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Leibniz-Handschriften zur Mathematik LH 35, 8, 30, fol. 45v

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: 0.78.

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The machine reads it as

  1. bxIE e (sit G=b. , fint Cx1 = c bbc 262 1Z C, et X- b- 262123- 1,: b
  2. sil fn Cy- - et (+ = b-el
  3. biiem a _ZC1C. bX V
  4. in intrgn st bX +H = gy, posito = 1. sorilatur 1 + H- 27. 2t, fiet 21 = 22- l
  5. vaeritur
  6. seu rb +bl = 2 e 2. et scribatur yminor b
  7. Faciamus 1b + ( = 21. 21 fiat 21 = b - l et prosibit 1b +l = bb - 2bl + Il et 11 = b -2l
  8. Aliter 21 = b - 22 fiet 11b + Il = bb - 2622 +22. 22 et 1 = b2. 22 + (22. 22 -Il, : b)
  9. Ergo quaeritur 22. 22- l, ib = integro 12 et fiet 2222 = 1gb + Il, quod solvendo
  10. ut ante fipt 22 = b - l et A = b- 2l et 2 cb bet 4n- b etgl 2
  11. et 21 =, b - b + l = L et 1 = b- 2b + 2l f, b-2 = 0. itaque sequens solutes non prodestprerri
  12. 3 +d = 5. 5 8. H + - 2. 2) sit 21- 8 fiet
  13. T
  14. 8. I1 + l= 8. 8 - 2.8l + Il fiet X = 8 -2l L6 fiet 8.6 +ll
  15. Aliter _ N + l = 21. 21 fiat 21 = 8 22, et 8. 11 + HI= 88 2. 822 +21.22
  16. et 11Z 8- 2. 22 + 22722- quaensur 22. 22 -l-AZ seu 22._ =8. p + 1
  17. fiat 22 =7 et 12 = 6 fiet 11 = 8 - 14 + = 6 undo 11 =0
  18. Znnor b
  19. 172- 1, :b = v. sit Z+1 divisebile per b fint Z= b-
  20. et V = b = + et Z1 - V et b et Z-1 = V = b -2 fiet
  21. enim bb = 2b + 1 - 1 = bb - 2b = b v
  22. 2
  23. LIX
  24. et
  25. r
  26. bfg Z1 - f 7+1 = g0
  27. F ZH1, Z-1 = f9V posito Z-1 = f Z+ 1 =gu
  28. Aliter .
  29. Z= f + 1
  30. 14
  31. 14
  32. yl
  33. f12 = 9
  34. l
  35. quot Tot modis fieri potest solutio, quot modiis effici potest, ut nom ut factor
  36. dati b, vrlut f, anctus unitate dicidi possit per confactorom
  37. a sit Z+I = f fint Z = f- 1 et Z- 1 = gV et f - 2. Ergo rursus tot modis potest
  38. bnario
  39. haberi solutio, quot modis unus factor binario diminutus potest dividi per confacto
  40. 1
  41. 2+1 =f5 et Z= f5- 1 et Z-1 = gt = f5 - 2=9l
  42. et ot + 23: f = 5. Opus ergo est ut alter factor factor per numerum aliquem
  43. Z+1, 2 1 = fgst si.
  44. rem. Aliter
  45. multiplicatus, et bnarium minuti dividi possit per confactorem
  46. est 3.1 +2 divisibilisper 5, fit F-1 et f = 1, sod ita Z=V
  47. moducta per.
  48. et
  49. Aliter
  50. 4 et Z = H 11 et v = 24
  51. e fiet = 12. 10 = 120 = 15. 24 Rursus 3. 11 +2 = 35 = 7.5 fit T=H et 5-7
  52. 3.6+2 =20 fit t= et s=
  53. f=3
  54. e
  55. sit b, = 15
  56. 3. 4F
  57. et ∞ =77 et Z = 20, sedua sit Z major quam b
  58. 93

Cite

Leibniz-Handschriften zur Mathematik LH 35, 8, 30, fol. 45v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068124:0090?run=73