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.

229191Conicor. Lib. VI. ad A M eandem

257[Figure 257] proportionem ha-
bebit, quàm X O
C ad quadratum
O C, ſeu eandẽ,
quàm habet X O
ad C O, & com-
parando conſequẽ
tes ad differẽtias
terminorum M A
ad A T eandem
proportionem ha-
bebit, quàm O C
ad C X: erat autẽ
prius T A ad A
E, vt X C ad C F; igitur ex æquali M A ad A E erit, vt O C ad C F, & fue-
runt oſtenſi anguli E, & F æquales. Quod erat oſtendendum.

SECTIO SEPTIMA

Continens Propoſit. XVIII. & XIX.

CViuslibet ſectionis A B C duo ſegmenta C F, A E ca-
dentia inter duas ordinationes A C, E F ad vtraſque par-
tes axis B V ſunt inter ſe ſimilia, & ſimiliter poſita, nec ſunt
ſimilia alteri ſegmento (niſi

258[Figure 258] in ellipſi, in qua quatuor ſeg
menta memorata in propo-
ſitione 8. ſunt æqualia, ſimi-
lia, & ſimiliter poſita, quæ al-
teri ſegmẽto ſimilia nõ ſunt.

Quoniam vnumquodque eo-
11a rum alteri congruit, nec non cõ-
gruunt duo ſegmenta GI, K H
in ellipſi (7. 8. ex 6.) at non ſunt
ſimilia alteri ſegmento: ſi enim
hoc fieri poteſt, ſit ſegmentum
L M ſimile ſegmento F C. Et
quia F C congruit A E. Ergo
duo ſegmenta L M, A E ſunt
ſimilia, producamus A E, L M
quouſque occurrant axi in N,
22b O, erit angulus N æqualis O (vti
demonſtrauimus in 16. & 17.

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