 35] ſciſſarum ramorum I L, I
M ab abſciſſa rami breuiſ-
ſimi.
Pari modo in hyperbola,
& ellipſi quadratum I L ſu-
perat quadratum I M eodẽ
exceſſu, quo exemplar ap-
11Ex 9. 10. h. plicatum ad H P ſuperat
exemplar applicatum ad H
L; ſed differentia exem-
plarium applicatorum ad H
P, & H Q æqualis eſt re-
ctangulo ſub P Q exceſſu
differentiali, & recta linea
compoſita ex X m, & u l, ad quam ſumma
differentialis P H Q eandem proportionem
36[Figure 36] habet, quam latus trãſuerſum ad ſummam
in hyperbola, & ad differentiam in ellipſi
laterum tranſuerſi, & recti, vt in nota
propoſitionis 5. oſtenſum eſt; igitur quadra-
tum I L ſuperat quadratum I M iam dicto
rectangulo ſub P Q, & ſub X m, & u l,
quod erat oſtendendum.
SECTIO IV.
Continens Propoſit. VII.
& XII. Apollonij.
SIfuerit menſura A
37[Figure 37] D minor com-
22a parata A E, (12.) aut
ſit pars lineæ breuiſſi-
mæ, & axis in ellipſi
ſit maior, erit A D
breuiſſimus ramorum
egredientium ex ori-
gine eius in omnibus
ſectionibus, vt ſunt F
D, G D, B D, C D,
& proximior illi minor eſt remotiore, nempe F D quam G D, & G
D, quàm B D.

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