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

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[181.] Notæ in Propoſit. III.
Page: 187 (149)
[182.] Notæ in Propoſit. VI.
Page: 187 (149)
[183.] Notæ in Propoſit. VII.
Page: 187 (149)
[184.] Notæ in Propoſit. IX.
Page: 188 (150)
[185.] LEMMAI.
Page: 188 (150)
[186.] SECTIO TERTIA Continens Propoſit. V. & VIII. PROPOSITIO V.
Page: 190 (152)
[187.] PROPOSITIO VIII.
Page: 191 (153)
[188.] Notæ in Propoſit. V.
Page: 192 (154)
[189.] Notæ in Propoſit. VIII.
Page: 192 (154)
[190.] SECTIO QVARTA Continens Propoſit. XI. XII. XIII. & XIV. PROPOSITIO XI.
Page: 192 (154)
[191.] PROPOSITIO XII.
Page: 193 (155)
[192.] PROPOSITIO XIII.
Page: 194 (156)
[193.] PROPOSITIO XIV.
Page: 195 (157)
[194.] MONITVM.
Page: 196 (158)
[195.] LEMMA II.
Page: 196 (158)
[196.] COROLLARIVM.
Page: 197 (159)
[197.] LEMMA III.
Page: 197 (159)
[198.] LEMMA IV.
Page: 198 (160)
[199.] COROLLARIVM.
Page: 198 (160)
[200.] LEMMAV.
Page: 199 (161)
[201.] COROLLARIVM I.
Page: 199 (161)
[202.] COROLLARIVM II.
Page: 199 (161)
[203.] Notæ in Propoſit. XI.
Page: 203 (165)
[204.] Notæ in Propoſit. XII.
Page: 204 (166)
[205.] Notæ in Propoſit. XIII.
Page: 205 (167)
[206.] Notæ in Propoſit. XIV.
Page: 206 (168)
[207.] SECTIO QVINTA Continens ſex Propoſitiones Præmiſſas, PROPOSITIO I. II. III. IV. & V.
Page: 206 (168)
[208.] PROPOSITIO Præmiſſa VI.
Page: 209 (171)
[209.] Notæ in Propoſit. Præmiſſas I. II. III. IV. & V.
Page: 209 (171)
[210.] Notæ in Propoſit. Præmiſſ. VI.
Page: 212 (174)
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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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