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Leibniz-Handschriften zur Mathematik LH 35, 13, 2b, fol. 139r

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: 0.80.

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. 140v); this page is its right half.

The machine reads it as

  1. si
  2. sit log. a 1hil
  3. a a = Z X = sdz:
  4. du = dx a seu d, a = dx a
  5. Sit log. b = 1 et log. a = 0
  6. s
  7. sa
  8. s
  9. s
  10. D
  11. N. X qV j X: a
  12. a
  13. ba
  14. dx = dZ. Z
  15. 7:a. Ergo
  16. X: a logb = log. a = log. Z - log. a. et
  17. seu per aeq. 1. et 2 fit X: a = log. Z. seu
  18. X: a = 5 dZ: Z et +X. Z: a = dZ. adeoque ex 7 et 3
  19. 1Xia (∞)
  20. fit dx b: a
  21. X: a
  22. 1
  23. =dZ. Ergo denique ax bia
  24. 0)
  25. c2d
  26. seu ax b:a = a. b: a (+ C)
  27. pore b: a. Xa = Z: a X: atlogX = log. Z
  28. 1391
  29. (. X: a
  30. seu X: a sax :X = (dz. Z. seu dx: a + Gdlx: X = dz. 2
  31. (C
  32. et fit dZ = Z ex Z: a + 4,Z. X dx. Ergo summando et
  33. q explicando in aeq. 5. summata per aequ. li fiet
  34. X: a
  35. dx
  36. a bia. X: a = (b: a X: a dx u+ b: a.
  37. X:a e 16
  38. Ergo per 6 juncta aequalo calculi praecedentis
  39. fit
  40. il
  41. a
  42. a
  43. b:a. X: a dx = b: a. X - a b: a.
  44. 1
  45. =Xda
  46. Generalius sit 1= XanC) qua fiet utique
  47. R.a
  48. dque = s a + n Z. X ax seu Z= (Z: a dx + n5Z. X ax. seu ex1
  49. 2
  50. a
  51. b: a X: a = b: a X: a dx + b: a X: a Pax
  52. a
  53. o
  54. (4
  55. id n
  56. Hinc habetur illud memoriale omnes dari summas talium
  57. talis
  58. b: a X: a. ax, qualiscunque sit n, modo sit
  59. rationalis integra, datur enim cum n = 1, ev anescente
  60. X. a, tunc eum habetur summ per aeq. 10 calculi primi;
  61. ergo et datur si n sit 1. Hinc ergo porro datur si
  62. n sit 2, et ex hac si n sit 3. et ita porro Hinc et
  63. vicissim datur si n sit sit - 1. quia posita n = 0 in aeq. 4
  64. ergo et si n; sit = 2, etc
  65. sed quid si n sit fractio.
  66. ut praeparemgue aditum ad alteriora, resumamus
  67. ert et proriontneti a tit srat

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2b, fol. 139r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068198:0277?run=74