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Leibniz-Handschriften zur Mathematik LH 35, 15, 5, fol. 8r

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: 0.84.

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The machine reads it as

  1. Cs
  2. Problema Leibnitianu.
  3. Esto Aequatio: bx +1 = vy. quaeritur ejus solutio in integris,
  4. sosito b esse numerum datum, X et y quaesitos, y autem mino
  5. rem quam b. Letitur autem solutio ea lege, ut dissimulentur
  6. factores numeri dati b.
  7. Solutio.
  8. Cum petatur y esse minorem quam b.
  9. ponat b -2 = y
  10. Ergo b2- 2bZ +3 = y 2 = bx + 1
  11. Unde bx = b - 2bZ +27- 1
  12. et X = b- 2b7 +E=1
  13. Proinde si Z sit unitas, evanescent +2 -1
  14. Atque ita habetur solutio in integrus, quantus cunque detur B. b. dummodo
  15. major quam 2. Frit enim b - Z = b = 1 = y
  16. = 2 = X
  17. atque ita bx + 1 = b = 2b + 1 = y2
  18. cujus S. b - 1 = y. O. F. F.
  19. Si vero Z assumatu major unitate, tunc quoque b datus debet esse a
  20. e major ternario, et (ut habeatu solutio in integrii) Z ea cautione su
  21. mendum est, ut ejus quadratu unitate minutu (22- 1) dividi possit
  22. sine fractione per b.
  23. Sista b = t 3. 2- 2. erit b-2 - b - 2 = 32 = 1 = y
  24. b= 2bZ 1 E 1 = qu 12 4 ut
  25. Esto b = 8. 2= 3. erit b - Z = 6-3 = 5 = y
  26. b= 262 +X2 = 25 = y
  27. b= 262 +22-1 = 24 =3 =x
  28. Hic assumpsimus Z = 3. quia Z =1 = 9 - 1 = 8 dividi pot est per b = 8
  29. Esto rursus b = 8. 7 =5. erit b -Z = 6-5 = y = 3
  30. b - 2b2 + 2-1 = b
  31. 5
  32. Nic 2= 1 = 25- 1 = 24
  33. = 1 = x. dividi potest pb = 8
  34. Atque ita. si b sit = 8. habentu tres solutiones in integris
  35. 1. P Z = 1. Quadit enim y = 7. X = 6
  36. da
  37. e
  38. etia
  39. c
  40. 2 2 3.
  41. 2 = 5.
  42. y = 5. X = 3
  43. y = 3. X = 1
  44. Lterud sit b = 12. 2 - 5. erit b - 2 = 12 -5 = 3 = y
  45. b=2b7 +7-1 = 4b = 4 = X divisibile p b = 12
  46. 2
  47. Iem b = 12. Z-7. erit b - 2 = 12 -7 = 5 = y. 22- 1 = 49 -1 = 48 dividit
  48. b2- 262 + 221
  49. 24 = 2 = X
  50. Iterud tres solutioneinintegrii posito b = 12
  51. ta p
  52. e
  53. 2daF Z 5
  54. 3ti a p2 =7
  55. 12
  56. = - evadit y = 11. X = 10
  57. y = 3. X = 5
  58. Y = 5. X=2
  59. Fb = 12
  60. 22 1 = 25 -( = 24
  61. Vertatur.

Cite

Leibniz-Handschriften zur Mathematik LH 35, 15, 5, fol. 8r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068207:0011?run=74