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Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 184r

Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German. Mean line confidence on this page: 0.83.

Original at the GWLB · Page image · Annotations (IIIF) · Download text

One image of two folio pages side by side, registered by the library under both labels (also fol. 185v); this page is its right half.

The machine reads it as

  1. dx aqu
  2. aequ
  3. De Quadraturis omnium figuramm rationatium
  4. per circulam et Hypelbolam adde dimentionet curvaesam
  5. xdu Sydx aequ Xy
  6. Nam d Xy aequ X dy + y dx
  7. quia X +dX. yrdus = Xy aequ d.xy posito
  8. quod crescentibus X. crescant et y. Sed si crescente uno
  9. alterum decipscat Tunc quando scribitur ex pro uno scribendum
  10. est -dy. vel contra.
  11. 2x x dXy aequi
  12. CgX. y f 9. Ergo + S a lu 4+ se aqu.
  13. eu dato d datur sd et contra
  14. X y aqu X dy + 29X s. Ergo s X sy 4 asyx. aequ Xy
  15. . exKydy + AsyyX x aqu XXyy
  16. Et
  17. (X dy + 3 6Xyax aequ. X’y.
  18. sit X aequ Xy + ay scribi potent X sy aequ X gaus 4 a yt du
  19. x aequ
  20. ax hxyt -yyx ex +: Axxyy
  21. 3Xdx aequex dy 1. Xy G 1 ag y Ergo 3 Xydx aq u Lu Xy ly 1 + 2X dy +2 Xy dy
  22. XLX
  23. X xy
  24. a
  25. 2Xcus
  26. Ergo 37dx aequ 3 Ay au + 2x dex f. - 2 Xy. X + s +29 9
  27. Ergo ex data quadratur assaguaae datur: 3 y xy d
  28. (1
  29. a + bx + cy + d XX + eyyt, fxy +g Aet h_ + R Xy+ lXy + MX ny +p X stquy +YKy eq.
  30. unde fci: b x + cdus f 2d Xdx +2C ydy+ fXdus + 39 X sxt3hitus + KX du El Xytus ra m d , 1 p du t Ertisdus 2p
  31. sdivedet
  32. + fydx
  33. tqu teruguto
  34. x et pro dy scribendo seu pro d
  35. +2Hrydy + lyy dx
  36. seu dividendo per x e pro x scribendo. V. fici:
  37. b + cv + 2dx + 2e yv + f xv + 39 X +3hy v + KX v + El xy v +4mX + g C t3gxyr
  38. x+ 9 +erxyy
  39. +2K XIs + l yy restabunt X et x. in aequat.)
  40. epe harum duarum aequationum, tolatr 1. et 3. tonatur
  41. vitur regnula
  42. y: restabunt X. et V
  43. deer data initur curva cujus fi aequatio explicata sit per ordinatam a
  44. jam
  45. natura
  46. et abscissam comp aequationem inter abscissam Xe et ordinatam v. comparetur
  47. aequatio data 5 cum arbitraria 4. quae comparatio si non succedit impossibile est
  48. cuvam,
  49. eofiguram curvilineam datam habere algebraicam quadratricem.
  50. s sed ut per partes eamus, quaeramus primum curvas rationales quadraboles.
  51. est autem corvae ratiovalis quadratri, etiam ratio nalis
  52. X
  53. +
  54. X aqu. Z X Ergo ZS_ X sx aqu. X
  55. H Habetur autem quadratura omnium figurarum per aequatio valores rationales
  56. integros explicatarum
  57. ut R. a + bX + CXX + dX etc. Erit suum quadratrix
  58. y aequ ax + b XX + CXY + d X etc.
  59. Habetur et quadratura omnium figurarum
  60. v aequ x vel X vel X vel X etc. vel
  61. 215 1
  62. 5
  63. vel L. vel etc. quorum summae:
  64. put 106
  65. simplicium rationalium denita
  66. 1
  67. ubi nota L esse aream spati
  68. ex Hyperbolni
  69. infiniti
  70. X
  71. in Tilimeo

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 184r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0363?run=74