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Leibniz-Handschriften zur Mathematik LH 35, 5, 25, fol. 17r

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: 0.74.

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. 18v); this page is its right half.

The machine reads it as

  1. B B. pay. ullima pro ifferentialibus so evendis
  2. et quod aequalio summatoria. determinatioo diffelentiali
  3. at
  4. sit aequatio differentialis generalis, differentiis non assurgencibus ad potestatem
  5. a 1bxacygexpxyeg.
  6. a +bx+ cy ++CXX+GXy+gyy dx +lemxrny tpxxtqry tryy dy aequ. 0
  7. rationalis
  8. bic
  9. 10eo y assumatur ejus valor in teger, per x et novam assumtitiam v.
  10. seu py aqu. heexin dicxillhorxnormm
  11. Si
  12. 1 aequ H + 1X +2V + PXX + 12 xV + jo
  13. et sipt aeq. 3
  14. substituatur is valor in aequ. 1. ascendet D ad stum gradum in aequ. 3.
  15. ssumatur aqu. 4. et fiaut formulae tollenda numerus viginti
  16. in gradu primo enim sunt mediae participantes de utraque: een
  17. sunt numero in est nulla, in secundo una xB, in certia duae,
  18. el in quarto tres XB. X Yp. XV inquinto quatuor summa
  19. X1B W
  20. facit decem, quae bis sumenda tam in dx quam cu ax, facil 20.
  21. At in aequ. 2. sunt solum C arbitiariae.
  22. Aequation. 3. uddenda et forcunta arbitraria
  23. differentialis generalis, summabilis. Seu diffednera
  24. formula generalis: 6+ 3X + 4v + 3 XX + 341V + 4 v ec. usque adi
  25. e
  26. ubi erunt arbitario cirius differentia etiam eris ascendet ad ro
  27. ubi etiam erunt arbitrariae ubi plures nova habebuntur arbitrariae.
  28. sed jam video prodesse solum nobis 34XV. 634Xv. 34Xp
  29. etct usque ad 3C34 X BE quae sunt numero (1+2+3+4+5) Quindecim
  30. unde addendo prioubus 6 fient 21.
  31. videtur sufficere ut faciamus _ aqu h4 KX + V
  32. y aequ h + fx +Z v. et substiluamus valorem in aequatione 1.
  33. partfiat a +bx +.
  34. (3)
  35. Oaeqo
  36. Bato pusx
  37. + CXX
  38. ch +cfx cZV + fAxX +f7XD
  39. +fhx
  40. g
  41. tnar
  42. +otax tersa
  43. Ztirtz iltb
  44. qta trH
  45. rh b)rhtx+(ta
  46. H1Z XV +BvDZd + βX
  47. O
  48. 0
  49. l
  50. I +mX tZB+ pXX + q22V +rZZBB
  51. nh+nFx arzo + Px +97XD + rZV Fdx nh + nt X +
  52. +BY
  53. 22+ r1Z7 + D ∞9
  54. d.
  55. Id
  56. Ih Eghsa Xgliqv +gFx + Eg ZXV + 926
  57. 4. M X
  58. Hd, ei senso) r trhtxrs EV + r Hux
  59. +B vodxAu Exvdo
  60. 4
  61. 7
  62. 10
  63. C
  64. aequationes A. B. C resolvendo evanestt
  65. 2. Exaequ. C fit qaequ. 29
  66. exaquiA sit axtrea m. Est. 29. equ. h facita put est in cerso
  67. u
  68. +) ex 3B d
  69. si
  70. s
  71. dutu eficere ut qil
  72. a qu. 29.

Cite

Leibniz-Handschriften zur Mathematik LH 35, 5, 25, fol. 17r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068043:0033?run=73