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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[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)
[151.] Notæ in Propoſit. XXXIII. XXXIV.
Page: 167 (129)
[152.] Notæ in Propoſit. XXXV.
Page: 168 (130)
[153.] Notæ in Prop. XXXVI.
Page: 169 (131)
[154.] Notæ in Prop. XXXVIII.
Page: 169 (131)
[155.] Notæ in Propoſit. XXXIX.
Page: 170 (132)
[156.] Notæ in Propoſit. XXXXVIII.
Page: 170 (132)
[157.] LIBRI QVINTI FINIS.
Page: 170 (132)
[158.] APOLLONII PERGAEI CONICORVM LIB VI. DEFINITIONES. I.
Page: 171 (133)
[159.] II.
Page: 171 (133)
[160.] III.
Page: 171 (133)
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page |< < (198) of 458 > >|
236198Apollonij Pergæi268[Figure 268] tione figuræ diametri A L (40. ex 1.) erit vt quadratum E Q ad M Q
1137. lib. 1. in O Q, nempe in eadem proportione figuræ diametri D M (40. ex 1.)
22Ibidem. quapropter duæ proportiones figurarum earundem ſectionum ſunt eædem
inter ſe; & propterea duæ ſectiones ſunt ſimiles (12. ex 6.) at ſuppoſitæ
fuerunt non ſimiles. Quod eſt abſurdum.
PROPOSITIO XXIII.
SI autem ſectio A B C fuerit parabola, & ſectio D E F hy-
perbola, aut ellipſis: manifeſtum eſt, ſectiones non eſſe in-
3313. huius. ter ſe ſimiles. Et dico quod duo ſegmenta G C, H F non ſunt
ſimilia.
Si enim ſimilia eſſent haberent conditiones ſimilitudinis, quod eſt im-
44a poſſibile, quemadmodum oſtenſum eſt in omnibus ſectionibus ad propo-
ſitionem 13. ſi vero vna earum fuerit hyperbole, altera verò ellipſis,
idipſum oſtenſum eſt ad propoſitionem 14. Et hoc erat propoſitum.
PROPOSITIO XXIV.
CViuslibet coniſectionis A C D portio B A C D non erit
arcus circuli.
Si enim hoc verum non eſt educamus in illa chordas A B, C D, A C,
quarum nulla alteri ſit parallela: & educamus E F parallelam A B, & E
G parallelam A C, atque G H parallelam C D, & per ſingularum dua-
rum æquidiſtantium ſemipartitiones iungamus K I, L M, N O, quæ

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