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Leibniz-Handschriften zur Mathematik LH 35, 13, 2a, fol. 85r

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.

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The machine reads it as

  1. e Tangentes curvarum transcendentium per
  2. exponentes indefinitos habentium
  3. X+ de
  4. dy aequ +a = a
  5. Ergo 0 aequ dy aqu.
  6. inquiratur valor
  7. X∞dx
  8. a
  9. x
  10. L
  11. yt dy
  12. X+Ax
  13. nta Xo
  14. Xtx
  15. seu +y
  16. 7 y+ dy
  17. Xtdx
  18. aqu 0
  19. per seriem in infinitam secundum calculum loganthmorum.
  20. Et ita puto lancentes quaesitas exhiberi posse
  21. ) + du xx p
  22. tus (tc) Ergo fiec = xy + x y = X)
  23. dx
  24. xrax
  25. L X, y X1 dy
  26. J x Y ita
  27. s
  28. sed nihil hinc salis duci potest. Rocuorendum
  29. ad exponentium in seres honsformaoem.
  30. aec methodus etiam utile erit ad aequationes infinitas tiariis modis revocandas
  31. ad aequationes finitas indelerminati exponentis dupliciter enim tangens haberi
  32. poterit, fum si curva ipsa ad seriem infinitam reducatur quo facto et habebitur
  33. aequatio secies differentialis infinita; tum si aequatiocdifferentialis ipsius currae
  34. revocetur ad seriem infinitam, quo facto habebitur aequatio differentiaalis correcta
  35. dem adhuc aliter tentandum; considerando ut series numerstm, et poster
  36. postea ponendo differentins infinite parvas, vel saltem semper ad ea
  37. accedendo, ut appareat in quae tunc desinatur.
  38. Via hoc erit ad quadraturam
  39. circul et Hyperbolae analytram ita enim labebitu
  40. ex la natora quadatura HExperbolae per logarchmos
  41. enim tangente quadratricis vel lonarichmicae habita.
  42. dx aequ. log. X.
  43. Et differentialis
  44. l0g
  45. y C3)O
  46. e aqu
  47. d
  48. 2
  49. si ergo sit equatio A et l0g
  50. 2)
  51. aequ X dequ e logx. Exnatura cognithmolum
  52. L; ergo per 2 et 3 erit y logX aequ
  53. seu per 1 et 4 erit V sax
  54. ipsius serit: art
  55. IV
  56. X
  57. N(5)
  58. aequ
  59. sax
  60. d
  61. X
  62. + y dx aequ. a XY. Ergo d X aequ. du, X
  63. C
  64. g. XYax
  65. a aequ’y.
  66. l aqu

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2a, fol. 85r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068197:0169?run=74