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Leibniz-Handschriften zur Mathematik LH 35, 13, 2b, fol. 148r

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: 0.79.

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. 149v); this page is its right half.

The machine reads it as

  1. Z dy
  2. e
  3. 5) + deo t
  4. 19 = e
  5. Assumta aequatio, in qua, b, c, e, deo sunt con-
  6. stantes, differentietur, fiet: dusa
  7. cy
  8. d2dy b7 + Zddyb7+ deo D + +Zdy cdy b + deo dtb7 + deo tcdy b = 0
  9. lc
  10. cy
  11. S
  12. ricu
  13. dividendo per (3 atque ordnando fit duoat + Cdco F dy + cdydus + ddy =0
  14. Aequatio ergo quae hiic iventifican.
  15. +1Z d9 pr ole
  16. sit aequatio data V dxdx + cdydus + ddy = 0 posito V dari per N
  17. dxax
  18. Unic aa ddZ = C dcode, et fiet aa ddz:
  19. erit v
  20. et
  21. agLadt:Z et quia abest dus, in data, fiet in praecedente C + deo + aadZ =0
  22. potest, poterit solvi.
  23. e
  24. C
  25. aa dcodt: vdxdx) seu d: den - - C vdXdx
  26. Sia Z progressionis Geometricae, erit dZ: dq = dq: Z et ddzue = d Z1Z: Z et ddz: 7 = dZdZ . 2
  27. (L andcod Coco de:
  28. -+ a
  29. y = - cvdxdx et fit dZ: Z = e dx 1 - cV. Et habetur
  30. per quadraturas ex, X adeoque et et proinde et c revera enim dz: Q =d(3
  31. Et habemus dz dur Z2
  32. ded
  33. ydyb + deot b =e solvi potest, nam transformetur in
  34. Habita autem Z et deo habetur et C
  35. porro aequatio
  36. C
  37. scy
  38. =C, et pro t7 ponendo fie L
  39. = e, uti omnia habentur praeter , adeoque et
  40. Icy
  41. 1 cdy b + deo F B
  42. hanc C
  43. quia ergo solvi potest aequatio V dxdx + Ac dydus Hanas
  44. y d + ded F
  45. seu Vdxdx + deoC gdcodso + adcod es =
  46. liet aa vdx cet
  47. siu de=
  48. dx
  49. A
  50. cc 4V= a
  51. Y-CV
  52. C
  53. cc8- a
  54. Vdxdx + p axdy + cdy dy + aa ddy =0
  55. et quia da=
  56. a Yt(V): V
  57. 7 d((rdx) X MdxdZ = aa dd7,: Cd co)
  58. sed ibi incommodum est, quod
  59. a
  60. nam
  61. tus tc dydus + ddy =0
  62. y = acco at; vdxdx et cdio et deo + aa dZ =
  63. y v da
  64. dx 1- cV:
  65. Sed talis aequatio aliunde solvi potest
  66. nam fit
  67. (id si hy in data non abfuisset, v. g. si habuisseruns vdx dx + B
  68. fieret vC 44 dcodb. Z7
  69. fieuet L
  70. en
  71. dy: deo = c: a et Ady: deo =: a, e his valoribus ubstitutis
  72. fit vdx dx + AC dco dco 88: aa taadcod8: a =
  73. ponatur
  74. a
  75. a
  76. etiam itar ad ddx
  77. ZaE
  78. yndx
  79. nam b habetu
  80. exs

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2b, fol. 148r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068198:0295?run=74