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Leibniz-Handschriften zur Mathematik LH 35, 13, 2b, fol. 103r

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: 0.82.

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. 102v); this page is its right half.

The machine reads it as

  1. data 1c + n e =0
  2. mna it posita e = dyidx. sit quaesita 20 + 2y =0
  3. nam altius assurgi um potest, f differentietur, et fiet d2o + yd2 +21 eo
  4. et tollendo e, fiet: 11 d20 + 11. a 21. y - 10. 21 20 seu y = 10. 21 - 11 d 20, : 1 d 21 = (per 3) - 20. 21
  5. et fit 10. 212 + 11. 20. d21 = 11. 21. d20. Ubi cum 20 et 21 sint rationales per X, exhaurientu
  6. tandem differentiando. Et, si quidem ponatur 20 non esse ultra 1omam differentiam ire nec
  7. 2) ultra nonam, continnaliis differentiationibus licebit tandem invenire valorem ipsius 20, si placet
  8. nam assuatu fiet 20 1. 21. d20 - 1a 21: 1 d et et Nempe d20 = 10. 21 + 11. 20. d21; 1
  9. quam disferentiando prodibit dd+20, d2o, 20, in aeg. (10) tollatur deo exaeque 10 perou
  10. habebitur , inde rursus quoratur ddd2o, et ita porro, tandem in altinia totlantur
  11. va ad. quae ∞g. 0 tollantur valores omnium differentialium pracedenum
  12. quine jeum dati, et habetur quaslaqu valor ipsius 2c sempliliter. Vel
  13. vel pote aeg. 10 reperta tollatur ex ea d2o, ope aeg. 9. ita fiet aeg. (11
  14. in quo solum dd2o et 20. atque ita poro. Hoc g. H si differentietur
  15. videndum au ex eogitair queat id habetitur aliqua (12) in qua erunt
  16. dad2o, d2o, tollatur a20, per aeg. g. fiet ae g. (13) in qua ddd20, et 20.
  17. quam differentiando prodibit daddro, et ita poro, donec finire placeal. Reperto
  18. quam galcre ipsius 20, oportet eum esse integrum seu sine
  19. A acpone, quam in rem galebit ipsius 2) explicao. Quod si non sit possibile
  20. eum esse integrum, nec potenit solvi aequad in ordinariis non altrus assugentibu
  21. possumus famen, et explicare in ay. 8, 1o, H, ex datis, et 20, 21, C generaliter
  22. per assamtilias secundumx et tum videre an es explicari possint et ssumlitaae
  23. ut proditat ideaticae aequad
  24. S.I 10 = 30 + uX + 32 X + 33X + 34 x + 35X etc
  25. H = 40+ 41X+ 42X + 43 X eu
  26. 20 = 70 + 71 X + 72 X +73X et. 2 = g0 + ∞IX + 82X + 93X eta
  27. et d2o = 71 + 2. 72X + 3, 73X + 4. 74 X et d. 21 = 81 +, 82X+ 3, 83X + 4. 84X etc
  28. 21 = 8D + 2. 80. 81X +2. 80. 82X + 2. 80.93X F 2.80. 84X, ∞ 80. 85 X +2. 80. 86 X
  29. + 81. 81 X +2. 81. 82X 2 81.83 +2, 81. 84x + 2. 81. 85 X
  30. 92. 8Z. + 2. 82. 83X + 2. 82. 8YX
  31. c83. 82
  32. 10. 2 = 30. 804 2. 30. 80.81X + 2. 30. 80. 82Xt2. 30. g0. gX + 2. 3. 881X + 2. 30. 80. 85X+ 2. 20. 80. 06
  33. + 31, 80. 80
  34. +C30. g1. X +2.3081. 92. 4 2.3081.83 r230. 81.94 +2. 30 81 85
  35. 16.30. 92. 92 +230, 82. 83
  36. 4 2. 38. 87583
  37. 42.31. 80.81 +231.80.92 +2.31. 8083 +23) 8084 +2.31. 80. 85
  38. F31. 81. 81 +2. 3181. 82 271. 81. 83
  39. 1. 31. 82. 82
  40. +32. 80.80 +232. 30.81 +3.32. 3082 + 2.31. q0. 83
  41. 35. 80. 80
  42. ut rectanus. LA, plus rectanus. AC ad quadrat. AE. et gdibit V1. 2. d20 = eodemmodo ut 11. 30. d 21. dummodo pro Z et 8, ponatur. 8 et 7.
  43. 32. 81. 81 2. 328187
  44. 2.33. 80.81. 2.33. 80.82
  45. 33. 81.31
  46. 2.31 81 8Y
  47. 2. 31 82. 83
  48. + 2. 3C. 80.
  49. 34. 80.80 234. 80.81
  50. 42. 73
  51. 43. 72
  52. 240. 7982
  53. 32 82.
  54. 2. 33. 80.83
  55. 35. 80.80
  56. 40. 75. 81
  57. H1. 74
  58. 2. 33. 81.82
  59. 2.34.80.82
  60. 134. 91. 81
  61. 2.35. 90.81
  62. 2. 32 81. 8.
  63. (I. 20 = Qu. 70 +41. 21 X 143. 72X + 40. 73X + q0. 74 X 4 qu. 75 X P. 7b X
  64. 41. 70 +41. 71
  65. 41. 72
  66. 43. 70
  67. 41 73
  68. +2. 72
  69. vn
  70. 41.74 41.45
  71. G2. 73 42. 74
  72. Ni 21
  73. si aisit lantum 30, 31, et 40.g
  74. 36. 8c. 80
  75. 40. 76. 81
  76. 41. 75
  77. 43
  79. 3.40 2sq.d2
  80. 3.90. 29 3
  81. 4. 40. 73.84
  82. 5. 40.72. 95
  83. 6. 40. 96
  84. 4578) 172. 92
  85. fiet 30. 80 440. 7081 = 40. 71. 50. _ 2. 30 g0 21 + 31. 80+
  86. +40. 71. 89+ 41. 7 81 +2.40. 70. 32 = (40. 71. 8)4 41.71. 80
  87. 1240 +2, 40.7280.
  88. 40.74. 81
  89. 41. 73
  90. 42. 72
  91. 43. 71
  92. 44. 10
  93. W. 20. 431 = 40. 70.81 + 40. 71. 81
  94. 41. 70.
  95. +40. 72. 81
  96. 40. 73. 81
  97. 11. 42
  98. 43. 30
  99. 11. 2120. deem
  100. ~itp. 72. 8
  101. 2.42 10
  102. 3. 40. 71. 83
  103. 41. 70
  104. 4. 90. 70. 84
  105. 2, 41, 72
  106. 3. 40. 72. 83
  107. 4. 40. 71. 87
  108. 3. 40. 70. 85
  109. 140. 73. 32
  110. iltaqi
  111. 3. 40.73.85
  112. 4, 90. 72. 83
  113. 4170
  114. S. qu. 2. H5
  115. 41. 70.
  116. 6. 40 70. gb
  117. 2. 40. 70. 82
  118. 240. 71. 82
  119. 2. 41. 70
  120. 3.40. 79.83

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2b, fol. 103r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068198:0205?run=74