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LBr. 57, 1 · Bernoulli, Joh., 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: 0.77.

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. 119r); this page is its left half.

The machine reads it as

  1. idem alia ratione demonstrare placet, q per finitas
  2. issit Et resumamus semem har
  3. quantitas infinitis accedentes
  4. in ipsis fin
  5. Et incipiamus a serje harmonicorum (1nol 1.- e = 0
  6. 1EB in iptis sintis sit A = : ( et B3to) B = ABC et Ato) A - B = 0
  7. 6to
  8. et 4+B = 1 2 et 1) et A+B, : 2 = AZ B + seu A = 2B - B. + 2. 1. Et
  9. (Imo) A -B seu O = (per 6) (2B -2B 2. 4 = 2
  10. Similite() 1 - + + = - = = C (Edo) L + L = A (3tiu) L + + = B.
  11. et (it) A+ B, : 2 = (7 + + + =) B + L + seu (to). A = 2B -B + 2. +-
  12. et (7 md) A - B = 2. = + = O = + Eodem modo si
  13. Eodem modo si sit - + = + = = C = AC et A = + 1 + +, et
  14. B= 4 + 4 + 15, fiet C = 2, 8 + = = + 5 +
  15. 4 - = = 2
  16. + = _ + H + H
  17. 1 = = + 3 = 4 = + . Ergo - 2 = + 4 = 2
  18. Unde generaliter
  19. L - h + 3 - + = = = + 5 + Ergo - + = = = + + = = +
  20. + - Z + 3 4 158= + - = + L + = + L argo - + 5 + = = + 2
  21. Eno 2+ = +
  22. 9 id
  23. 3
  24. 4
  25. 4
  26. -a + y - 4 + - + - + 9 - 10+ 1 - + = 2 + + b + 1 + + sgo - 14 L 1 + - 121
  27. 1 =L +b - + 1 - + - + d - L + , - lt - = lg + + + + + + fgo 24 L + + n 4+
  28. uttie ubi tamen calculi adjecti mediante Ergo nihil novi docent, sed solum prora consicmnt
  29. Nam ex + = +L - + f l + = + 1g- L + - + Ba L (= + b+ L + L +t t + fit 1 ct + 1 d. + 3 - = 4+ 5. t
  30. et ex hoc rursus fit - = + ∞ = + . Et ex hoc rursus fit L - 1 = =
  31. Nunc pergamus ad quadratas fractiones: = O A sit A = et B =
  32. Fet d A+ B, 14 = B+ et A= 6 4 =1B + 4. . Ergo A - B = 4 -2B + 4. + = C vel
  33. et B = C - 4. :, 4. 7 et At B et A = 4 - 1. C -4. + 4 - 2. 4. , :, 4-2
  34. seu A = 4 - 10 - 4. :, 4 -2.
  35. eodem modo
  36. et A+B = A- B redit O, et A+ B = 40 (0 4. 60) 4. 8
  37. seu A+ B = 40 - 2. 4. +,:, 4 -2 seu 4 = 4 (, :) -v 4. p . 1 4, 4 -2
  38. Similiter + - + - = 0 A = + G B= 4 +
  39. A+B, : 4 = B + 6 + sq et A = 4- 1 B + 4. 7 t . Ergo A - B = 4- 2 B+ 4. 3
  40. seu B = C - 4. 56+ ., 4-2 et A = 4- 1 O - 4 ( + ) , :, 4-2
  41. et A + B = 4C - 2. 4. (56 + 54), :, 4 -2 (9 + + nt 1 - 4 (: 4 , G 1) -
  42. seu A + B = 2C CF
  43. +25436-
  44. (9 + 16)
  45. Habemus ergo N = 2C+ - 1) -(. 4 (5)
  46. 4+ht 19+ = L (tai 4 9 7) = 4 (36+ 54)
  47. ++-
  48. + 4 = 2(,- =) -
  49. L+ + + = 2 (1 4 + - 1) - + 16
  50. e+ = +
  51. 1
  52. + L
  53. =2(. 1t 2 35) = (15 + + 35
  54. 16, 2536) Et ita porro. Videndum ergo an demonstrari possit, dimidiam partem posteriorem terminorum ad
  55. priorem, habere rationem ita decjescentem, ut fiat major quavis data minor
  56. 4 est ad 1 ut 1 ad 4) + est ad + 4, ut 54 ad 36) + + est ad L + L + L ut 67 ad (700
  57. itaque hoc moto
  58. seu ut
  59. ad 4, 1 ad 77, 19 ad 103. Quod si i numeri semper plusquam ternario
  60. 15 + 233 = 10+3
  61. 6, - 3 =
  62. 6
  63. 6
  64. 167.5
  65. 1b
  66. 67. 3
  67. 17
  68. crescunt, fiet ratio minor quavis data
  69. ad 10
  70. Ergo tandem continuata serie in infinitum,
  71. 49 64
  72. fiet: + + = + + + + L + = + ex = 2 (- 19 15 36 ay 5q n)
  73. hies lin 0 = 1. 1 9 t1s ele - 2( 4 1. 51 3dsen +. 1G ser - E, 1. f 4 4g eut 2
  74. FR 4u 2
  75. A - B-
  76. to
  77. 4.0-010-
  78. 30
  79. 87
  80. 19= 4
  81. 9=c
  82. +. 9-3
  83. 149
  84. 1876: 49. 1b.25
  85. 469: 49. 4. 25
  86. 672 7, 4, 25
  87. 5.
  88. o
  89. e
  90. 67

Cite

LBr. 57, 1 · Bernoulli, Joh., fol. 118v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/DE-611-HS-958803:0238?run=74