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Leibniz-Handschriften zur Mathematik LH 35, 3 A 26, fol. 16r

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: 0.84.

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. 15v); this page is its right half.

The machine reads it as

  1. C
  2. differentiam inter Logarithmox suoientis et fractionis
  3. vocabo E. Erit Lagarithmus scis quotiens
  4. e
  5. aequ Erit la aequ. lf = E. Jam f aequ. lD. 1d. Ergo fiet:
  6. Ergo
  7. Cq aequo ld - ld - E. Iam logarithmus quotientis additus ad logarithmum
  8. divisoris erit
  9. erit logarithmus differentiae inter residuum et numerum. Nam
  10. Si logarith qualientis quotiens ducatur in divisorem, productum sub–
  11. trahatur a dividendo habetur residuus, per definitionem supra
  12. dictam. Ergo si logarithimus quotientis d - ld - E addatur
  13. logaribhmo divisoris ld habetitur differentia residui a dividendo.
  14. itaque quaeeratur
  15. e
  16. O
  17. in labula. n 1d -E
  18. egu D - n ID -E
  19. jam Rugu Y hoc modo pertabulam Logarithumorum inventus fia t(d)
  20. et S fiat (D). et habebitur: (Y) aequ. (D) - n l(D, -E. vel
  21. Y) aequ. d - n lS = (5). sed (E) aequ. l (0) - 1(5) - 19)
  22. Ergo uti Yaequ. D - n l5 + t tD - lS
  23. ita fiet
  24. (Y) aequ (D) = n (,5, + + 1(D) - 1(5, sensrt, d - n Ir + t15 - Ir
  25. seu ita invenpi posse communem seu (1) aequ. d - n (∞ D - n 15 +
  26. b
  27. 15, +1D - 1d=E aequi seu erit lD =E. qui
  28. ile
  29. et porro progrdiendo fiet. Seu (Y) oqu d= n 1
  30. seu rn D -C
  31. b
  32. 7(V7
  33. et ita porro, continuando, donee ficit r ultimum aequ. 0. quod
  34. an fiait exacte mox patebit. Quo facto proxime
  35. precedens erib
  36. maxima communis mensura. Sacile autem 2d partebit ab
  37. continuum decrementun. Possumus ergo invenire communes
  38. ur autem mensuras invenire per logarthmos non difficulter

Cite

Leibniz-Handschriften zur Mathematik LH 35, 3 A 26, fol. 16r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068239:0031?run=74