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Leibniz-Handschriften zur Mathematik LH 35, 7, 15, fol. 2v

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.

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. 1r); this page is its left half.

The machine reads it as

  1. indemebat,
  2. dunt
  3. diffrae
  4. Ima
  5. + et
  6. ete
  7. etc
  8. inveniebaerino p suimo a, di
  9. posit
  10. a- ca = 15 + 1g + ih + 1i + 1k + etc
  11. a- = il + 2m + 3n + 4co + 5p + etc
  12. a- cd = 19 + 3r + 65 + 10t + 15u + et
  13. a - = 1β + A) + 106 + 20E + 356 + etc
  14. etc
  15. a--
  16. Et rursus
  17. 1t - i
  18. +1f - 2l + 14
  19. +it _3l +38 = 14
  20. Al +69 - 45
  21. n en etd ete
  22. et
  23. Unde differentias primas, secundas, tercias, quartas
  24. a
  25. vecande ddd Unde loquendo stylo atre a se
  26. etr
  27. o, inveniebat
  28. postea introducto, et terminum seriei ponendo vocantos, (quo caso etiam est a = y,
  29. voca
  30. differentiam primamdu, secundam ddy, tertiam d’y
  31. quartam dTy; et rarsus 1+ 1 + 1 FI et Vocando X,
  32. 12+3+4 t etc vocando fx et 1+ 3. +6 + 10 vocundo sX
  33. et terminum alterius seriei vocando X ummam horum fx vocare sx
  34. et summam summarum seu secundam summam secundam s(x,.
  35. et summam tertiam s3X, et summam quartam AX
  36. Hinc posito 1+ 1 + 1+ 1+ 1 + etc. esse X, = f tunc 143+6+10 + etc fit =. sx
  37. et 1+ 4 + 10 + 20 + etc fit = s)x et 145+15 +35 + etc fit = sX, et
  38. Ita porro. Unde tandem sit:
  39. ya - c0 = dyX = sddy sX + desy ssx d’y p.X + etc
  40. quod est = Y posito continuari in infinitum, seu fieri co = 0
  41. et fiet a vel y du X ddyx Unde etiam
  42. sequitur summatio serie ipsius serier, seu fit.
  43. y = yX = dysx + dx s(X - d X PX + etc. quae bina
  44. Calculo diferentiali, utam At Numerico, quam infinitesimali; de quae discime infradicemus.
  45. quorum,
  46. theoremata id habent egregium ut locum habeant tam in in utroque
  47. dolescens
  48. sed ea nostro tunc peoni, tunc prorsus ignota erat, sat su
  49. habebat ille talia in numerorum seriebus cum voluptate observasse
  50. licert
  51. = seu X esse numeros
  52. naturales, quorum
  53. cx = 1
  54. +ad pomciriam
  55. applicatio et ad
  56. setres etium rifinitas
  57. Numericarum autem

Cite

Leibniz-Handschriften zur Mathematik LH 35, 7, 15, fol. 2v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068086:0004?run=73