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Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 44r

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: 0.75.

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. 45v); this page is its right half.

The machine reads it as

  1. In numeris s, B = bxade pe V, B - 1. Ergo b = 5b (b. C- 1) Erx sb x ad (b= (bdi-issen ad b, ut b -1 a
  2. Ergo SBx da = BX dx : (b lX -1)
  3. in numeris d, X. B = X lb) + b dx. Ergo Lib dx = fe X db) = X, b - s b dx
  4. ad saqulbus est ad sx x
  5. aim s (tdex pragressionis Geomessicae, ad eoque summabilis; tty b . bs a e . (. L 3
  6. Ergo sit
  7. ut pax -1 ad dx Ergo SX bxde sua B) dx
  8. Rursus d Xx, b = (2 xdx + dx dX) bF + XX d(b). Ergo (XX. d) (b) = XX. b - 2 sX b dx = sb du ax = (XX. b
  9. Et ita habentur ha summae. A) b - V s (bx- Ergo b Ergo dei
  10. rgo ent fb SXX. b ex = XX A - 2B H . dx L2
  11. A-52
  12. =(dx: B nosito B- (dX: s ar-, 2
  13. Carsnu
  14. In numeris d, b = Bx+x - bx = b =, b -1. (Ergo b. = sb= bb - 1). Et posita
  15. de constante, erit b (dx: , bar - 1) = SbX dx
  16. d, X. b = X d,B) + b dx seu X d (bY) = dCX. bF) = b dx = X. b, bd -1. quam multipti
  17. aequationem Multiplicando per dx:, bX -1. fet et productum utrinque summando fiet
  18. X. bE dx = X. B dx (, b. - 1) = S b dxdx(i, b - d) ac denique per canonem praecedentem
  19. pro sbx ponendo valorem, fiet (x. BB a (Xde X b tx. ()
  20. fet pro sb x ponendo valorem fict, l. X. b dx = X. b (dx:, b = - 1) - B (dx:, b - 1). (+ be drdn :, bt - 1
  21. +b dxdx.
  22. +b. dedx
  23. d, XX. B = XX llb7 2b. X lx = XX b. (b.= - 1) + 2b: pdxC Empo Xx b = RX. b = (37 - 1)) g 2. X. b (1r: 9b = - ) bs l. 1 2)
  24. di niniurdele
  25. -b dx (ax:, fdu
  26. dex d, X. b =- X db) + 3b. Xx x (= X. b ( (b7 - 1) 43 b XXdx Ly. X b = (X W(t Y 1) 12 + 3HX. b du P X sudx
  27. + b dx. Ergo (x. b dx = X. b (dx :3 b - 1) = 3 XX. b dx: , b x - 1) 3 + 3. 2. X. b (dx:, b7 - 1) - 3. 2 b (dx:, bX- 1) 2 +
  28. 3 (X dx(dx: bdX - 1)3 = 3 X b= (dx:, b - 1) + 3 bX dx (dX: , bX.1)3 = BX Axdx (dX:, bx- 1): eu ordinando
  29. et per compendium dx dx:, bax - 1 appellando B, fiet
  30. (X b dx = X( X3 bs B i 3XX b + 3. 2 X. BX
  31. (LXdx = b= B
  32. SX. bE x = x. bxB - b BB
  33. IXX. Bdx = XX. BB - 2X. bX BB + 2 X 93
  34. _ axDB
  35. X. b dx = X bF B - 3Xx. H 3B + 3 2 X. b. B3 - 3.2. 76 X. 94
  36. +3 b x3
  37. p. Lxdu:
  38. dx bY = Xt bB +A X ax6X aplxtaX b rb
  39. Ergo sx Vx - X 68. 4X 28B, 43 NX V 84 3. 2x b 197 + 3. 21 fr95
  40. F+. 3. Xb x B3 - 7E1B2
  41. -31X. b BD + 32b 4- 133 b B.
  42. = b dxdxBD
  43. (x b k = X bB - 4 X b + 4 3 XrbB3 - 4. 3 LXb Ct + 43 2b95
  44. =6Y X(. a BB H4 X B deb - a (3. b dx 4
  45. +4 X. S ax xb F est B apax B
  46. bx dx BB
  47. aid alaxo.
  48. 26XX6 d BB +6. 2XV axB - 6. 2. GX A. B1.
  49. +6 bXdxdx B3
  50. +x6 deBB 24 (Ax B
  51. 1b dx D
  52. ita continuando poterit inveniri
  53. regula continuationis

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 44r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0087?run=74