Leibniz Legible

Machine transcription of the Leibniz Nachlass

Search the Nachlass

Leibniz-Handschriften zur Mathematik LH 35, 13, 2c, fol. 10v

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

The machine reads it as

  1. dy: dx = 2x + yy,. aa
  2. p
  3. _ fis gionaD naa y 12aa yy
  4. a 20Xx +Z1XXy + 22XX yy
  5. son
  6. sit dy: dx = 10+ 11Y + 18Y
  7. +20yy + 21y + 22y
  8. compendio 30 + 31 y + 32 yy + 33y+34 y =0
  9. d+ =V
  10. a b + dD = 0
  11. -D -dD: +C. fit
  12. Unde pustra sex sumae
  13. d30 + d31y + 314 +432 yy + 32Gdy +33 p 13339y dy + 434y + 4. 34y dy
  14. yi
  15. siet -dy = d30 + d31y + d32yy + d33 7 + 349 = Xx 4.
  16. 1) + 2.324 3. 33,+4. 34y
  17. ast
  18. aa
  19. ade sit a quatio conferenda aequatim O multiplicatiae per
  20. multiplicando illam per m + ny fient summi dermini, _, 3 m y + 34ny
  21. ab una parte e ab altera 4. 34p y + 333pXX 1
  22. et sit p n
  23. aa
  24. 33n y4
  25. et 3. 33pXX = 34m + 4. 33P
  26. constans
  27. sit. 34 in Constanti ratione ad 33 fiat rx habebitur a p: M
  28. a
  29. ua
  30. ta
  31. supersunt ergo aequationes pro y, yy, y, 9, numero 4, pro quibus
  32. 2. Pro quibus
  33. aosunt literae arbitrariae 30, 31 32, 33
  34. biem prodeum equationes d ferentrates
  35. quae in fellor folvi possunt
  36. Mimi gradas
  37. somplices plurm
  38. incognitarum quae ebuci possunt ad aequationes differentrales
  39. simplicesdem, quarum quaelibet sit unique incognitae
  40. totidem
  41. qualiones sunt 4, tollantur d31 et 432, habentur duae aequitione
  42. in 8 in quibus 30, 31, d30 431 32,33. Unde differentiando
  43. abebimus 132, et33 30, 31 d30, d31, dd30, dd3 ita jam
  44. lavebim 54q. duas in quibus 30, 31 d30 d3, ad30, dd 31
  45. sed ita ut tollatur ad30 et d d30, 4 veui descendum ad 3
  46. rursus ad dd20
  47. 130, d. 30, d130
  48. Iti lindem aderi aequalio ubi 3C, d30
  49. si jam eo
  50. sit X+ X 30 + XX d30 + X dd30 = 0
  51. 1
  52. a
  53. idendum an arbitrariae sufficientes
  54. si 30 est rationalis gradus n erunt termini graducum n + 1., A et arbi
  55. nariae lolidem, sed si sit XX30 + XXx d30+ X dd30 + x nen licet
  56. assargitur altiu unde et judicari pte quid possibile et quo casu. Nam
  57. aquaatio reddenda deurca
  58. 20+219f229y
  59. C
  60. ∞d6 - - 49

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2c, fol. 10v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068199:0020?run=74