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Leibniz-Handschriften zur Mathematik LH 35, 3 B 5, fol. 31r

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: 0.84.

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. 32v); this page is its right half.

The machine reads it as

  1. A
  2. sa
  3. Et
  4. +1 1+a F
  5. al -al
  6. = al =at e
  7. ndi
  8. paritu
  9. e
  10. la jc P
  11. il Ita
  12. al -al
  13. +al + a
  14. -al + a
  15. -2al
  16. a
  17. plici ut ante
  18. El
  19. a
  20. Divisio dyarithmica
  21. ice
  22. Notatu diguum
  23. 1ceseetb et
  24. Si a = 0 et l = 0 fit X = 1 si
  25. sie a = 1 et l = O fit X = 1 sit
  26. sin a = 1 et L = 1 fib X - 1
  27. Si a = 0 et l = 1 fit X =0
  28. sit X= 410, 2a + 1l + 13 al
  29. si a et b 20 fit = 10 = C
  30. si a a = , e C e = 0 fit X = 1 + 11 = 1. Erp
  31. si a = c et l = 1 fit X = 1 + 12 = 0. Ergo 12 = -
  32. Denique si a = 1 et l = 1 fit X = 1 - 1 + 13 = 1. Ergo 13= 1
  33. Et tandem genicaliter X = 1 -. L + al
  34. sit y = 10 + na + 13b + 13 l + 14 alri5 B l+ 16 ab + 17 ac
  35. Si a = 0 et b = 0 et l=0 fit y = 0 ergo 10 =0
  36. si l= 0 et a = 1 et b = 0 fit y = 1 = 11. sin a = Det b = 1 fCy 20
  37. Nin a = 1 et b - i fit y = 1 = v + 16 fit1 b e
  38. Si l = 1 et a = 0 e b =0 fit y = 1 = 13 sin a = l et b -0 fit g
  39. fit y = 0 = 12
  40. fit 9 -0 = 1 + 1 + 14 et 14 = = 2. sin a = 0 et b-
  41. fit y = 1 = 1 + 15 et 15 =0 sin a= 1 et b = fit y-0
  42. = , + 1 = 2 + 17. Ergo 17 =0 et tundem erit
  43. generaliter y = a + l - 2al
  44. e
  45. si a = 1 fit X - 1
  46. si a = 0 et b = 0 sit X20
  47. el
  48. -al
  49. si a = O et b = 1 et C = 1 fit X =1
  50. fit X = atb -ab- b + ab + abl + bc ( abe si A = 0 et b = 1 et c = 0 et la0 fi1 X - 1
  51. si a =0 et b = 1 et C = 0 et l = 1 filXe 2
  52. X = 10 + 1a + 2b+ BC+ 14 L+ 15 ab+ I6aC + 1 7bC + 18 al+ iu bl + 20 clt 2t abeF
  53. + 7 abc + 2 ab l + 23 acl+ 24 bcl + 25 abcl
  54. 120 si omnia 0, nempe a, b, C, l, fit X =0. Ergo 10 =0
  55. si a = 0 et b = 0 fit x = 0. si C = 0 et l = 1 fit X = 0 = 14 sin C= 1 et 1=0
  56. fit X ~0 = 13. si C = O et C =) et l = 1 fit X = 0= 20
  57. si a = 0 et b = 1 et c = 0 et = 0 fil X = 1 = 12, siy c = 1 et lc0 fil X = 1
  58. = 11 + 17 Ergo 17 =0 sin C= D et l = 1 fit X = = 14 19 et 19 = - 1
  59. sin C = 1 et l = 1 fit X = 1 = 1 H - 1 + 24 fit 24=1
  60. sit si a = 1 et b = d et c = 0 et l = 0 fit X = 1 - 1
  61. si C sin l = 1 fit X = 1 = 1 + 18. Ergo 18 = 0. sin c = 1 rt (=0
  62. fit x = 1 = 1 + 16 fit 16 =0 sin C- 1 et 1 = 1, fiet X - 1
  63. 1 +6+ a 23, seu 16+ + 23 -0 seu 23 - - 16
  64. = 1 + 23 Ergo 23=0 si a = 1 et b = 1 et C = 0 et l-0 fit x1
  65. X = 1 = 1 + 1 + 15 et 15 = -1 sin C = 0 et 1 = 1 fit X = 1
  66. 1+ 1 = 1 = 1 + 22 fit 22 = 1. sin C= 1 et l = 0 fit X~I
  67. fit X = 1 = 1 + 1 = 1 + 21 Et 21 = 0. sin C = 1 et l=1 fit X = 1
  68. (fit X = 1 - l + al ut aute
  69. 11114 1 - 2 Et tandem X = a + b - ab - bl + abe tabl + bel- 2afel. Hine si pro a ponamus opro b, F, , )
  70. = 1 + 1 - 1 = 1 + 1 + 1 + 1 + 25 et 25 = -2
  71. si = sit = A + B - AB - BL + ABC + ABB + BCL - 2ABCL
  72. sit aL A = l- al B = a - al
  73. = + l = al
  74. + a = A + abl
  75. +Dabl
  76. +al, e
  77. +al
  78. ab
  79. C =b. et et L=l
  80. +d - 2al b ut ante
  81. pivi damus ... a)b).
  82. si a = 1 et h - 1 fit X = 1 si d = 1 et h = 0 et b 0 fit x = 0 si a = 0 et h = D fit A-
  83. = +l te
  84. sit X = 10 + ua rih. per. hl
  85. sed a = 0 et h = 0 incommodum est quod possunt satis facere tam c quam
  86. et fit X - 1 =9 et X =0 =0 Ergo XX = 1 X + 1. 0 = 0 seu X - x =0
  87. seu X = sese o,t sit si a= 1 et h = 0 fit X = 0,l + 11 = 0 seu
  88. Ergo 11 = = 0,l sit si a = 0 et h = 1 fit X = 0 A = 01 + 12 et 12 = -0, 1
  89. denique si a = l et h = 1 fit X = 1= 0,t F - 0, bt = 0, 1 quod est
  90. impossibile, itaque non licet relinquere in divisore generali ellaquere
  91. primam incertam
  92. licebit dividere per
  93. ipsi ergo non licet dividere per h, multo mmus
  94. sid si
  95. Generaliori adhuc calculo opus
  96. non per 1) l
  97. sore dividendo per h
  98. sed video rem non procedere

Cite

Leibniz-Handschriften zur Mathematik LH 35, 3 B 5, fol. 31r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068255:0061?run=74