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Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 195r

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: 0.88.

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The machine reads it as

  1. si aequatio differentialis sit, quae non in qua aliqua differentia
  2. non ducatur in suam integralem ea replicatione infinita
  3. non incommoie tractari potest.
  4. sit du = a+ lx + Cy4 e dy = mdx + nydx posito in et n dari per x, utcumque
  5. fiet y = smex + fn smendy x Sn smaxdx 1 snydx
  6. fiet y = Smax + Sn yax = (max + Snfmax + Gnibsnysu =
  7. sindx + snpsmax + Indx snax smax + suex sax suyax
  8. Eogo y = (ndx + suax smax + suax snox smtx + suctx snax suax siudx
  9. Si sit du = mdx + n dx y + pdx yy. fiet
  10. y = smax + sndx y + Spax yy = smdx + suax smax + sudx smaxus + Sn _ sper yy +
  11. Spax. qusnex + pax 25mex snaxy + spud p ly + s pax. qu spax yy
  12. sed non puto hinc aliquid magnopere ad finitam solutionem duci
  13. Ailiter ut non ascendamus ad summas, sed descendamus ad
  14. differentias. Nempe ex aequatione erfferentiali per se vel
  15. p adhibita differentio differential quaeramus y ratio naliter
  16. eamque differentiando quaeramus et dus rationaliter, cumque valorem
  17. substituendo in valore ipsius habebitur y per X, dx, daque, nam ddx =0
  18. inde simbiter tollumus dous, et ita pergendo habebimus semper accuratius
  19. Exemplo utamur sit y =aadytax dx i adx + xdx + xdys
  20. fiet du adx +X vel per conpoad. y = 13 - aadg:i2 + Xdu. Ergo siet
  21. s
  22. fiet
  23. sit y
  24. dy = 12 + Xdy, 413 = aa day ∞ - 13 - aadus d12 + Xddus + dx dy:, (E+ du
  25. du 12 + dy orX L dus 2AX + p du = 12 diz - 12aadius + diz xdus C aa xdydaus)
  26. 13d12 = 13X ddy = 13dxdy + aady d12 (+ aady Xddy + nadu dX
  27. quae aequatio si differentietur i poterit d ipsius dus valor rationalis
  28. haberi, qui substituatur in ae vulore rationali ipsius y. Et eodem
  29. modo mepertetur valor rationalis ipsius ddu, et ita porro

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 195r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0385?run=74