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Leibniz-Handschriften zur Mathematik LH 35, 15, 5, fol. 79r

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. 80v); this page is its right half.

The machine reads it as

  1. Vir clarissime Amice
  2. honoratissince
  3. Vaeris mihi profunde admodum
  4. in aenigua implicatissimum penetrasse
  5. et pulchiam quandam coefficientium pro generali
  6. additione duadica compositionem detexisse,
  7. qual descio an geertiliter saltent metior
  8. Quoniam tamen in in primis duabus
  9. columnis commudae qua commodiores quaedam
  10. expressiones se detexere columnis quaedam
  11. sese compendia offerunt; videntur. vid
  12. per otium poterimus, an non liceat (procedere
  13. ad etiam ad columnas alteriores. dabo
  14. modum quo ea compentia calculo literali prodiere
  15. qui fortasse nonnihil pro caeteris inservire aliquando
  16. poterit: (∞) = sit sit prima columna, D secunda, et su
  17. P, nova nota addenda (C) - D,: p vocetur S
  18. et (D) -D,: P vocetur 2. Hinc si fia
  19. ponatur O = 1a + 12 ab + 13 abc + 14 abcd + 15 abede + erc
  20. erit ~ = 11 + 12 a + 13 ab + 14 abc + 15 abcd + ere
  21. jam ex nostris Theorematibus constat esse 1 = 52 +20
  22. et fet se- 11 + 12 a + 13 ab + 14 abc + 15 abcd + etc) = ∞
  23. 20 =. + 211a +2. 12 ab + 2. 13 abc + 214 abcd + etc
  24. Ergo sit 11 = 2 Et 12 - 2 et 13 = + 4 Et 14 = - 8 Et 15 = - 16
  25. fiet
  26. et ita porro. Atque adeo
  27. O = a - 2 ab + 4 abc - 8 abed + 16 abcde + ete
  28. 22ab + 23 abc + 24 abcd + 25 abcde + etc. Erit
  29. t O- neab n abe drtaled + 15 abedet etc quia igitur
  30. 5
  31. Eut2 Est jam
  32. 3 = 22 a + 23 ab +24 ab 125 abcd + etc Et quia
  33. Et quia 4 = C - 20D, prodibit aequatio identificanda sequens
  34. 20
  35. seens + 22a + 23 ab + 24 abe + 25 abed + 26 abede + exc )
  36. +20D =-
  37. -C =.
  38. - 1
  39. + 2. 122 +2.123 +2.124 +2. 125
  40. - 16
  41. +8
  42. + ex
  43. + eted
  44. 2 Et 29 + 2. 123 = 4 Et 25 + 2. 129 = -8
  45. + 2 - 4
  46. Et. 2. 124 = - 8 - 25 Et 2. 125 = + 16 -26
  47. vet quia duorum gonerum sunt incognitae assumtitiae
  48. Unde 27 = 1 Et 23 +2. 12 =
  49. identificatoriae, nempe 22, 23, 24 eHc; et 122, 123, 124 etc)
  50. ideo nova adhuc aequatione est opies, nempe.
  51. (1D) O3: p. (O D) -OD,: p = D - 20D
  52. jam (5) (C D) - OD,: p = 122a + 123 ab +14 abC + 125 abcd + etc.
  53. Ergo fie
  54. (C5) - OD,: p =
  55. 20D =
  56. 1n2a +123 ab + 124 abc + 125 abed + 126 abede t erc
  57. 2.122 +2123 +2.14 +2.125 +2. etc 3 =0
  58. -otc
  59. nq - 24 -25
  60. Unde prodibunt aequationes identificatoriae sequentes
  61. 22
  62. 122 =0 Et 123+2. 122 = 22 Et 124 +2. 123 = 23 Et 125+ 2. 124 - 24
  63. et ita porro. Et hanc aequationum, seriem conjungendo
  64. Cumpriore siet 123 = 22 +23+2 se in his aegg. pro
  65. 2. 122, 2. 123, 2. 124 etc. substituendo valores ex prioribus
  66. fiet 123= 22+23+2 124 = 23+24- 4 125 = 24+25 +8
  67. 2. 123 = 2. 2242. 23 +4 2. 124 = 2. 23+24 - 8 2 125 - 2. 24 +2. 25 + 10
  68. 2. 126= - 26+ 16
  69. 126 = 25 + 26 -16. et vel
  70. 2. 124 = -25 + 8
  71. 22 1 25-
  72. 2. 123 = - 24 +4
  73. Ergo hos valores aequando fit 2
  74. 24 = - 2. 22 - 2. 23 25 = - 2. 23- 224 26 = -2. 24 -2. 25
  75. potuis meodat porilade egactores aret in (at maear eae aadsue

Cite

Leibniz-Handschriften zur Mathematik LH 35, 15, 5, fol. 79r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068207:0157?run=74