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Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 299r

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. (2)
  2. dx: dy = a X - 2XXy, : 3a ay - 2Xyy seu 3aaydx - 2Xyydx = a xdy - 2xxy dy
  3. seu aa = 2X yydx - 2XXy dy, : 3y dx - x dy. unde ut tollamus a, fiet
  4. (5
  5. 5ydx - Xdy, fxyy dx (+ 4 X ydyd + Lyy dxdx - f xX y ddys - f xx dydys ( _ vy dr dy)
  6. e
  7. ZXVydx = XxXy dy, 3yddx + 3dydx - x ddy= dxdy, sed
  8. 2
  9. (Sy, dx dex + Sy dxcxdx- Syyxx dx dey -(3y Xx dx dydy
  10. e
  11. (- 8 Xxyydy dex X e axdyX (+ X3y dus ddu
  12. + X dydydy
  13. ex yyy dx ddx +Xyy dydxdx (-XXyy dx ddy
  14. (3X X yu dy dax - 2 Xx y dydydx t XXX 7 dy ddy
  15. seu fier
  16. 3y dx - yx dx dys + X du - 3 Xy dy = 2yx dx ddy - 2 X 5 dyddx
  17. 17) (dx adu = dy ddx 18)) ds
  18. dx
  19. ex
  20. jam d F adhuc aliter haberi potest per eg. 1. et fiec aeg. 9 cuope
  21. 29yXX dx
  22. ex
  23. valore ut duos valores et a + ex aeg. 7 et comparando, fiet
  24. lis
  25. ex
  26. aequati in valor ipsius dx: dus sed quem puto coincidere debere priori
  27. eduarum literanum decundi gradus
  28. Cmnis aequatio diferentialis constat ex sequentibus termonis
  29. quantitalibus X: y, dx: dy, adx: ddus, X ddx: dx,
  30. X ddg: dy, xddu: Ax, X ddy: du, y ddx: dx yddx: du,
  31. y ady: dx, y ddy: dyt
  32. posita ex constante
  33. aeRKyZ: a = EXC B coGPirngr sit. dy: _v et data
  34. equatio 1o+ ny + n Y etc + ∞8 21V + 22V, etC + HY. 9,V.) 13 1
  35. 2
  36. +10 yY 12C yVy V yPr eu + 22( 00 + Ory + 03y + 0
  37. _ a +bB cy + dx. a + by + cV + OYV, + C y +f V + g7 v+ hYv CH =0
  38. a
  39. (abi b, et c dantur ex x; fingenda est aliu aequalio ipter V et
  40. quoe sit l+ my + nP + p y2+ 9Zy +YZV et C=0 cujus quoratur
  41. differentalis (posito C, n n, p, ecc constantes) et sit dusdus =Cet v
  42. v:a = sib y:a

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 299r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0593?run=74