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Leibniz-Handschriften zur Mathematik LH 35, 4, 3, fol. 10r

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

The machine reads it as

  1. s
  2. ML L =
  3. fgg
  4. 2M = f99 + fht
  5. Oc
  6. N+ M = bCC
  7. M = L = fhh
  8. 2L = fgg- fhA
  9. N(-M = b dd
  10. V = fgh
  11. A = bcd
  12. nAN (V= (nH Pet Mn +ZnA LHH L n
  13. ,ob VV = MM = LL
  14. ob AN = NN - MM
  15. sit M = A + V A f fiet M = (AL tVIFNE + 2AV = 2NN = 2VY =(NAAVV)
  16. sit V = Ea H et fiet N 4 2X e - 2 = 2E H = 0. Et A = HC, 1 - 28,i, 2, s - C
  17. Seu f= 28 - 1, FF, 2, (C- 1)
  18. 2
  19. V- e
  20. a
  21. = f +g fg9 + f hh
  22. CL = fgg- fhh
  23. =bcd fit b = 2C- 1. I
  24. agh
  25. 2N = bcc + bdd
  26. 2, C- 1, cd
  27. 2M = bcc - bdd fit fgg + fhh = bcc D bdd
  28. et pro f et b substitutis duobuqvaloribus sit eid + =
  29. seu
  30. et
  31. Ogua sih
  32. dum
  33. Rg
  34. =
  35. infit 20. = (C+ ) r(F 1) = Ld, +)
  36. a n
  37. a g
  38. 20-1
  39. c
  40. 20-2 0 ln 20-2 C
  41. 20 -1 cc-dd. - - ((2 - 1) = (C t.d)1
  42. 2C22 Cd
  43. fint (c+d) Y = gc +V
  44. e
  45. 2-2 = cd; cad
  46. (Cc - dd)r = cd + C - d sit d= 4(c- d)
  47. d= C9:, et 9
  48. C+d= c +C (C +9c; Y = 9c + 1, 9+ 1
  49. Haec aequatio ib solvenia superest
  50. ed his missis videamus autres Aequationes Wre = MM+ LL
  51. VV
  52. aY
  53. re-1 d
  54. Wr= mn- LL
  55. Z MM = L.L Ad = NN - MM, n M = A A + VV solvere
  56. dficent per suries series dyadicas. Quommus
  57. et ssumimus _ L = 10 + uY + 12 yy + etc. posito y signisieare 2
  58. de 10, 1, 12, etc esse 0 vel 1. similiter sit M = 20 +217+ryy
  59. s
  60. N = 30 + 31 ) +B2yy + etc quia autem et = 40+4050 + 51y+ 5rqu
  61. L
  62. et M = 60 +61y +62yy + et. et V = 70+71y17 2yy+ etc
  63. dratur Ve A per aeq. 1. et V per aeq. 2, et A per aeq3
  64. ingendo, quid fiat si finiamus, et pro fin progressionem quaerendo efficiendu
  65. videndo
  66. Si cautem semper ut numeri sint positivi
  67. isile erit condere generalem
  68. F iCanonem pro differentia quadralor quadrulo aequanda, vel quod ide
  69. summa quadralar quadrato aequanda sit quia NN = NN. MM, ponere
  70. possumus aN + e L egq N - M = fhR 2N = fgg+ fhh 2M = fgg = fhh
  71. Ergo pro serie us solum assumere duo quadrota. sit N = (9 M= fR. fiet R.g = 9 +hh
  72. R = 99-kh si N, M, X priminter ge
  73. ent f=1
  74. ex AC
  75. +-
  76. a2
  77. 11
  78. 1
  79. 1a
  80. e
  81. 2

Cite

Leibniz-Handschriften zur Mathematik LH 35, 4, 3, fol. 10r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068000:0019?run=73