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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193155Conicor. Lib. VI. 208[Figure 208]
Ponamus itaque C B ad B D, vt H F ad F I, & diuidantur tam B C,
quàm F H in punctis K, L, M, N in eiſdem rationibus, & educamus ſu-
per eas ordinationes O P, Q R, A S, T V, X Y , E Z. Quia B C ad
B D eſt vt H F ad F I, & A C eſt media proportionalis inter C B, B D
11Ex 11.
Lib. 1. (12. ex 1.) pariterque E H inter H F, F I (12. ex 1.) igitur A C ad C
B eſt, vt E H ad H F , & A S dupla ipſius A C ad C B eſt, vt E Z ad
H F; cumque B C ad B L poſita ſit, vt H F ad F N, erit B D ad B L, vt
22a I F ad F N; igitur Q R ad L B eſt vt X Y ad N F; atque ſic oſtendetur,
quod O P ad K B eſt, vt T V ad M F, quare proportio ordinationum
axis vnius ſectionum ad ſua abſciſſa eſt, vt proportio ordinationum alte-
rius ad ſua abſciſſa, & proportiones abſciſſarum vnius ſectionis ad abſciſ-
ſa alterius ſectionis eædem ſunt. Quare ſectio A B ſimilis eſt ſectioni E
33Defin. 2. huius. F. Quod erat oſtendendum.
PROPOSITIO XII.
SI duarum hyperbolarum, aut ellipſium duæ axium figuræ
fuerint ſimiles, vtique ſectiones ſimiles erunt: Si verò fue-
rint ſectiones ſimiles, figuræ etiam ſimiles erunt.
209[Figure 209]
Sint ſectiones A B, E F, earum axes inclinati, vel tranſuerſi B a, F b,
& erecti earum B D, F I, & maneant ſigna, ordinationes, & proportio-
44a nes eædem, quæ in præcedenti propoſitione. Quoniam figura ſectionis
55b

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