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Leibniz-Handschriften zur Mathematik LH 35, 5, 14, 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. 29s ept. 1680.
  2. De Logarithmicae aequationibus. et sement
  3. Scheda I. Calculo curborum transcendente expressarum differentiali
  4. pay.1
  5. seu comparatione calculorum differentialis, expo nem tlis
  6. replicats et insiniti
  7. Ntdu
  8. 4 aequ Z. Ergo dz aequ. fa 7 a
  9. exprimatur
  10. jam inventa,
  11. a per seriem infinitam, methodo
  12. et per consequens a
  13. per
  14. faci habetritur opinor
  15. has
  16. similem seriem infinitam,
  17. differentia finita inter his duas serio, infi
  18. jimo non finita, ut in fine schedulas sequentis depretens.
  19. nitas, quia altioras ipsius du potestates
  20. negliguntur
  21. quaesitam.
  22. quae differentia dabit tangentem
  23. itaque duobus mocis eadem
  24. opera inveniri poterit a
  25. uno modo dum
  26. exprimitur per seriem infinitam, in qua
  27. invenitur cujus differentia
  28. us
  29. dist
  30. a
  31. t a se invicem subdracuntur, habetur
  32. differentialis infinitae differen
  33. tiali supra dictae aequalis.
  34. Hinc nova
  35. erit b+x ag. sitqu Sa aex constans e fiet:
  36. ta tunc ratio b+ H seu CX ad seu WY ad CA seu b. est
  37. multiplicata rationis seu C ad CAS in ratione C_ sive KX
  38. seu b
  39. logarithmdate ipsigse. seu in ratione
  40. sit b unisas erit 1+H aequ. ()
  41. t
  42. on nngentendo
  43. Ponatur C esse talis, ut sit ejus logarithuy Cβaequ. CA seu a aequb aequi
  44. l.+ _ aequ. l at2b ad minus hscribendum +
  45. posito sclicet _1+N et X esse numeros
  46. a diversa parte ipsius unitatis 1+_ brevitatis causa vaemus V. fiet:
  47. foret. 1+R aequ. 4C
  48. Aa
  49. consice.
  50. 1C et b7 qu lb (Tetragonistici, itemque cur prop. 45. us scholium jungi debe
  51. D equ.. Eandem aequationem ut exprimamus per series infinitas
  52. randum est quod etiam demonstravimus. Si sit f. equ.
  53. 2l10
  54. b, 41
  55. fore L ad (1) ut n - n + p - p +P, etc. ad (n) - (N) + (1)- (2)
  56. 1b 3b +b3
  57. si utraque ratio sit mivoris ad macq vel ma
  58. 56
  59. Y ~K
  60. sive erit.
  61. pro Logarithmica inspiciatur figuratra ctatus mei Tetrago.
  62. nistici. So CAequ b. AN aequ. M
  63. b+
  64. quantilites
  65. finitas seriebus infinitis aequales
  66. methodus
  67. ad 9E)
  68. prentialis
  69. modus dum series infinita aa t serres infinita
  70. facile
  71. a
  72. pay. 2.
  73. inven
  74. invenitur pe aliat Seriem infinitat, alio
  75. est
  76. civeniendi plurimas
  77. s
  78. cb 3b 4b 5b

Cite

Leibniz-Handschriften zur Mathematik LH 35, 5, 14, fol. 2v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068032:0004?run=73