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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8547Conicor. Lib. V. figuræ compoſitæ, vel diuiſæ, & c. Quia E K ad K D, atque C F ad F D eandem
proportionem habebant, quàm latus tranſuerſum ad rectum; ergo componendo in
hyperbola, & diuidendo in ellipſi erit E D ad D K, vt C D ad D F.
Et ponamus re-
11h62[Figure 62] ctangulum F G cõ-
mune, & c. Scilicet
rectangulũ F G ad-
datur in hyperbola,
& auferatur cõmu-
niter in ellipſi.
Et propterea E
22i K ad B G, nempe
K R ad R G, & c.
Quia propter ſimili-
tudinem triangulo-
rum E K R, & B G
R erit E K ad B G,
vt K R ad R G; qua-
re K R ad R G maio-
rem proportionẽ ha-
bet, quàm G M ad
M K; & componen-
do K G ad G R ma-
iorem rationem ha-
bet, quam eadem G
K ad K M, quare
K M, nẽpe e i æqua-
lis D F maior eſt,
quàm G R.
Et auferẽdo ho-
33k mologũ ab homo-
logo in hyperbola,
& coniungendo e
a in ellipſi, habebit, & c. Scilicet comparando homologorum differentias in hy-
44Lem. 4.
præmiſ. perbola, eorundem ſummas in ellipſi, ideſt C T ad B O, nempe C H ad H O (pro-
pter ſimilitudinem triangulorum C H T, & O H B) habebit maiorem proportionem,
quàm I C ad C S, nempe C D ad D F.
Poſtea educamus ex E lineam occurrentem ſectioni in V, & c. Educamus
55l ex E lineam occurrentem ſectioni in V, quæ ſecet axim in Z, & S M in Y.
Et per f producamus f g h parallelam axi A D, & c. Et per f ducamus f g pa-
66m rallelam axi A D, quæ ſecet tangentem B a in h, & L F in g, atque V c ſecet illam in
i, & S M in e.
Et ponamus rectangulum F f communiter, & c. Et communiter addamus in
77n hyperbola, & auferamus in ellipſi rectangulum F f, fiet rectangulum B fg æquale
rectangulo g F C. Nomina Inuerſi, & Trutinatæ definita fuerunt in primo libro ab
interprete Arabico.

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