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

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[121.] Notæ in Propoſ. LXXVI.
Page: 137 (99)
[122.] Notæ in Propoſit. LXXVII.
Page: 138 (100)
[123.] COROLLARIVM.
Page: 143 (105)
[124.] SECTIO DECIMAQVINTA Continens Propoſ. XXXXI. XXXXII. XXXXIII. Apollonij. PROPOSITIO XXXXI.
Page: 147 (109)
[125.] PROPOSITO XXXXII.
Page: 147 (109)
[126.] PROPOSITIO XXXXIII.
Page: 148 (110)
[127.] Notæ in Propoſ. XXXXI.
Page: 148 (110)
[128.] Notæ in Propoſ. XXXXII.
Page: 149 (111)
[129.] Notæ in Propoſit. XXXXIII.
Page: 149 (111)
[130.] SECTIO DECIMASEXTA Continens XVI. XVII. XVIII. Propoſ. Apollonij.
Page: 150 (112)
[131.] Notæ in Propoſit. XVI. XVII. XVIII.
Page: 152 (114)
[132.] SECTIO DECIMASEPTIMA Continens XIX. XX. XXI. XXII. XXIII. XXIV. & XXV. Propoſ. Apollonij. PROPOSITIO XIX.
Page: 154 (116)
[133.] PROPOSITIO XX. XXI. & XXII.
Page: 155 (117)
[134.] PROPOSITIO XXIII. & XXIV.
Page: 156 (118)
[135.] PROPOSITIO XXV.
Page: 157 (119)
[136.] Notæ in Propoſit. XIX.
Page: 157 (119)
[137.] Notæ in Propoſit. XX. XXI. XXII.
Page: 158 (120)
[138.] Notæ in Propoſ. XXIII. XXIV.
Page: 161 (123)
[139.] Notæ in Propoſ. XXXV.
Page: 161 (123)
[140.] SECTIO DECIMAOCTAVA Continens XXXII. XXXIII. XXXIV. XXXV. XXXVI. XXXVII. XXXVIII. XXXIX. XXXX. XXXXVII. XXXXVIII. Propoſit. Apollonij. PROPOSITIO XXXII.
Page: 162 (124)
[141.] PROPOSITIO XXXIII. XXXIV.
Page: 163 (125)
[142.] PROPOSITIO XXXV.
Page: 163 (125)
[143.] PROPOSITIO XXXVI.
Page: 164 (126)
[144.] PROPOSITIO XXXVII. XLVI.
Page: 164 (126)
[145.] PROPOSITIO XXXVIII.
Page: 165 (127)
[146.] PR OPOSITIO XXXIX.
Page: 166 (128)
[147.] PROPOSITIO XXXX.
Page: 166 (128)
[148.] PROPOSITIO XXXXVII.
Page: 166 (128)
[149.] PROPOSITIO XXXXVIII.
Page: 167 (129)
[150.] Notæ in Propoſit. XXXII.
Page: 167 (129)
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page |< < (191) of 458 > >|
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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