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Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 25r

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.

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The machine reads it as

  1. Pro A differenti saetem pro parte, ad Terminos serici rediri
  2. potest. aadue = XXdx + gydr. es)L aay sit
  3. aa ddy = XX 2x dxdx + XX ddx + 2ydydx + yyddx est autem sel
  4. _ dy dy = () - y dedbus = 4y) (5), et fiet Tollatur dy fiet.
  5. aa, (y) (7) = 2x dx x + xX dex + 2yd xf(y) y) + gyddx (∞) C
  6. addus = 24 dx ux + aa xx ddx + 2dx: 2 yxx dx + 2y dxdx + aa yy ddx
  7. dy = (y) - y 5 (dy) = D + ddy = (yD - (y) et ddy = (y) - (y) - (y) + y = (y) - 25y) + y
  8. (dysidddu = dd (dy) = (y) (3) et dE. d’y = (Iy )) - (y) sI) e ((,) + (y)
  9. ddy = (dy) - dy = (y) - (y) - (y) + y = (y) - 2 (y) + y
  10. dy = (dy odys) = ddu = (dy)) - 2(dy) + (dy) - (y))) () - 2 (y)) + 2(7) + (y) - y
  11. dy -. dy = (y) -y
  12. seu d’y = (() 6 (Cy ((y)) - 3() + 3(3) -y
  13. et d’y = (y)) - 4 ((y1) + 6(yy - 4 (y) + y. Et ita porroin infinitum.
  14. similiter (7) = P+ dy (y)) = ddy + 2(y) = y ( = ddy + 2y + 2dy - y = ddy +2dy + y
  15. et dy = et (Ry)) = d’y + 3 d dy + 2.3 dy + 3y = 3 dy = 3y + y = d3y + 3ddy + 3dy + y
  16. CVy
  17. et eadem modo () d’y + 4 d’y +6 ddy + 4 dy + y et ila porro.
  18. Bdy +Vddy sic explicari debent ut tollatur () fiet β(y) - By+ ) (1is oces
  19. (aapyse pay= a dyxa dx et Gya
  20. _) sit B = 27 et prudibit (dy +2 Bddus = 2D 2B((y)
  21. Et quia ex problemate habentur dus, ddus, d’y etc. ex primis Xydy,
  22. (yD), etc habentur solas
  23. il
  24. accedentibus var dx, ddx, etc hinc (9) (7),
  25. si dy fuit prog si dy ddy d’y d’y essent progressionis
  26. primas Y, et dus, et progressus ipsuis X
  27. 14
  28. beomeliveae etiam Y, (9), (9), etc progressionis Geometricoe forent
  29. A X doge = dE dZ deZ d d2d ddv + de
  30. dvq) = d vd Z + avdeZ dd (1Z) = d vdZ 2d vdZ + d ssa 2
  31. e
  32. Z d (VZ = d v dZ + 3 dvd Z + 3d D d Z+ d’vd
  33. e (uu) = Z dvd
  34. 1.2
  35. Hinc dXxx = de ExXdx) = PXX L L sex de Hxt 28 X d + 2. C- 12 4
  36. que ete
  37. de _ axX) = 2Xdx c XX = 2X ddx t2dx dx d’xx = 2 X de+ 3) deddx F 2d xdax
  38. et generaliter d
  39. I5 XX = 2 2 X dX + 2dx dX + 2dx d X + 2ddx d3x + 4 dx d Ex + 4 ddx d X + B dex dex
  40. Xx =2X d X F2 dxd3x + 4dx d’X + 4 ddxdax
  41. a
  42. A d’Xp = 21 Xdx d’ XX = 2X ddx + _B N 2 dx d 2, Xddx + dudx
  43. = 6 2. d Xdx
  44. d3XX = 2, x dX + dx ddx + 2 dx ddx = 2, Xd3x + 3 dx dax = 2, d xdx
  45. seu dsXX = 2X dX + lodX d
  46. d+ xx = 2, _ XdEx + qdx d3 +3 dexdex d’xx = 2, nd 5 dxdx HC ddx d3X = 2, d’ Xax
  47. X XX = 2, X d’X + 6dx d5X + 15 dexd X + 10 d’X dX = 2, d3, Xdx
  48. N XX = 2, Xd EX + 7 dxdX + 21 dax de x + 35 dXd X = 2, d, xdx
  49. 6
  50. d’.Xdx = + X ddx + 1 dxdx
  51. d, Xdx = + X deX + 3 dxddx
  52. d, Xdx = + Xd X + 4 dX d3 f 3 ddxddx
  53. a
  54. de, Xdx = + X deX + Sdxd x +19 ddx dX
  55. d, xdx = +X dbx + 6 dxdsx F15 cdx d EX F 10d XdX
  56. d’yxdx = + X d X + 7 dxd X + 21 ddxdsX + 35 dex d X
  57. 5. 8. G
  58. G. 6. 7 38
  59. Ex his patet regula progressionis
  60. Numeri scilicet cuiusque columnd
  61. demto primo in columna
  62. sunt ordine sumti naturales
  63. Triangulares
  64. d, Xdx = + X dBx + 8 dx dx +28 ddxde X + 56 ddX + 35 d X d
  65. , xax = +X d ∞ +9 dx adx + 36 dlx 47 x + 84 d x dx + 70 d x d5
  66. et
  67. exex
  68. pystamidales e
  69. d
  70. M
  71. etS
  72. et f, eA-f, ek
  73. L. 2. 3 ete usque ad f
  74. nisi cum e+1-f =F. _C
  75. seu et 1=2F, tun
  76. cur dii-
  77. 10-4.3
  78. f0 2203
  79. iu trais
  80. 4. 5. 8

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 25r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0049?run=74