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Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 363r

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: 0.80.

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. 364v); this page is its right half.

The machine reads it as

  1. dy: dx = e
  2. Var
  3. aite
  4. sit le dyfeax le Et ay =axe + e. firt ady = a xde taedx + de de
  5. Ergo fit a e= ax de: dx + ae, + de de: dx. unde destinc
  6. Unde destructis destruendis fit ax + de =0 unde ex aeq. 2 et 4 habetur
  7. t
  8. quaesitum absolute, quod est memorabile tuo res adhuc generalior reddi potest.
  9. Sit it ay = aXe + e fit ady = ax de de a ede + de de
  10. fit a e = aX d e derx + a C + det do ixund geentuus.
  11. seu de: Ax = + aC D- a C : a x de + det se elt exy- ry
  12. Seu dx: de = X. ade
  13. t
  14. + 4u t
  15. aeca +acl a
  16. ry+ Xe + sxdus
  17. uturum exemplo sit Cy= axet aec f posito dy: dx e fiet dy = Xde+ edx traede
  18. jam dy = eax ex 2. Ergo sit (e dx = Xde F edx) +2ae de seu x= iac u unde tollendo
  19. e’ex aeq fier y- naec y =LXX: 2a + (aXx: 4a seu y = ax:qa. Videamus
  20. jam au succedat ag. 1. rempe dus: ax = x2a seu eZ BX: 2a et ee = G2xO: taa
  21. et fit a3 ex , 2 per 7 et 9 -exxiaa = _X AX: 2a + saXX: ral seu sit
  22. 3XX = 6XY + 4XX seu XX = - 2XX + XX quod succedet
  23. s alculus ergo mug et
  24. y = xdy: dx + a tus. du fit dy: du + _dq + = 5 + X seu dy: dx = = 4y +X C
  25. si jam sit ae = a + e dulu
  26. 4
  27. (
  28. t
  29. de + e X ax + X de de
  30. Pix =q sit dy. dx = Z ex dato problemate Ex 1. fit Xdy - ytx : xx = dq, seu dy. X - 2 dx x = d3
  31. seu dy: AxX = Z: X = dZ: dx seu Z: X - Z. X = dz: ax seu dX: x = a Z : 3Z Z. Hinc
  32. si dy: dx A - Z = Z. X: a posito dy. dx = y: X = Z, seu si dy: dx = a 1.X +y.
  33. Seo si differentia inter dy:dx et inter y: X sit producta ex duabus quantitatibus quam unisit facta
  34. 7X = Z fit asdx + xous = dque seu Xydx + Xxdy = xdZ seu Z + AX dy: dx = x aqu. dx
  35. ex Fia altera ex y: x
  36. grx = Z du Y emade 7X:, yAx = Z y+ k yax + Xdus = yX dx - 9X dus, 1 y x d
  37. si sit XX dy: dx = _ y. d
  38. sb seu gu ax + XXay, :, ( yex = dZi
  39. : a = du. du _ sit i _ y: a= dv: dco fit sit ddeo =0 fit dy: dx = dd videz
  40. et f sit deo sit az. deo ddv: ddue
  41. X . y y: x = dv: du
  42. sed non licet explicare constantem deo, seu ipsam lad dus vel aliam, quia, duae sunt solum
  43. quantilites lg. du: di et ddv: ddZue Ergo non possunt tres X: a, et y: 4 et dy: dx per
  44. idia eblum habert nam danentur in inter se ex ipsis duae, u Hypothesim
  45. Aater co, non sit constans faciamus: dx: a = deotz - dZ adeo,: ded et dy: a - deo ddv- dx ddco:
  46. fit dy: dx = dco ddo - dr adco: d eoddze- dz du
  47. g: a = dv: a dlio x = d X x: a = ax: addeo dy: dx = du ddx: du daque
  48. du
  49. ()
  50. dy: dx = 1: Zv: 1: 22 (2 z. v
  51. setq: p - - a. 2) y: a = s, a dx: XY
  52. sit aequdata dy: dx(Z XX + y: aa fiet: Z: v = aa + da sA2. 2B aa seu J. v - 1 + sdY. 2B, D
  53. X: a -
  54. d
  55. EZ ex du = d. v. 2 = Zdv - vdzo: 2
  56. X: a = (Z10 - vdZ, : Z7 = v. Z (y: a = (Z dv - vdz: ZV dy: dx = 1: ZV: 1: 7Z = Z. v
  57. seu
  58. (Kut - vlzu - du
  59. sed hoc absurdum nam daretur relabio inter X: a et dy: dx
  60. Xta fZ X: a = sidv: v
  61. y: a = (dv: X fit dy : dx = v: X sin 2- d
  62. dge sit dy: dx = x + 9: a fiet v: X = 5dv: D + Sav: ∞ seu _2dv. vdZ = dv + A
  63. linc si haberetur si sit tynax C Hinc patet si X+y detur per ayiax et constantes
  64. utcunque haberi solutionem per quadraturas. seu si detur X+y, ia per dg: dx uscunque
  65. 1
  66. sit x+yC = G
  67. fiit dxtius = dque et ag dg= dq. dx Ergosi ziadetur per dq. Ax = 11
  68. Sed ita res jam tunc patet
  69. Xia Soto. Cy. a = Z. bf dg. dx - t vtu -
  70. X: a = A dZ - Zdv,: vz
  71. y a = fudze 240. flo3
  72. N: a = dp. 1X g: a - R. f. dy. ex

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 363r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0721?run=74