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Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 376r

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: 0.85.

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The machine reads it as

  1. Aequatio differentialis (1) differentietur (2)
  2. Et ope egg. 1 et 2. sollatur dus fiat aequ. (3)
  3. Exinde si liceat aeq. 3. sic disponere, ut pars in qua
  4. comnia cuembra in qua sunt X, y, a, fiant (4) aequ. de
  5. et constanti, restabit aeq. (5) in qua erunt dx, dax
  6. de, ddy. quae pendet a quadraturis. Si coti-gat vel
  7. semet, ut suo membra haba ex ax, ddys, du com-
  8. posita habeant coem multiplicatorem compositum
  9. utcunque (X X, y, a; possunt ognia per commu-
  10. inem ille verbigo si sit Xxrac, _: gy do: dxd
  11. NX+a: gi ddd rodx nadx daus e
  12. = X. y. a, dx
  13. 3
  14. XX+ aa: y dax + nddu = dx X. y. a
  15. fint, ddx + nddus, : dx- X. y. ay: xetaa
  16. at= de et si et es fiet
  17. dax ddy =- d dx + dx de seny = dx+ X
  18. tade +bde. ubi cessat ubi nec impedit violati
  19. E segis homogeneorum, ve hoc casu posset
  20. tacu alio ipedire, at si fui qu
  21. fiet de quid s pro ddx + huldus fut) (et
  22. cddu +nadlus nddu: dax,: de = de
  23. efiet andays = de dura de dxdix
  24. dax dxa sed ita turbatur summatio
  25. Ed si esset Xx raa: gu dx + nddu dx-
  26. E. addX X. y. a + a ddu X. 9. a + dx X. 9. a
  27. = de. fiet dx + nadus: dax ex = de. seu
  28. dx ddx et nddydx = de ddx. seu fret
  29. n ndy + de + bdc - de dux: x
  30. pc
  31. vite.
  32. hubrae tamen adhuc an hinc exilus
  33. aady + Xydy + Xydx + aydx axdx. seu y - axax = ady,:,
  34. seu X seu y y = axdx = aadque): Xdu + Xdx + adx
  35. dy = axdx + a pdu + pax + adx
  36. qa
  37. dus = axdax + adx =aa daus Xdy + Xox + adx + axax - acdus rdlily , dndyt relix ralx tadius
  38. (2t xdy +xax +aax
  39. si faceremus ddy = 0 fict haberetur dy: dx per a et a : X per adax: dx
  40. (6
  41. si facionus Xdy + Xdx radx = ade frerbt ex aeg. 3
  42. adedu= Axdax + adx -ddu et ex 4 difperentiando fiet X ddys + dxdys + xddx + dx Taddx =0
  43. tolle fiet X ex X = ade - adx,:, dy+dx = dedy- ex +addu = - dx- addx dxdu
  44. dtX
  45. daus + ddx
  46. fit adedax = adX ddx dectus - dx du + a ddydus + deaxdus-dx tadxadus. si
  47. si opi aegus s et 9 tollatur du habebitur aequatio in qua daus: dux, et du: de, et addx: de
  48. Ex consit ax L aadaus adus radx= dx radix deX _: dxddx + de ddy + dax du Ex 10 et 11 sit aequ. (12) in qua
  49. verte eago
  50. extibunt dibe ddy: ddx per dx: de, et a ddx: de sendas. ddna

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 376r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0747?run=74