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

< >
[71.] Demonſtratio ſecundæ partis. PROPOSITIONIS LI.
Page: 81 (43)
[72.] Notæ in Propoſ. LII. LIII.
Page: 83 (45)
[73.] Secunda pars buius propoſitionis, quam Apollonius non expoſuit hac ratione ſuppleri poteſt.
Page: 87 (49)
[74.] Notæ in Propoſ. LIV. LV.
Page: 92 (54)
[75.] Notæ in Propoſit. LVI.
Page: 93 (55)
[76.] LEMMA VIII.
Page: 95 (57)
[77.] Notæ in Propoſ. LVII.
Page: 96 (58)
[78.] SECTIO NONA Continens Propoſ. LVIII. LIX. LX. LXI. LXII. & LXIII.
Page: 98 (60)
[79.] PROPOSITIO LVIII.
Page: 98 (60)
[80.] PROPOSITIO LIX. LXII. & LXIII.
Page: 98 (60)
[81.] PROPOSITIO LX.
Page: 100 (62)
[82.] PROPOSITIO LXI.
Page: 100 (62)
[83.] Notæ in Propoſit. LVIII.
Page: 101 (63)
[84.] Notæ in Propoſit. LIX. LXII. & LXIII.
Page: 102 (64)
[85.] Notæ in Propoſit. LX.
Page: 103 (65)
[86.] Notæ in Propoſit. LXI.
Page: 103 (65)
[87.] SECTIO DECIMA Continens Propof. XXXXIV. XXXXV. Apollonij.
Page: 105 (67)
[88.] PROPOSITIO XXXXIV.
Page: 105 (67)
[89.] PROPOSITIO XXXXV.
Page: 106 (68)
[90.] Notæ in Propoſ. XXXXIV.
Page: 106 (68)
[91.] Notæ in Propoſ. XLV.
Page: 107 (69)
[92.] SECTIO VNDECIMA Continens Propoſ. LXVIII. LXIX. LXX. & LXXI. Apollonij. PROPOSITIO LXVIII. LXIX.
Page: 108 (70)
[93.] PROPOSITIO LXX.
Page: 109 (71)
[94.] PROPOSITIO LXXI.
Page: 109 (71)
[95.] Notæ in Propoſit. LXVIII. LXIX. LXX. & LXXI.
Page: 109 (71)
[96.] SECTIO DVODECIMA Continens XXIX. XXX. XXXI. Propoſ. Appollonij.
Page: 110 (72)
[97.] Notæ in Propoſit. XXIX. XXX. & XXXI.
Page: 111 (73)
[98.] SECTIO DECIMATERTIA Continens Propoſ. LXIV. LXV. LXVI. LXVII. & LXXII. Apollonij. PROPOSITIO LXIV. LXV.
Page: 112 (74)
[99.] PROPOSITIO LXVI.
Page: 113 (75)
[100.] PROPOSITIO LXVII.
Page: 114 (76)
< >
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

Text layer

  • Dictionary

Text normalization

  • Original
  • Regularized
  • Normalized

Search


  • Exact
  • All forms
  • Fulltext index
  • Morphological index
Impressum