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Leibniz-Handschriften zur Mathematik LH 35, 7, 15, fol. 12r

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: 0.86.

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. 11v); this page is its right half.

The machine reads it as

  1. Cum itam sit
  2. t erit et ita in aeteris quodeunque patet L + L + L + L + + etc in infinit.
  3. 12
  4. 20
  5. in infinitum esse L = 0 = 1, et proinde
  6. +1 + + L + + erc. in infinit. esse 2.
  7. quod cum it a assecutus essem miratus est Hugenius,
  8. nam ipse hoc obt cum Huddenio problemata circa
  9. aleam agitans alia longe ratione assecutus faerat.
  10. Ego autem monstravi eadem ratione etiam summam
  11. haberi si denominatores essent pyramidales, au triangulo-
  12. triargulares, aliive Numeri quos combinatorios supraas pellari
  13. Et cum _ pascalius tale dedisset Triungulum Arithmeticum
  14. ut ipse pellabata ub aon
  15. praecedentis; et differentiis sequentis. Ego ad ipsius
  16. + - + 1 =
  17. (E+
  18. 5
  19. 30
  20. 7 21 3)
  21. 8 28 56 70
  22. ubi quaevis series obliqua est summatiix praecedentis,
  23. et differentialis sequentis Ego excogi
  24. ita exemplum exhibui Triangulum Harmonicum,
  25. ubi cujus batis est series Harmonica , 1Z1q
  26. etc
  27. ut prioris series Anthmetica 1, 2, 3, 4, etc. Et utrolius quavis
  28. series obliqua est summatiix praecedentis, et differentialis se quentis
  29. 6 15
  30. in Triargalo parmonico Arithmetico series quaevis est
  31. tummatu praecedentis, et dserentaus sequentis, Nam emper sautor
  32. 0
  33. C
  34. 1 4 10 20 35 5b
  35. 6
  36. 10
  37. 15 21 27
  38. in Triangulo harmonico contra quaevis
  39. est summatris sequentis, et diffrentialis
  40. 9
  41. 2o
  42. 54
  43. series (sed per datam constantem multiplicata)
  44. 842b
  45. paretar s uito

Cite

Leibniz-Handschriften zur Mathematik LH 35, 7, 15, fol. 12r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068086:0023?run=73