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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[171.] PROPOSITIO IV.
Page: 179 (141)
[172.] PROPOSITIO X.
Page: 179 (141)
[173.] Notæ in Propoſit. I.
Page: 179 (141)
[174.] Notæ in Propoſit. II.
Page: 180 (142)
[175.] Notæ in Propoſit. IV.
Page: 182 (144)
[176.] Notæ in Propoſit. X.
Page: 182 (144)
[177.] SECTIO SECVNDA Continens Propoſit. III. VI. VII. & IX. PROPOSITIO III.
Page: 184 (146)
[178.] PROPOSITIO VI.
Page: 185 (147)
[179.] PROPOSITIO VII.
Page: 185 (147)
[180.] PROPOSITIO IX.
Page: 186 (148)
[181.] Notæ in Propoſit. III.
Page: 187 (149)
[182.] Notæ in Propoſit. VI.
Page: 187 (149)
[183.] Notæ in Propoſit. VII.
Page: 187 (149)
[184.] Notæ in Propoſit. IX.
Page: 188 (150)
[185.] LEMMAI.
Page: 188 (150)
[186.] SECTIO TERTIA Continens Propoſit. V. & VIII. PROPOSITIO V.
Page: 190 (152)
[187.] PROPOSITIO VIII.
Page: 191 (153)
[188.] Notæ in Propoſit. V.
Page: 192 (154)
[189.] Notæ in Propoſit. VIII.
Page: 192 (154)
[190.] SECTIO QVARTA Continens Propoſit. XI. XII. XIII. & XIV. PROPOSITIO XI.
Page: 192 (154)
[191.] PROPOSITIO XII.
Page: 193 (155)
[192.] PROPOSITIO XIII.
Page: 194 (156)
[193.] PROPOSITIO XIV.
Page: 195 (157)
[194.] MONITVM.
Page: 196 (158)
[195.] LEMMA II.
Page: 196 (158)
[196.] COROLLARIVM.
Page: 197 (159)
[197.] LEMMA III.
Page: 197 (159)
[198.] LEMMA IV.
Page: 198 (160)
[199.] COROLLARIVM.
Page: 198 (160)
[200.] LEMMAV.
Page: 199 (161)
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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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