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Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 287v

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: 0.74.

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. 288r); this page is its left half.

The machine reads it as

  1. 2
  2. duiap sit na + xy: yytya=F
  3. fiet xa + yy = yyt + y at.
  4. faciamus g ga = E. t et xa + 5 y ZV Abs La
  5. vo
  6. ex aq. T est y - - a + Z. 0 + aa Ergo xa - L xa + x Y.. = Z. V
  7. mex a. 4 est a = 7b - yy, : y fit 0 = _ydZ.V dZ + d x du -(9yy ag - Z. v yjay
  8. A)
  9. et Z. V =O et Z0 = 9 et f.. = 8et ex aeque 7. et g. fiez
  10. et
  11. H
  12. fiet y = ha + Y et ex 59. 9 fit y d0 dZ Fy d9 do - ec py dy - ay
  13. X et ex aeg. 5 pt A = 9 -xy
  14. =c
  15. facimus Yy+y a= O et Xa +Xy = D sie ut tam C, qquam D dentur ex Z.B.
  16. e1 t d0 = 5oZ + do do et (3 = a D aZ + s9 av
  17. EEx ag. 4 fit a= 0-gy: y cujus differentialis yde -Ovydys - Oaque 4 yy a9 20
  18. et pro dC) ponendo vatorem ex b. fit 7 d0 dZu + 4 y a dv - yy dys - Odus 0
  19. psus ex aeg. 5. fit a D- xyB,: X ergo cujus differentiali erit
  20. cet 0 = xdB - XKdy = Xy dX = D ex F xy dx Et ex 7. et 2. fer
  21. (9
  22. O= X dD dZ + x dv - Xx dy - D dx, ex 8 et 11 fit OX - yyx = Dy - xgy
  23. (13
  24. F ex aeq. 9. fit dy = yd0: 47+0
  25. 1
  26. B
  27. =. dy: dX
  28. Z= X. y. a
  29. (2)
  30. _ Z. V = +
  31. V X. y. a
  32. (4)
  33. ra v. a
  34. differentiulis ipsis 3 sit R e dy = de
  35. fix 3 et Z. fiet y = _X B X. Z. ∞
  36. differentialis ipsius 3, dab
  37. AE E liberata ab a dabit y = F. Z. dy. dx. dZ et differentialis ipsius 4 liberata
  38. 8
  39. a52
  40. ab a dabit. y = X. v. dy. dx. d. Ex Ret
  41. Aequando ipsius
  42. valores 5 et 6. fl habebitur X = Rel. 6) Z. v. dq. dy dx et
  43. Similiter aequando ipsius Y valores 5 et fit X= (Xel. 7) Z. v. dv. dy. dx
  44. Aequando duosvalores ipsius X, nempe ex 8 et 9. x et pro dy: X
  45. ponendo Z: V (ex Ag. 1. et 2) habebitt et ponatur dv: d3= Y. tunc
  46. ex ag, 8 et g. fiet aequatuo, nova AZ: dx = Bel. 8) Z. v. Y, ubi efficcendum
  47. et, ut hel. D Zv.Y foret =0 et haberetur desideratum
  48. si xa+ ny jyaga = t. tantum poni
  49. si esset __yae Xar Kg y Kalt 7t a: 4 1B: (1)
  50. set si etset Xta in t Cra +B y ta a = + = ty: dx
  51. amendo Xt aL Z et bF y+ 48B feret ZY: a2+ av = t (1)
  52. (2)
  53. si esset Xta in yta iP x + 2Xy + yy + 4Xa + 4y a + 4aa = + = dy: dx
  54. ponendo X+a =Z et y+ a = fieret Zve: Z + 2ZV + v0 = t
  55. jam dx = dZ
  56. e
  57. et dy = dv. fiet, t = dv: d2., Ergo aeg. 5. est quosita
  58. tolli potest a et a, et quorendo differentialem ipsius aeq. 4
  59. sed hoc non procedit quando quamer
  60. non sinmil tolli potest et a.
  61. si aeg. 3. fuisset XX+ aX = ZZ. feret X = VZ + aa - 2 a
  62. (11
  63. loce
  64. (10)
  65. et feret
  66. et e a = ZE - XX, : X , et Emque
  67. est
  68. sed patet nihil him posse disci novum
  69. (1) +ty u sit yt a = v+ Z
  70. quid ergo si sic: Xa +Xy: gy+ya
  71. fict X VLXZ,: sit, Xa+ 9a = yX +ya = t dy: dX. et
  72. scribatur. ytaZ nt Z+, 0 +pC et X+ a = 9Z+ rV+ se
  73. differentialis est, o = _ 2X Z dX = (3XX dx = ZZd x (+ XX dx. seu dx L3) 2x Zd2: Mr 12
  74. dx = d 1Z7 aa c
  75. 11∞ X 2
  76. 2
  77. n
  78. a
  79. e 1
  81. t (1I
  82. d
  83. c+
  84. e
  85. is

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 287v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0570?run=74