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Leibniz-Handschriften zur Mathematik LH 35, 14, 2, fol. 69v

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

One image of two folio pages side by side, registered by the library under both labels (also fol. 68r); this page is its left half.

The machine reads it as

  1. itaque res six potius: be + c. P. eut = 1b). e ent et (6) eret + (. d. . ea t - E (bB. e. t.1 1
  2. imo ne sic quidem quare potrus sic:
  3. be = C. e. C- 1. C-
  4. f+he
  5. ubi est data reliquae quaesita
  6. Sbiee - 1 fb)e
  7. et fiet. bse + bh +, C eC - _ 112 cC + 1 2C b)feC + hib) C - 1. hb).
  8. fe+ h
  9. et fint ) C = 5(B) et bf ∞ IF2C = - 1f (6) + hlb) et bh + 12C = - 1 hib)
  10. Ex 2 et 3 per 1. fit (41 bf - 14 2 f(b) = - 1 f1b) + h(b) et (5to) bh + 12f(6) = - 1 s(b)
  11. b unde (6to) (6) = bf (6) :b = f:, 142 - 15 + h. (7mo) = -h :, 1. 27 + 1h. ergo ex 2. funt
  12. (1) 1. 2H + ih f = -. + fhhh seu 1. 255 + hh + 13 ft = 0
  13. g0) hh +, t ft + H = - ff sit h + f = f 1 - 1 se R es h. f = -1 - 1
  14. ergo (bd) ib = 1 1, 2 + Y1 -1 seu (b) 2 b = 1 seu (b) = b
  15. (8V0) 12s + ih f = - 12 - 1 fh ∞hh seu 1. 2 f) + 12 fh + hh seu tit 4 3 5tr + s = - f
  16. (9nd) seu ti a f -H seu h: f = f1 - 1 (6) :b - + 1 - Y- 1, i, D + Y 1(1)
  17. (10) seu (b): b = 1- Y- 1:, 14 f 1 siu _ (b). b = 2f - 1 : 2 seu 6): b =
  18. ((c4d) seu (b): b = ( - 2 f. 1 (D, :, p - seu (6). b = - 1 - + hh + 3hf. + 3 H = 2, s - 255 - L
  19. jam pergendo faciemus
  20. (b) C. e - 1 + (). e. C- 1. -2. C. 3 = ((6). e. 8- 1. e -2
  21. (8) e + (h)
  22. fit h + 3 f = + L fsr b - 142 Tut
  23. seu h: f = -1 si 4 ∞ +
  24. et 16) : b = 1 : 1. 2
  25. seu
  26. (b)=
  27. fit (6) (F) e + (B) h) + (e) ee - 2F 5 E + 2. 3(1) () (b) ee - 2 (f) (b) + (h) (6) e =E X qud vaum est
  28. ex 2 et 3 per 1 fit ) (6. (5) - 2 +3 (5) (B) = - 2(f) (b)) + (h) (bD et (to) (b, hi f 2.3 (5) (bs = - 2 hXbD
  29. unde (6to) (b) : b = (5) :, 2t 2 (5) + (h) = (7noo) +h) :, 2. f) + 2(H). Ergo ex 7. fit
  30. 800) 2. 3(55) + 2Ch) () = - 2 1B - E(f) (h) - (h h) seu 2. 3(ff) + 2F3(fh) + (hh) = 0 ere.
  31. t= e
  32. Chh) + Et3 (h) + 2F5 fs = 243 - 235f = 2 + 5 4 2. 23 ff. fit h + 2+3 f = +3 fs
  33. seu ( = 2 (h) : (5) = - 2 fit (b): 1) (b) = 2 :, 2. 3 = 22 = 1 ∞:, 4+3 - 2 - 2 - 1
  34. ergo ebD : (b) = 1. et semper huc res redit ub sit ): _b) = 1:, 4 - 3 seu 1 et (h)): (5) C-3
  35. Ergo res tandem egregre sic constituitur
  36. e + B. C Itaque prodit e. e.1 4 C. P 1. C. 2. el. 3 = e. 2-1. C -2
  37. seu e. e- 1 + . C- 1. C- 3 = C. C- 1. e -2
  38. et jam paulo ante erat et e. e- 2 = e. e-1
  39. Ergo e + e. e-2 + C. C - 1. C - 3 = C. C - 1. C - 2
  40. l + C. e-1. e- 2 + C. C - 1. C-2. 6 -3
  41. e 2
  42. C. 8- 1. C- 2. C. 3, C-4 8. C. 1. C- 2. 6-3
  43. + 1
  44. 2. 2. P. 4. P. 5 expl 3. es +
  45. XH
  46. + L
  47. + e-5 =
  48. AXAX
  49. C - 4
  50. C25
  51. C- 1. C- 2. C 3. C- 4. C- 5 C-1. P3. P-4. C5
  52. Asterisci notant terminos omissot, Nempe si termini sint C, e-1, e- 2, e- 3, e- 4, C -5,
  53. sepe scribetur
  54. X, C - 1, X, C. 3, P. 4, Cus H, H, C. L, H, P- 4, C - 5 H H, K, C. B H, C =s X, H, H, A, B-4, H (-5 ee
  55. quod est theorema per pulchrum, et universaliter verum utcunque termini continuentur
  56. quae est series quae e tunc cum e est interer abit in productum continuorum, sin sit
  57. finitorum; qun e non sit integer, tunc series ista in Onfinitur continnari pt, sed quaeritur an tunc
  58. quantitati finitae aequetur. Vene hoc non videtur quod non puto, sed nec videtur necesse
  59. ubi duam serierum hujusmodi una alteram dividit
  60. e + C, X, e- 2 + C, C - 1y X, C- 3 + C, e - 1, C-2, X, e - 4 + e, C - 1, C -2, - 3, H, e - 5 = C. 2-1, e- 2, C - 5
  61. quemadmodum e et quod
  62. X et A, Cd C. 1, N , _. DC
  63. Seu 1 + 2. C-2 + P. C - 1. C-3 + N. C- 1. C- 2. 8- 4 +X. C.1. C- 2. 8- 3. C-5 = p. P. 1. P. 2. . 3. P. 4)
  64. ent
  65. 1
  66. a
  67. eoner bee) b15
  68. fit (1) () (b) et (6) (5) = 2 +3 (C) (2d 2 2 (f) (bD + (h) (bD et (b) h) + 2. 3 (5) 3 2his b)
  69. Seu 1:, 3-2
  70. Ergo tandem generaliter
  71. e
  72. 1-
  73. Hinc e
  74. seu fe
  75. +

Cite

Leibniz-Handschriften zur Mathematik LH 35, 14, 2, fol. 69v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068202:0138?run=74