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Leibniz-Handschriften zur Mathematik LH 35, 4, 5, fol. 13v

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. 12r); this page is its left half.

The machine reads it as

  1. At pro numeris trianguli Harmonici summandis contrariae
  2. insistendum est viae. Nam Summae columnae sequentis continentur
  3. in antecedente; et praeterea summantur ne
  4. columna
  5. ente
  6. in
  7. aut termini omnes feriei, non ab initio sumti, sed sumti a
  8. finc id est infiniti. Sillud tamen
  9. interest accedi quod series columna continet summas sequentis non
  10. simpliciter sed constanti numero multiplicatas. Nempe columna
  11. reciprocorum naturalium continet summas reciprocorum triangularium
  12. multiplicatas per 2, et columna reci horum continet rursus
  13. continet summas reciprocorum pystamidalium sed multipliatas per 3,
  14. et denique columna horum rursus Et columna reciprocorum triangula
  15. rium continet summas reciprocorum pyramidalium Multi
  16. Tolumna reciprocorum atralicontinet reciprecorum
  17. reciproco naturalibus
  18. friangularibus
  19. pyramidalibus
  20. summas
  21. divisas
  22. multiplicatas
  23. triangularibus
  24. pyramidalibus
  25. bitriangularibus
  26. ex
  27. Itaque si velis summam columnae secundae in serie Haraom Triangul
  28. in triangulo harmonico deflescentem in infinitum seu usque ad o
  29. ab inde ab aliquo termino
  30. praecedentis eumque
  31. sume terminum respondentem columna
  32. divide pulva si divide multi plica
  33. si sit in columna
  34. mulisilica per
  35. n
  36. 4 et
  37. etc
  38. et habebis quaesitum. sic si velis in unum addere columnam
  39. secta summare columnam secundam ab 1 infinitum; sume erit
  40. terminus primus l, cui in columna praecedente respondet1, qui multi,
  41. plicatus per 2 dat 2 summam clumnam quaesitam itaque
  42. 2+ + et in infinitum
  43. 1 ++ 20 + etc
  44. e3 a + etae
  45. + 1 L + L +L etc in infini
  46. +8F
  47. + etc
  48. =+ + 3 + + = etc in infinitum L
  49. 24 + 1 4 + ete Cerlt letl = i.
  50. Z+ = + += et
  51. L + ~ + L etc
  52. t + 1 t etc
  53. 10 +2 +5 etC
  54. + + 4+ etc
  55. 70+ 20 +35 etc
  56. L + + L + = etc
  57. +
  58. 35
  59. is + 5F = YC
  60. is lieoit
  61. 2.
  62. =
  63. in finito
  64. ppondentem
  65. primo termit
  66. summandorum

Cite

Leibniz-Handschriften zur Mathematik LH 35, 4, 5, fol. 13v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068002:0026?run=73