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Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 270r

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: 0.87.

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. 271v); this page is its right half.

The machine reads it as

  1. quaeritur
  2. ax: XX = a4. Estraatem M: XLa + n: X -a x
  3. Estvantem m: X+ a + n: X - a = 1: XX - aa. fiet
  4. MX = Ma + nX + na, : XX-aa = I: XX - a4
  5. Ergo M + n = 0 seu r n =-m et
  6. =ma +na (seu -2ma) = 1. fiet m = - 1: 2a
  7. ex et n = 1: 2a. ergo fret
  8. j: 2a 1: X - a = 1: X+a = 1: XX - aa. Erso
  9. dx : XN - aa = 1: 2a l0g x - a = log. X + 4
  10. seu dx: xx =aa = 1: 24 log X -a: x+ a
  11. Ergo (dx: XX+bb = 1: 2b -1. log X - b r1 : X + bs-1
  12. v = by: X
  13. si sit
  14. et habeatur V = d dy: dx
  15. ile reducitur problema transcendens affectum
  16. cud parum seu quadraturas. nam bdn ady + Ydx
  17. Ergo dus: dx= b d0. Xdx - nam bdy = xdo + vdx
  18. Et dy: dx = Xdv: bdx = v:b = v
  19. Ergo dv : v. b + V = bdx: X
  20. Si sit bv = VX et habcatur v = dy: dx, tentemue
  21. bdv = ydx + xdu et dyc b dv:x = bv dx : XX
  22. et dy: dx = b dv: X dx = bv: XX =
  23. seu dv: dx V. X: b + v: X
  24. ffine
  25. S aequatio reduci potest ad D. Xx = dy: dx
  26. posito
  27. vid
  28. XYq quadhaturas
  29. potet reddi pura seu reduci ad
  30. dx: dy = 2xXY = 2ax: 3aa = 2Xy 1
  31. sit 344 - 2Xy ∞ V felia a 2XY - aa = V
  32. seu aa = 2X9 = V. fiet dx: dy = XV: 4Xy - 3V
  33. A
  34. et 2Xdy + 2ydx=
  35. Av et dy: dx 4y: v = 3: X
  36. potest geaeralius sumi aa = MXV + n XX + p yy +qVX + YVy + SBC
  37. s
  38. +25vdv
  39. et M Xdy + m VdX + 2HX dx + 2 p y dy +9udx + qxdv +rvaytryd
  40. honc ∞g.2. jungendo cum aeq. D videamus an eadem opera possimus
  41. collere lX et dx (occbigr. ) N. vel s et dy
  42. verté

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 270r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0535?run=74