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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[91.] Notæ in Propoſ. XLV.
[92.] SECTIO VNDECIMA Continens Propoſ. LXVIII. LXIX. LXX. & LXXI. Apollonij. PROPOSITIO LXVIII. LXIX.
[93.] PROPOSITIO LXX.
[94.] PROPOSITIO LXXI.
[95.] Notæ in Propoſit. LXVIII. LXIX. LXX. & LXXI.
[96.] SECTIO DVODECIMA Continens XXIX. XXX. XXXI. Propoſ. Appollonij.
[97.] Notæ in Propoſit. XXIX. XXX. & XXXI.
[98.] SECTIO DECIMATERTIA Continens Propoſ. LXIV. LXV. LXVI. LXVII. & LXXII. Apollonij. PROPOSITIO LXIV. LXV.
[99.] PROPOSITIO LXVI.
[100.] PROPOSITIO LXVII.
[101.] PROPOSITIO LXXII.
[102.] MONITVM.
[103.] LEMMA IX.
[104.] LEMMA X.
[105.] LEMMA XI.
[106.] Notæ in Propoſ. LXIV. & LXV.
[107.] Notæ in Propoſ. LXVI.
[108.] Ex demonſtratione præmiſſa propoſitionum 64. & 65. deduci poteſt conſectarium, à quo notæ ſubſe-quentes breuiores reddantur. COROLLARIVM PROPOSIT. LXIV. & LXV.
[109.] Notæ in Propoſ. LXVII.
[110.] COROLLARIVM PROPOSIT. LXVII.
[111.] Notæ in Propoſit. LXXII.
[112.] SECTIO DECIMAQVARTA Continens Propoſ. LXXIII. LXXIV. LXXV. LXXVI. & LXXVII. PROPOSITIO LXXIII.
[113.] PROPOSITO LXXIV.
[114.] PROPOSITO LXXV.
[115.] PROPOSITIO LXXVI.
[116.] PROPOSITIO LXXVII.
[117.] Notæ in Propoſit. LXXIII.
[118.] LEMMA XII.
[119.] Notæ in Propoſ. LXXIV.
[120.] Notæ in Propoſit. LXXV.
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8648Apollonij Pergæi
Igitur C a eſt li-
11o63[Figure 63] nea quinta propor-
tionalis
aliarum.
quatuor, & c. Quia
poſitæ
fuerunt qua-
tuor
rectæ lineæ F C,
N
C, O C, C A con-
tinuè
proportionales,
eſt
que C A ad C a, vt
O
C ad C A;
ergò pri-
2237. lib. 1. ma F C ad tertiam,
O
C eamdem propor-
tionem
habet, quàm
O
C ad quintam C a
continuè
proportio-
nalium
, quare com-
parando
homologorũ
33Lem. 4.
præmiff
.
differentias F O ad
O
a eſt, vt F C ad C
O
;
ſedfacta fuit vt
F
O, ad O C, ita f O
ad
O B;
ergo compo-
nendo
in hyperbola,
&
comparando dif-
ferentias
terminorũ
44Lem. 2.
præm
.
ad conſequentes in,
ellipſi
, eſt F C ad C O, ſeu F O ad O a, vt f B ad B O;
nempe vt f h ad eandem O a,
propter
ſimilitudinẽ triangulorum B fh, &
B O a; & ideo F O, & fh æquales ſunt.
55p
Et ponamus rectangulum g e commune, & c. Et addamus in hyperbola, &
77q auferamus in ellipſi rectangulum g e communiter.

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