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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[201.] COROLLARIVM I.
[202.] COROLLARIVM II.
[203.] Notæ in Propoſit. XI.
[204.] Notæ in Propoſit. XII.
[205.] Notæ in Propoſit. XIII.
[206.] Notæ in Propoſit. XIV.
[207.] SECTIO QVINTA Continens ſex Propoſitiones Præmiſſas, PROPOSITIO I. II. III. IV. & V.
[208.] PROPOSITIO Præmiſſa VI.
[209.] Notæ in Propoſit. Præmiſſas I. II. III. IV. & V.
[210.] Notæ in Propoſit. Præmiſſ. VI.
[211.] SECTIO SEXTA Continens Propoſit. XV. XVI. & XVII. PROPOSITIO XV.
[212.] PROPOSITIO XVI.
[213.] PROPOSITIO XVII.
[214.] Notæ in Propoſit. XV.
[215.] MONITVM.
[216.] LEMMA VI.
[217.] LEMMA VII.
[218.] LEMMA VIII.
[219.] Notæ in Propoſit. XVI.
[220.] Notæ in Propoſit. XVII.
[221.] SECTIO SEPTIMA Continens Propoſit. XVIII. & XIX.
[222.] Notæ in Propoſit. XVIII. & XIX.
[223.] SECTIO OCTAVA Continens Propoſit. XX. & XXI. Apollonij. PROPOSITIO XX.
[224.] PROPOSITIO XXI.
[225.] PROPOSITIO XXII.
[226.] PROPOSITIO XXIII.
[227.] PROPOSITIO XXIV.
[228.] Notæ in Propoſit. XX.
[229.] Notæ in Propoſit. XXI.
[230.] Notæ in Propoſit. XXII.
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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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