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Leibniz-Handschriften zur Mathematik LH 35, 13, 3, fol. 200r

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.

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The machine reads it as

  1. les ententi
  2. 1090
  3. solutiones quarundam problematu quibus quountur
  4. linea ex data proprietate velocitatum descriptoriarum
  5. seo differentiali aequatione supponendo Zdp = dy. Et quaerendo ez
  6. s
  7. sit Generaliter q= dy: dx. jam sumavius ZX = y. seu N = y: Z fixy. E
  8. = fit _ dx = dy. Z - dque y177 et tollendo x pr fit Zdx + Xdy = dy. et
  9. Lo
  10. tollendo dy per aeg. 1, ob restet solum Z. dZ. X. dx. fint (2d∞) + x dZ = (Zdx) id est 47 =0
  11. cque estendit l cuncessa ad Ergo Z est constans. Quod ostendit locum esse ad
  12. e+lineam rectam. ubi sane dy: dx = y: X e = a: b
  13. (4)
  14. p sit 7X = - y fit Z de + X dZ = - dy = ZdX (per ag. 1.). Ergo fit dx: X = - dz.
  15. C2)
  16. seu 2sAx: X + a5 dz. X = a seu log XN 1 A log Y = x a V. posito b esse
  17. numerum cujus lag 1 est log ipsius 1. esse ,
  18. +seu bis l0g. X + log. 7 = a. sed log. Z = log _ - logu + log -1)
  19. Ce
  20. +
  21. a
  22. 6)
  23. a
  24. o Ergo fit log y + X = a seu log. yx = a seu yx - b
  25. 2
  26. d
  27. in
  28. posito b esse numerum cujus log. est c. et log 1 esse 20
  29. staergo aequatio ad Hyper bolam quod et verum est
  30. e
  31. at
  32. y
  33. 4
  34. fit
  35. S
  36. Z. X Ergo , dy X dZ dx.
  37. 16
  38. jam per 1 est du =Zdx Ergo sit XX Z ex = XdZe - dx
  39. ZXX = sdy: Y +a
  40. (1
  41. fit 1Z: 7 et = XXdx + dx seu log. _ Z = Lx + x + a
  42. log. Z = log X + sog. y fit erqu log. 9, 3 x + X + a = log. X
  43. sn ex dx:y = x dx + dx = dx: X. Ergo dy: dx = _ x X 1, :X :: yX
  44. et foret 5 = X +x+C,: XX dy 9X ly +29x dX = 3X dx + AX
  45. Ergo ay: dx = 3X F1 - 2XY, . Xx = pexarenus yx foret
  46. 3X +1 = 2∞y = X3y. (eu y = 3X+ + X+ 2X quae non consentiunt
  47. C
  48. Z = yX y E Z: X X dy = dZ X - Z dx XZ ax = d ZX - Z dv
  49. Mur quae Causa latentis erioris
  50. 2 (
  51. Zax = dy.
  52. seu X Z dx + Zdx = dZ X seu X X dx + dx: X = dZ: L
  53. Zdx = dy
  54. seu
  55. ZXX = log. Z - log X + a seu jam log Z - loy X = log. y
  56. Ergo fit EXX = log. y +a, ut constat ut constat aliunde
  57. (+Z+XC du et ax + By = bq dy = d dZ = a dx = Z dX
  58. (2
  59. fiet ea X + C b( dZ: a +3
  60. A a X + by = CXZ + CyZ. fiat cZ- a = m et eZ - b = n.
  61. fiet _ mx + ny = 0 ( Est autem din = dz = dn es
  62. Asique ccz vel s differentialis 1y = = mx: n cujus differentialis est nn dy= Bxd ax t mxaz
  63. sed Lvictoria
  64. seu per 1 et g. nnZa =. nn Zd∞ + m aX = MX dZ = X dy
  65. graitam aesit et in derimum destigia rettatit annum
  66. cu dxl: X = dque m-n : nn Z + mn dantur autem in et n per Z. Res ergo reducta
  67. est ad quadraburas, sed
  68. lale per se sola
  69. poteramus aliunde quia x ety servant homogenei
  70. Xax = ag. y
  71. yX = Z
  72. =xy
  73. Z: X = dy
  74. =Xd
  75. s
  76. XXdY =X
  77. q = Xaytyax
  78. = Xxdys +ZH, p
  79. JXX
  80. E
  81. seu

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 3, fol. 200r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068200:0401?run=74