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Leibniz-Handschriften zur Mathematik LH 35, 13, 2c, fol. 115v

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: 0.83.

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. 114r); this page is its left half.

The machine reads it as

  1. generalius sit 100 + 112 du + 12Y yy =0 siat 200 + 211y + 212 dy + 221 yy = 0
  2. seu +200. 112 4 211. 112 y (+ C. 212. 112 dy 4 221. 112 yy destuatur gy, faciendo
  3. = 100. 212 _ X - 112. 212 de - 121, 212 9y
  4. 221 : 212 = 121 : 112
  5. fiei y - - 200. 112 + 100 212 et dy = - 112. 211 (l 112. 200 + 124200 + 112. 2114100. 212 + 100 d 12)
  6. 112, 211.
  7. ergo (100. 112. 112. 211. 211 + 1120
  8. 112311
  9. y=
  10. =(112 d 211 + d112. 211) (-200. 112+100. 212)
  11. 112. 112. 21. 211
  12. - 200. 112+100. 212
  13. 112. 211
  14. =
  15. C
  16. 112. 112,. 21.211
  17. sed hoc sic nil lucramur facile
  18. f +202. 112 + 211. 112y = 0 fit differentiando ti2 groo + du2 R y + 2H. 112dy = 0
  19. = 100. 212
  20. ubu pe 12. dy ponendo galerem - 100 - 12199
  21. 1 10 F y + 12dy destrmatur v. 22ydy + 12. 21ydy
  22. 30+ 219 +21 dy
  23. 10.10 +,..
  24. fit m 10
  25. +200. 1126.
  26. - 100. 212
  27. = 100 (221. 112
  28. 121) =121. 212
  29. 7aeq. )) Fist al (200 2)
  30. d (103. 212)
  31. 200 di2 +1I2 d21
  32. = d100. 212
  33. - 10Dd212
  34. sin sic potius se aepelatur aequ
  35. in aeq.) pro ju = substitiatur = 100 - 12dys, et prodit
  36. 121 121
  37. + 21I. 12y 4 - 1125+ 221 112 gdu mult per 400 + quy
  38. 121 7=12. 212
  39. compendio 300 + 311y+ 312dy mult per 400 + 41y
  40. fiet fil 300. 400 + 31. 400 9 + 31 quodu
  41. 4 g00. 41y + 8
  42. 31. 447, +312, 11F ydy
  43. +dtt 12) du + y d (211. 112) + de 221. 112- 121. 21 ) gy ∞22 1 12 r2 124) rgily
  44. si aequentur 312. 412 et 2. 221. 112 -2. 121. 212 si at =112
  45. e habetur 41I et frd 1. 300 400
  46. + d (200. p2)
  47. et 12l. t1V)
  48. + gl (218. 112)
  49. 211. 112y
  50. 2
  51. e 41+ = 2.
  52. d(20012) + d (21. M)y f. a(El. H2y + d (~2t. 12- 121. 27) 9y
  53. d (100. 212) - 311.400
  54. + d (L. H12) G -. 300. 40 300. 411
  55. = H2 f2ut. 1)
  56. 121 L- 131 2V
  57. = 317, 4019 = 311. 411 3y)
  58. +d (2I1. 12) 100
  59. =312. 400. 212l. Gy
  60. habetum aequalia mova sie differenlialibis
  61. coincidentiavida
  62. a g
  63. 112
  64. comparanda ipsi r200.112 + aru. Burly + 221. 12 yy
  65. 100. 2
  66. quatur
  67. = t21. 212
  68. Habemus tres aequationes, et Hteras 200, 211, 212, 224. Maber insam eo
  69. quae ad curquid destinendum infervire potest
  70. sunt simplices
  71. 100 4. 1117 + 112dy + 121+ 122 dH =0
  72. 20+ 211 y + 212 dy + 2 : 1 + 222 d =0
  73. ipsae autem aequationes
  74. per P+m
  75. Explisando y todatur 10 in una
  76. et explicando ollatur 210 in altera
  77. abebimus duas aequationes plane simcles istis, niso quod absunt absoluti. Jam
  78. tollatur nempe
  79. +311V + 312 d si possemus tollere absoluto erum
  80. omnia essent in subvo, sed res redit ad ae quades his ipsis aequales similes
  81. estrta
  82. =d (100, 212
  83. 1F20. 11)
  84. o
  85. 206. 112
  86. = 100. 2l1
  87. = 100 (27. 12

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2c, fol. 115v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068199:0230?run=74