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Leibniz-Handschriften zur Mathematik LH 35, 4, 9, fol. 1r

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: 0.95.

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. 2v); this page is its right half.

The machine reads it as

  1. Demonstrato, quod columnae serierum
  2. exhibentium potestates ab Arithmefficis
  3. aut numetos ex his conflatos, sint periodicae.
  4. Omnis series numerorum rationalium, qui sint arithme
  5. tioorum potestates ejusdem gradus (exempli gratia
  6. series omnium X, posito X esse progressionis Arithme-
  7. tica numeros) continuatis quantum opus differentia
  8. tionibus dat differentiam constantem. Fultima diffe-
  9. rentia nabur alium est 1, quadratorum ab ipsis, Z, cuborum
  10. 6, quadrato quadratorum 24, surde solidorum 1o eeo
  11. id est l; 1. 2; 1. Z. 3; 1.2. 3. 43 1. 2. 3. 4 5. ( Simile aliquidsit
  12. Si arithmetici non sint Naturales, sed alic quicunque,
  13. verbi gratia impares ordine positi, 13,517, cec 7
  14. Idem est, si series exprimi possit per formulam
  15. analyticam integram ex potestatibus conflatam, verbi gr.
  16. X 3 6X = 7X + 1.
  17. dem est, etsi formula habeat numeros in denomina-
  18. na multiplicata
  19. per denominutorem communem dabit seriem arithmetico-
  20. rum. Ergo et non multiplicata, id enim aequalitatem
  21. differentiae non mutat. Exempli gratia Numeri XX+X
  22. sunt semper integri itaque horum series aliquum
  23. differentiam (hoc loco secundam) habet constantem,
  24. primae vero differentia sunt progressionis Arithmelicae.
  25. Hinc etiam omnes series Liguratorum continuatis
  26. differentiationibus dabunt seriem Arithmelicorum
  27. et generaliter omnis series Neumerorum integrorum
  28. qua Analytice expressa per formulam, incognita non cudit
  29. vel in denominatorem (ut fit in progressione tarmonica) vel
  30. in Exponentem (ut in Geometrica) continuatis quantum
  31. roduc
  32. vel quod idem est, vice versâ omnis sujs modi series fit per
  33. Summaetionem arithmeticorum replicatam. Omnis enim

Cite

Leibniz-Handschriften zur Mathematik LH 35, 4, 9, fol. 1r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068006:0001?run=73