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Leibniz-Handschriften zur Mathematik LH 35, 14, 2, fol. 68v

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: 0.79.

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. 69r); this page is its left half.

The machine reads it as

  1. 1- X A usque ad ne = + Z = - E + et P. e. t 1 - e. ert. 6
  2. Ergo si C= 1, 2,3, en. fit + - = ble,: - = + + - 2 + 3
  3. 1
  4. E82- e 2.9 g0. + eet e)
  5. A. 2.3 - 3e + C. P1 23,4 - 3. 4C + 42 - C P1. e.t
  6. + C. eet _C. e. 3. 2 et = o+1
  7. Si C. 2 dat 21 5. si (. 3 al 234- 234+ 21 4. 123
  8. 2.24
  9. sed haberi pl ex natura summmationum
  10. in integris ses ostendi experentia,
  11. quaerenda demonstrati
  12. Nam six = 8(.C VC B = 1- 2Z a
  13. Z Ergo ipt E (gdZ est ire, ut asserebatur
  14. et id pulchui lit haec demonstratio, quod nem ostendit, etsi e sit numerus
  15. Ergo si : y ull. = 1 fit L - en = e
  16. fractus, imo sunu, inio quicunque
  17. sola inductione.
  18. cum Wvallisius cogatur esse plentus
  19. bEodem modo sumuari pt
  20. eodem modo summan pl
  21. 1 + - = + 8. C- t C. B. 2. C. 3 ete
  22. 1.23 1.23.4
  23. Nam 1+X = f + e x+ e. C. 1 X 4 C, . 1. P. 3 X + e. C. 1. e. 2. C.) erC
  24. (Xt = ex = 1 si x- 1
  25. t Sida X + E. X = C p cene R+ canar em X M = (Z. s
  26. Haec tam mirabilis pronuitio vera est tam in integiis quam in fractos quicunque sit punee
  27. sed si integeo sit experientia accurata venficari pb, sin minus appropinquatorit
  28. ia
  29. uti e est integer es et X est 1. prodit regula rocllisiana
  30. 1=X dx = dy si tu x - Z fit xax = aq et X = siZ et dy = Z dX: B1. Z
  31. Si X dx - 1X- 18
  32. Siuni ex _ IX - ZX K
  33. Sme d = X 3 + 3X - 1 X
  34. 1-X dx = F Y X - E X + eerat - C t t g) etc.
  35. Cy eut, P- 2
  36. si oll. A 21. fit Sux ax = 3 Su Ex -13 Sume dix = 2. 95 + sm ap - Et u u uatereri
  37. ele + mee e et L e = e Ego l.f) BC + m. C. 1 = be. -1 fit ge + mee -me =qe e
  38. 9b
  39. e
  40. mi
  41. pui asuut
  42. 9. Hid situ grmalibu) sivere t e eree2
  43. 10 e + 2, 8. (-1 =, 11. e. e1 fit
  44. seu fit 20 = 121 sed ila 10, 21 =0. absund
  45. Ergo non licet . 2. 3, vel 112. 3.4. sic exprimere, ut in finitis per se finiatur, seu non
  46. e fC = We D
  47. licel pro tali producto afferre valorem universalem. Quanquam nondum rem possin negare
  48. absolute. Si daretur generatis ista expressio simul serviret pro sixx ax licet e esset pur
  49. negativa vel fracta. Itaque hac expressio (I-XX du = 2. 12. en. C.
  50. hisi pro e rationali Ac proinde est expressio imperfecta. Talis earanenda
  51. fiactetur in rationalibus daret serien infiuntam in aliis. Excoritum tale quid candem paus latima hujus
  52. Nolabilis interm haec summatio quod - = = 2
  53. vel hoc 192. 3. 4 - 3. 134 = 3. 12 4 - l. tag
  54. : . 1 - 2 + 1
  55. = 3 quae sunt pulchia Dheoremata, sed demonstratu difficilia
  56. = 1+ - 2 = 8 L - 2 + L - 1 - L + - 2+ L - Z + 3 - -, - 2 + 4-
  57. =1 - 4 + = - 4 L- 4 +6 - 2 + L, -, - = + - 4 + +, . 3 + E - +
  58. 1 = 1 7 = 36 a 1. 47 1 = 3 6.9
  59. + 5 9 = 4. 8
  60. 1 - e + C. C -1
  61. O+ - e 2c
  62. 3 = C. 8- 1. C-2 =0
  63. An; 1+Zn; 1. 2
  64. L. = 3 + 3 -1 - 4. 8. 12
  65. = e: . D. C.2 et
  66. = 4, sit 3.21 = E. E. 1. E. 2. E~ 3 ;d E. 1, E. 2, 6.3; 4b. E. 2, 5. 5. B; 4 7. P. E-3
  67. 1-X ax =sy dx datur ergo et datum
  68. N datur ey a d B, - Vy dg
  69. = L4 + 6 - 4 + 1 3. 6. 9. 12 et 5- 2 et n impar
  70. Sic ego datur (1 - X dx = y cx
  71. 1- X = Hy et X = 1 - y
  72. 2 d N, 12. 3us ad e = s, XB dx
  73. idem tamen est, sit e quidem sit numerus
  74. integer sed n sit fractus
  75. 10 13 4. 7. 10. 13
  76. 1+I, 1+ Zn, 1+ 3B usque ad 1+ en
  77. 2 e, c- T, e- 2, C. 3 er 1 1t C. L 1
  78. 1. 2. 3. 4., 1, 2, 3; 1,2;
  79. + = 2. + = = 2. 4 L -3 + 2 - 1 - 24. 6 ralifer (X- X d
  80. et ib booro uti 1 = = = - 2 + 1 - 1. 2 et 2 - 2 +3 - 1 - 1. 23 et
  81. vel. Hoc esset demonstrandum:
  82. 152.3 = 251.3, + 1512
  83. + - = = 4
  84. 17 (, 1 + ea2
  85. ed seem sit serhame m ebm
  86. 10. 2le + 20 ect 2oC= 11. Ele . 2e
  87. non valet
  88. quasismuz sit n

Cite

Leibniz-Handschriften zur Mathematik LH 35, 14, 2, fol. 68v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068202:0136?run=74