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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[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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141103Conicor. Lib. V. non ergo perpendicularis C F æqualis erit Trutinæ K, ſed priùs, neque maior
illa erat; igitur perpendicularis C F neceſſario minor erit Trutina K; quod
erat oſtendendum.
Iiſdem poſitis, ſi in productione breuiſsimæ A I ſumatur quodlibet
11PROP. 8.
Addit. punctum C citra terminum D perpendicularis D E, à puncto C duci
poterit alter ramus breuiſecans ſupra C A incedens; & ſi punctum C
ſumatur vltra punctum D poterit ex C duci alter ramus breuiſecans
infra ipſum C A.
126[Figure 126]
Quoniam quælibet recta C F parallela perpendiculari D E interpoſita inter
productionem breuiſsimæ A I, & axim minor eſt Trutina K nouæ menſuræ B
F (ex præcedenti propoſ.) propterea ramus principalis C O cadit ſupra ipſum
C A, quando B F minor eſt, quàm B E, & tunc quidem duci poteſt hyperbola
ex puncto A circa aſymptotos (vt in propoſitione 51. & 52. factum eſt) quæ pro-
ducta occurret ſectioni B A inter B, & O, vt in P, & coniuncto radio C P,
2251. 52. 53.
huius. erunt duo rami C A, & C P breuiſecantes, quorum infimus eſt C A. Si vero
punctum C ſumatur vltra punctum D, tunc quidem menſura B F maior erit,
quàm B E, & propterea abſciſſa N B maior, quàm H B, & ideo principalis
ramus C O cadet infra ramum C A; & denuo facta eadem conſtructione propo-
ſit. 51. & 52. huius, erunt duo rami C P, & C A breuiſecantes, quorũ ſupre-
mus verſus B erit C A, quod erat probandum.
Sit coniſectio, vel ellipſis portio quadrantis B A G, cuius axis B
33PROP. 9.
Addit. E, perpendicularis E D, euiuſque Trutina L ſit minor perpendiculari
D E, & centro D, interuallo cuiuslibet rami ſecantis D A circulus Z
A γ deſcribatur, & ex puncto A ducatur recta A x contingens

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