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Leibniz-Handschriften zur Mathematik LH 35, 13, 2c, fol. 80r

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: 0.83.

Original at the GWLB · Page image · Annotations (IIIF) · Download text

The machine reads it as

  1. sib _vIx= ft duc mx exdmet am= dtdum lv. vdx+ XX= Ado rax sik
  2. sit aequatio X. Y. V (X. y. B = a. (X. y. ∞ unde fiet
  3. differentialis primu
  4. adus:
  5. a X. y. D leg. a: X. y. ∞ = d. X. y. D: X. V. B. it
  6. 3
  7. 2
  8. ust
  9. jam aequalio X. Y. V = 0 cij cujus diffelentialis HM.
  10. ua
  11. d X. y. V = O ex aeg. 2. tollatur V ope aeq. 3, et dv ope v9. 4
  12. va
  13. et sola restabit aequatio inter X y. dx. dy. quae proinde
  14. constrin poterit per 64 e3 aequediones 1 et 2.
  15. Exemplo utamar. sit agua
  16. a sutvo et fiet
  17. sit X+y+ V (xty) = a (Xyv). fet
  18. loga. Xt y+B _axyd + Xvdy tyvax Pa - log. a XyV extdy+ dV
  19. =Xty+p (qu) in dx + dy + dv (: X +y+V)
  20. sit vi=aa et vdy + ydv = 0 seu du = vdy: y seu
  21. Hiuc tolli possunt _ et Av ex aey. 2.
  23. dv2 eady: yy
  24. pomimo sumam brevius, exempliu
  25. = a (∞) fiet dyt du: y +v= bogdx+xdv
  26. XX
  27. sit v= aa : et duZ-aa dy: yy. et habebimus;
  28. y+ D (X
  29. ix
  30. dy g au. gu fe dyXX - aa dx: yt aa: X XD = legB 24d: X
  31. seu fiet dy X3 aax x= log. a
  32. dyr aadx = bga
  33. seu, dy x+ = aux dx = log. , - 2aay X dx A- 2 a dx
  34. itaque aequationem propositam differentialem impli–
  35. catam: 2 dy XY = aa X dx 2aay xdx 2a dX
  36. V + aa : X X) = num. C saa: X
  37. nemo facile divinabit. endem generalius tertari possumt est eumna aperta
  38. solvi posse per hanc.
  39. L
  40. sit aequalio
  41. quadratrix ut y = sna - XX dX
  42. su = saa-xx dx videnmus au licut facere sua x
  43. Si
  44. = 4. Y. V. S.F onuamta scili et relatione inter X et V e y videam
  45. vil eamus an liceat mutare in Logarithmicam, nempe feri multiplicetur
  46. uncumuo ut nen alter aequalio per iig et ner Aix et fief.
  47. ponatur Iaa = XX = C + 1: X is, et per
  48. dy: = cAX + dx: X seu log. y - log X = Scd sed nihaue
  49. ninc

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2c, fol. 80r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068199:0159?run=74