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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[131.] Notæ in Propoſit. XVI. XVII. XVIII.
[132.] SECTIO DECIMASEPTIMA Continens XIX. XX. XXI. XXII. XXIII. XXIV. & XXV. Propoſ. Apollonij. PROPOSITIO XIX.
[133.] PROPOSITIO XX. XXI. & XXII.
[134.] PROPOSITIO XXIII. & XXIV.
[135.] PROPOSITIO XXV.
[136.] Notæ in Propoſit. XIX.
[137.] Notæ in Propoſit. XX. XXI. XXII.
[138.] Notæ in Propoſ. XXIII. XXIV.
[139.] Notæ in Propoſ. XXXV.
[140.] SECTIO DECIMAOCTAVA Continens XXXII. XXXIII. XXXIV. XXXV. XXXVI. XXXVII. XXXVIII. XXXIX. XXXX. XXXXVII. XXXXVIII. Propoſit. Apollonij. PROPOSITIO XXXII.
[141.] PROPOSITIO XXXIII. XXXIV.
[142.] PROPOSITIO XXXV.
[143.] PROPOSITIO XXXVI.
[144.] PROPOSITIO XXXVII. XLVI.
[145.] PROPOSITIO XXXVIII.
[146.] PR OPOSITIO XXXIX.
[147.] PROPOSITIO XXXX.
[148.] PROPOSITIO XXXXVII.
[149.] PROPOSITIO XXXXVIII.
[150.] Notæ in Propoſit. XXXII.
[151.] Notæ in Propoſit. XXXIII. XXXIV.
[152.] Notæ in Propoſit. XXXV.
[153.] Notæ in Prop. XXXVI.
[154.] Notæ in Prop. XXXVIII.
[155.] Notæ in Propoſit. XXXIX.
[156.] Notæ in Propoſit. XXXXVIII.
[157.] LIBRI QVINTI FINIS.
[158.] APOLLONII PERGAEI CONICORVM LIB VI. DEFINITIONES. I.
[159.] II.
[160.] III.
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page |< < (38) of 458 > >|
7638Apollonij Pergæi gulorum C g, g e, in hyperbola, vel eorum exceſſus in ellip ſi maior,
quàm M e in e V, ergo rectangulum C M, nempe rectangulum E M mul-
tò maius eſt, quàm V e in e M, &
propterea E K ad e V, nempe K Y ad
Y e maiorem proportionem habet, quàm e M ad M K, &
componendo
11Lem. 5.22r patet, quod e Y minor ſit, quàm K M, &
conſtat (quemadmodum antea
demonſtrauimus) quod breuiſſima egrediens ex V abſcindit ab axi maio-
33s rem lineam quàm c Z.
Simili modo conſtat, quod breuiſſima egrediens ex l eiuſdem ſit rationis.
44t
DEindè ſit E D æqualis Q, inde demonſtrabitur, (quemadmodum ſu-
pra factum eſt) quod B H tantùm ſit linea breuiſſima, &
quod mi-
55a nima egrediens ex V abſcindit ab axi cum A maiorem lineam, quàm A
Z, &
quod minima egrediens ex l ſecet maiorem lineam, quàm A m.
Tandem pona-
52[Figure 52] mus E D minorẽ,
quàm Q, ergo E
D ad B O minorẽ
proportionem ha-
bet, quàm Q ad
eandem;
& demõ-
ſtrabitur (quemad-
66b modum dictũ eſt)
quod G O ad O B
minorem propor-
tionem habeat,
quàm F O ad O C;
& ponamus O G
ad O o, vt F O ad
O C;
& produca-
mus per o ſectionẽ
hyperbolicam cir-
ca duas continen-
tes S M, M F, quę
ſecet ſectionem A
B in V, l, &
iun-
gamus E V, E l,
77c&
producamus ex
V, l duas perpendiculares V c, l P, quæ parallelæ ſint continenti M F,
ergo o G in G M eſt æquale V e in e M (12.
ex ſecundo) & quia G O ad
O o eſt, vt F O ad O C erit o O in O F æquale rectangulo G C, &
pona-
mus rectangulum F G commune fiet rectangulum C M (quod erat ęquale
rectangulo M E) æquale ipſi o G in G M, quod eſt æquale ipſi V e in e
88d M;
ergo rectangulum E M æquale eſt ipſi V e in e M. Tandem proſe-
quamur ſuperiorem demonſtrationem, vt oſtendatur veritas reliquarum
99e propoſitionum, &
hoc erat propoſitum.

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