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Leibniz-Handschriften zur Mathematik LH 35, 6, 2, fol. 6r

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: 0.78.

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

The machine reads it as

  1. exdy adx + Aydy =0
  2. cujus differentialissH
  3. lonamus d
  4. BO aa
  5. B
  6. 2
  7. sint sx dy- acd
  8. X ddye + Paxdy +sa ddx + Ayddus +aydu
  9. mx dy +nydx + pxex + gudus +ratx+ tal
  10. Et differntianto ipsam 3. filt: M Xdd + maxdy + ny dax + n dydx +
  11. Pxddx. + paxax + quddue +geudus + raddx + taddy =0
  12. sequationes 2 et 5 (mulliplicata pliua per h) addantur in unum
  13. fiet: +MX daus + maxdy + Laddx + q yddys +q aydys +
  14. 6)
  15. si
  16. + ny ddx e
  17. +La ddy
  18. + pX ddx + p dxdx
  19. formulam arbintu
  20. praeterea aeq. 1. multiplicetur per arlitardam fax + gdy- talem
  21. ut fict homogenea ipsi 2 vel E vel 6 et productum multiplicationo
  22. enit tr fxaxay + afdxax + fy dxdys + 9xdy dy + ga Klyrgy dy
  23. addantur in anum aequationes b et 7.
  24. +in Xddys +r a dex +quydy +q dydus
  25. h
  26. es
  27. t
  28. emaxay
  29. +n yddx + ta ddus +pXddy pdx Ax d
  30. fiet:
  31. Exaraus +gxaya
  32. axdy
  33. al
  34. e
  35. a
  36. potuissemus quidem promibiliaria fdX+ odue sumere fdx+gagik B
  37. Afum itemque for tam ag. 3 multidicare per similem arbitrariam, sed
  38. videamus quid 3fut, abstinendo a s in differentio differentialibs.
  39. sumotur jam alia formula differentulis nedulus 10f
  40. dictn (adxuli + n fay. G+b ai seK. XrC
  41. + Ca (1a ag +15M: 19y+ISXFb + 16 X: a + 17 y: a =0 quae differentiata
  42. lio ddu +nddx: 10dy+naX
  43. +
  44. det homogeneam ips E
  45. nam ex ipsa differentiata sublacis fractionibus siet :36
  46. a 14 dy +152X 10dy + 11 x + 10 ddy 4 nalx. 14y 415X + b 6, 2
  47. X1bdx. 10dy + ndx. 149+15K +b + 17 dy. 10dy + udx. 149+ 15XrI.
  48. quae aequatio 10 Eomogenea est aequationi B. Sed quia video
  49. et quidem plena, sed quia in eq. e deest yddx et Xdda: poco ad sup
  50. plendo aliquid aequationem diuisam prius perteax differen
  51. tamus, fiet: Xdy: dx 4 a 4 ydy: dx 20 seu Xdydx: X + Xdly. dx+ dy
  52. sed non sul cedit. Num istud. itaque si volumus ira retinere plena
  53. e1
  54. potusset initro fieri: X = 20∞+ 127C et y 220+23Z+a
  55. quae sobstituenda in aeq. 1.2 ita tamem ut in a9. 3. meet tantum puo xseriba
  56. tur x et pro escubitur ilemque in aec 9 et 10. tiac melhod u
  57. replebimus oes terinos, si jam hac arte resdamus vet e comparabiles. et e
  58. ipsam et surmabilem mac summaeissius ad axB Gaem
  59. imgemus se Bhd est vai
  60. 10
  61. 2

Cite

Leibniz-Handschriften zur Mathematik LH 35, 6, 2, fol. 6r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068047:0011?run=73