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Leibniz-Handschriften zur Mathematik LH 35, 7, 12, fol. 1v

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: 0.77.

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. 2r); this page is its left half.

The machine reads it as

  1. Ut autem pro summis talium serierum generalem Methodum
  2. demus, aetem icique calculi differentialis a lineis ad numeros
  3. transferamus generaliter sic licebit procedere: sit du differentia
  4. ipsorum y. Et significet exponentem gradus potentiae quam pla-
  5. cet imitatione veterum quorundam Arithmeticorum vocare pronicam
  6. Gradus Ii Directis primus
  7. in Directis
  8. y-y
  9. secundus Tertius
  10. in Reciprocis -y
  11. Quartus
  12. J. yrty. g y. ytag. 9 r2ty - 2 y. V2oh. 92 . 19 +rctus -
  13. .- 5
  14. y. yt ay
  15. 1. gitus. yreous
  16. in Reciproris autem Generalier autem Y oy = yta et Y yeF - 1
  17. (2) pr
  18. y. praty. 9 Atgs. 9 43Ey
  19. in nerunt pa etauralis et ya +Idy = y iti senis at + s dre piscis
  20. Ergo subtrabendi a4 ex aqu. 1. ab aequatione 2
  21. st et y y - pri dus =
  22. y p+1
  23. Et subtrahendo aequationes l et 2 a se invicem fiet:
  24. y+ u - y B = PFI Ay. Y. ser. S y su =
  25. in Directs pinittr VC. j = 9+ y et y. y apnus =
  26. In directis alio opus est artificio
  27. PF1
  28. tale quid
  29. siniliter in directis alia arte nonnihil procedendum est, ut idem
  30. pe
  31. concludatur, nempe tau. yrius yrdus et y. 9+ p- idus =
  32. nempe yra. et y = y et B ) podu et et y rdy. y du = y +du
  33. odatasum tat syt (seu fy S y+ tu dus = Y + 4y. seu s ylay =
  34. Generaliter ergo y dy =
  35. er
  36. 1P+1
  37. Ly et1
  38. ar
  39. in Nrumerois
  40. p
  41. Josito p este exponentem potentiae pronicae, et valere in tirectis, in neciprocis.
  42. peute vi
  43. ipso p existente numero gradus in directis positivo, in reciprocis privativo. Quod
  44. ipsum in linera verum est pro. potentiis communibus;
  45. perae pretium autem erit potentias communes revocare ad
  46. q pronicas selssgntas seu aritimetice afsectas. vig. gta estt L y
  47. ab (2) in Exponente significal potentiam pronicam. Ergo y9+y = . yl)
  48. Erqu. y = y - y
  49. ubi notandum y et seu y esse idem
  50. jam y - y+1 -1 et y g4 = E ) ergo fiet
  51. y C2d - so). rursus y = y+2 - 2 = y+ 1 - 1 e y2 in P - y. fiaetus
  52. 3 13 + 2. 3y2)
  53. 2) - 3 y + y0
  54. -6 f4y ce
  55. + 7
  56. 2γ
  57. egosis)
  58. - y a- 5. d 1 410)
  59. +25 - 25.3) 15. 2g21
  60. = 5 - 6 y + 1 - 1 y
  61. .∞ +1 y
  62. (2) (1)
  63. p 10 3 +25 - 15y + y
  64. - Y y 73y tog. et = y + 1 3 3 Y 3y Ea y, = 1)
  65. V = 1. 2 s y - y et y - 943- 3. Ergo y=
  66. Generalius ergo y. _ =
  67. yy =
  68. fietue ist = y - 21
  69. ∞1. +y=
  70. sid -3
  71. 4 (4)
  72. s 1 g 2 9e 3 9. 3et. 18 1)
  73. in dinctis pa 1oe 2 eet 3
  74. Hocest in direcie si iste atae
  75. seu differtalia
  76. sie
  77. Et qud in Reciprocis
  79. si seriti e
  80. progressione aricha
  81. proudere ineum
  82. sse e
  83. umma
  84. uuda sit
  85. s
  86. moium
  87. quaeritum, aen cum infinito)

Cite

Leibniz-Handschriften zur Mathematik LH 35, 7, 12, fol. 1v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068083:0002?run=73