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Leibniz-Handschriften zur Mathematik LH 35, 2, 1, fol. 25v

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. 26r); this page is its left half.

The machine reads it as

  1. in infinitum decrescentium
  2. summae. 6 +
  3. Demonstrabitur ad modum propositionis praecedentis, nam
  4. quemadmodum ostendimus 4 3 + L + + etc. esse 2.
  5. ita demonstrabitur + 1 + 24 = dsc esse 2.
  6. Nans) io fH, d. sit A
  7. et
  8. X+ (+ 1) + Rc. siu B ses pmme
  9. semper scilicet series praxime praece
  10. Nam
  11. Nam series proxime praecedens + L + L + L + +, 8c. sit A
  12. et series proposita s
  13. Ergo
  14. 4 + 1 + L + 2 + + &c sit 2B
  15. 2+ 2+ 2 + ∞+ 2 dc ent B
  16. Auferantur a singulis quantitatibus seriei A, singulae respondentes seriei B; residui
  17. 1
  18. 30 60 10
  19. erunt termini sequentes ejusdem seriei A, ut 2- 2 dat L, et - = dat , et -2 dat-
  20. et ita porro quod semper futurum generaliter ostendere non difficile est. Er
  21. Et Ergo. + + L + L + , + + etc. erit A - B
  22. At
  23. 3 + L + L + + + 2 dsc est etiam A- 1
  24. go aequabuntur A- B et A- 1. sive B et 1. et 3 B id est series L + L + L + L, + L etc. erit 3
  25. idem in caeteris fieri et generaliter eventurum demonstrari non difficulter potest
  26. Habetur ergo aequalitas inters A- B, et A- 1, sivae inter B et 1.
  27. inter 2. B et Z; Ergo 2B sive + + + 4 e dc. valebit 2.
  28. SR0 P051710 X L
  29. Sit Triangulum Harmonicum, sive cujus numeri sint reciproci numerorum Trianguli
  30. Arithmetici a Pascalio editi
  31. Triangusum
  32. Harmontum
  33. sive
  34. TRIANGULUM ARITNMETICUM
  35. UtUM HARMONICUM
  36. Ee
  37. E
  38. 0
  39. Trianus
  40. Anct
  41. i
  42. AA
  43. runt de
  44. serierum trianguli- Harmonie
  45. riangulum
  46. Harmonicu
  47. Triangulm
  48. Hagmonia

Cite

Leibniz-Handschriften zur Mathematik LH 35, 2, 1, fol. 25v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 39). https://leibnizlegible.com/page/00067993:0050?run=39