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Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 118v

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: 0.79.

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. 117r); this page is its left half.

The machine reads it as

  1. 6) =
  2. sit c= tab et b d = aa: Vab
  3. e= scd f = CE : NCd. Ergo e = a f = ab: a = b
  4. Ergo hc erravit Gregorius, putans hanc feriem convergentem
  5. c = Vab d = 2ab:, a + tab seu d = 2CC:, a + C
  6. e= sed f- rec:, C+C cd = 28: a + ergo C = c YC :, a+C)
  7. = 2(cc 29:, a +C): (C) + H(2C: , atC) seu f - + ab:, a + vab, 14 at hab
  8. seu C = tab AE tab : 3 at +ab) f = 4ab: a + fab + 2 +ab
  9. seu f- 4ab., a + 3tab
  10. e = sCd f = 2cd; C+ sed
  11. = 2ec: c+ C
  12. e = H2 ab Vab:, at rab) f - 4 ab tab
  13. seu f= 2ab tab
  14. a vab + ab + rab tab
  15. seu f=
  16. 2ab
  17. 4ab vab
  18. 2644 4025 +el
  19. sit E = cd feri a
  20. ab Vab
  21. Trabrab
  22. atrab
  23. b+ Sab + Y(E ablabrelb.
  24. a= ad + cd = 2cc. fit a = 2Cc = cd, id
  25. d = 2 ab: 7 a +C
  26. (2cC - cd, :d) seu b = cd:
  27. 2cc ed
  28. b =
  29. 2es
  30. at rab:, sab
  31. atab + ab + Y (raab sab + 2 aa bb)
  32. cc = ab d = 2Cc:, a+c
  33. a b = cc: a
  34. et b = cc:
  35. a =
  36. a
  37. b
  38. Rcd
  39. 2C - d
  40. a
  41. 2c = d
  42. 408 - 2ccf
  43. 2ef-s
  44. rec -ef d=
  45. es
  46. bes
  47. 20-f
  48. 2dc = cr a = a = 21dc = c. 2cd - 1
  49. c
  50. i
  51. 2ad
  52. seu s 20d - 1, 28 - 1
  53. simplicior, si a: b = (6) c: d = (d) et ita ponro
  54. videtur res reddi
  55. fiet
  56. rec-cdrcd
  57. 25dd
  58. 25d) -1
  59. a cb7
  60. et a = c, 21d) -1 et (b) = qu. 2(8) -1,
  61. ita et si serres non sit lonvergens.
  62. tamen si in ipsa haberi posset relatio
  63. ila constans, haberetur utique nova proprietas
  64. Notandum hoc modo a et b) ex ipsis c etd)
  65. habentur non modo rationaliter sed et integre
  66. in indeterminatis.
  67. S.
  68. seniei per
  69. Hinc amplus
  70. 7) ete per se spectatae datur relatio
  71. spuplicior, sit enim (b) = qu (2() -1) se se
  72. b
  73. d
  74. seu 26= qu (2) -1) Ergo proter terminis
  75. c
  76. b, (C), (3) (6), (d) (f) ete assumamus 26) , 2(d), 2)f)
  77. XA, et fiet (() = qu 20
  78. et fiet (2) = 2 β = qutd 1) aquod est simplicissimum
  79. ultinum est
  80. scribendo β, id G,
  81. siet (3) = qu (G=1) Ergo = qu (qu (es 1) 1)
  82. 1S +B+1 = 8. Vercor nesit ersor, nam ut est2
  83. d= 2cc:, a + c
  84. ad + cd = 2cc a = 2cC - cd 2 d b = fc d:, 21c- +d
  85. d= Zab: a + fab
  86. sit c 2a b =B et 2 ci d a S fiot na iam 2 bi sit a : b = (b) et c: d = (d)
  87. Calculus resumatur c= sab
  88. fit (6) = (24c = Ed, : d) : ((d :, 2c- 8) = (2C = d,: D) qu = (2() - 1) qu
  89. CC = ab ergo b = cC: a
  90. tabemus ergo broprietatem simplicissimam seriei (b), (d) (), qua est
  91. (b) = qu (2d-1). Hinc dem quod verum in casu convergentiae
  92. ubi (b) = (d) = 1. Restituendo a, b, c, fiet 4 = qu (2C - 1)
  93. E
  94. propr i0 a
  95. A3 GGreg. Quadr. Cin et Wyp prop. 10
  96. B = 6)=
  97. o
  98. a2

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 118v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0234?run=74