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

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

[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.

234196Apollonij Pergæi nempe e, f ſunt æquales: deinde ducantur V Z, Y a ad axes ordinatæ;
ergo (propter ſimilitudinem duarum ſectionum) T Z in Z e ad quadra-
11d tum Z V eandem proportionem habebit, quam X a in a f ad quadratum
a Y, & angulus e æqualis eſt angulo f; igitur V e T ſimile eſt Y f X, &
22Propoſ. 6.
pręmiſſ. pariter O T R, Q X S; & propterea O e ad R V eandem proportionem
habebit, quàm Q f ad Y S, & propter ſimilitudinem duarum ſectionum
B I ad I A eſt, vt E K ad K D, & A I ad I O, vt D K ad K Q propter
ſimilitudinem duorum triangulorum; ergo (ex æqualitate, & comparan-
33Lem. 1.
lib. 5. do antecedentes ad ſummas vel differentias terminorum) erit B I ad B O,
44e vt E K ad E Q, ſed B T ad B I erat, vt X E ad E K (propter ſimilitu-
dinem duarum ſectionum)

265[Figure 265] ergo ex æqualitate, & rurſus
comparando antecedẽtes ad
ſummas vel differentias ter-
55Ibldem. minorum B T ad T O erit,
vt X E ad X Q, cumque T
Z in Z e ad quadratum V Z
6637. lib. 1. ſit vt X a in a f ad quadra-
tum a Y (39. ex 1.) & qua-
dratum V Z ad quadratum
Z e eſt, vt quadratum a Y ad
quadratũ a f erit T Z in Z e,
ad quadratũ Z e, nempe T Z
ad Z e vt X a in a f ad quadra
tum a f nempe G a ad a f, &
comparãdo antecedentes ad
differnntias terminorũ in hy-
perbola, & ad eorum ſummas
in ellipſi, fiet Z T ad T e, nẽ-
pe quadratum B T (quod eſt
æquale ipſi Z T in T e (39 ex 1.) ad quadratnm T e eſt, vt X a ad X f,
7737. lib. 1. nempe a X in X f, quod eſt æquale quadrato E X (39. ex 1.) ad qua-
dratum X f; ergo B T ad T e potentia eſt, vt E X ad X f; & propterea
88Ibidem.

266[Figure 266]

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