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[Differentiae in seriebus numeralibus constituendae ad instar regulae Slusii in figuris] Differentiæ in seriebus numeralibus constituendæ ad instar regulæ Slusii in figuris, fol. [2]r

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: 0.81.

Original at the GWLB · Page image · Annotations (IIIF) · Download text

The machine reads it as

  1. s
  2. isferentiae, in series mimeralibus constituendae ad
  3. instur regulae sta
  4. 14
  5. iguris
  6. it aequatio a = 3a + +a p
  7. men non difficite. Kilicet:
  8. N.
  9. Ergo 3 a E
  10. a8 a +1, a +2 seu Sa + sa p
  11. 112, 3
  12. Hoc method.
  13. sit da pB
  14. api a a+ β. Ergo 2 sap a + a.
  15. Ergo: 2a p dae + β. Ergo da 2a - β.
  16. a +a
  17. 3a
  18. a
  19. 2
  20. a
  21. 2 2a
  22. a3 3a L
  23. a+ 3a +2a
  24. Ergo a 7 65a - 94- 7a
  25. 2
  26. (2a-(3
  27. it ergo da p β. erit
  28. 6
  29. tori
  30. ergo a =a integeu
  31. a + 3a + 2a. Ergo sa, a +9a +7 a
  32. ta 3a + 3a
  33. e
  34. La 43a - 9 da
  35. u
  36. =7 da. Ergo da3 1, 3a -9a + 9 B 3a -ga Fβ
  37. 2c
  38. -
  39. ZC
  40. da 2a - β. et das 3a= 9a + (.
  41. Hinc facite demonstratur pi si primae differentia ab a sint 1.
  42. func
  43. eundus ab a fore 2. tertias ab a3 fore 6. quartas ab at. fore
  44. in fallor 124.
  45. nempe. 1. 1,2. 112, 3.
  46. Nam dd a 2β -0
  47. 6
  48. 2
  49. 12, B, 4
  50. 24
  51. 1V (3
  52. dda3 6β 96a6a - 3( - 9β +0
  53. Ergo ddd a2 116β-0-0+0 Unde facile patet
  54. 7
  55. biud
  56. latro cur non nisi
  57. isti numeri, 1. 2. 6. 24. de. prodeant facti scilicet naturalium in
  58. senevicem caeteris evanescentibus. i quia semper dβ 0. ex hypothesi
  59. Hinc proposita eformula: a F +Ba + ea B N erit LN
  60. 3a - ga + β
  61. ta
  62. 1
  63. daN 6a = 12β
  64. + 2b6
  65. intervallum B
  66. ddd NB
  67. 6(
  68. e
  69. huius progressionis
  70. Arithuraticae valde parvum non tntam duo ingentia commoda
  71. +c
  72. habebimus, unum quod omnis numerus intelligi protest cadere in hanc pro–
  73. pressionem, alterum quod evavescent multa, ut dec fiet 3a. dafierba
  74. E
  75. mo si C tum parva est, nogligentur et differemtne disferentiarum
  76. gusti
  77. 16777

Cite

[Differentiae in seriebus numeralibus constituendae ad instar regulae Slusii in figuris] Differentiæ in seriebus numeralibus constituendæ ad instar regulæ Slusii in figuris, fol. [2]r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 39). https://leibnizlegible.com/page/00066619:0003?run=39