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Leibniz-Handschriften zur Mathematik LH 35, 6, 6, fol. 16r

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.

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. 17v); this page is its right half.

The machine reads it as

  1. Vinit adn
  2. sit formula irrationalisus = fax tabxx + ux + reducendues
  3. ad talem, ubi sub vinculo indeterminata non ascendat ultra gradum rdm
  4. explicando X rationaliter; ita nempe at ex non sit irrationalis. fiat
  5. pu si posset tolli temminus unxi maximus res esset confecta. Sed tunc oportet
  6. valorem ipsius X habere inde terminatam in nominatire de, quo max. pitum
  7. ergo sentemus collere duos terminos infimes sibque X = inZ tnn: a
  8. et fiet ax = nZ3 + 3mmnnzZ + 3 mnt Z + n6: aa
  9. yy B2h
  10. accx =
  11. ad3
  12. +ab mnZZ + 2 ab mmZ + abrt: aa
  13. +aacc inz + aacemn; ac
  14. +ad: aa
  15. Verum hinc patet posse quidem tolli terminum infinium, per n
  16. sed hoc sublato non est in pte ut tollatur penultimus per m,
  17. quia m in eo evanescit
  18. faciamus X = mZ + nn: y+ p habemus nominatorem 1Z+ p
  19. in balore ipsius y. et ita non habemus intenta.
  20. si la
  21. quod si mulliplicemus numeralirem adhuc per Z+ p
  22. ut videamus, an licet enim sic assurgatur ad Z, vider tamen
  23. potent an liceat tollere duos terminos summos
  24. sit ergo _. X = mZ + nn: Z+ p = 0: d, fiel
  25. auyu = a O + ab O0D + acc OD) +ad 3
  26. = a CD + ab 00D) + acc O V + ad 3: 3)
  27. quaeramus teminus summos in a0D est am Z + aBmp
  28. in
  29. +3 amumBZ.
  30. ab edD est, abmmiz tabmmp
  31. +rabmun 33
  32. ac cOD est facemZ Haacemp 23
  33. in ac ad s est ad
  34. R
  35. 2
  36. +aaccnn 13)
  37. 93
  38. +4ad B Z et X d = Z - nn. d,:, Z-
  39. Ar est constans Ergo hoc casu res nonceder
  40. Ut ergo autios terminos simul tollamus fiet m bmm + cc m + d =0
  41. et p L am + rab mun 1 aaccn: et - p = Sammun + 2 ab mtn pa ce
  42. e
  43. regulanter,
  44. Hinc sequitur fimmutam quamvis irrationalem simili Methado
  45. Es 19
  46. 1
  47. deprimi posse ad inferiorem, et hanc rursus ad inferiorem, atque ita hinc sequibe
  48. formutam quamvis posse ubbi extrahibilem. Hinc sequitur et compositas
  49. reodi posse itales sit enim exempli causa
  50. YEX + Px+q
  51. V YX pX∞ + qXar + Y aX + 1Xx + ex +d, reddatur primum
  52. una ex partialibus extrahibilis, deinde et altera fiet denique non formula ratio
  53. ncet lactu suceta i qua arqur petato aotrum tinti
  54. icet.
  55. :aa
  56. O: aa
  57. O. aa
  58. d. O= numZZ L2munZ+n
  59. 2
  60. D.
  61. -Q13piZ3php
  62. ID = 22 + 2pZ + B p
  63. D-
  64. 2
  65. 2
  66. D- 21 a p ebppi
  67. +p
  68. si estet b4c, -0, finet
  69. u
  70. y= Xa ida
  71. et m = dH et mm= dd
  72. et M = d3 et fiet
  73. p
  74. =p= 3add Lad + 4d3
  75. seu p = = pn. d
  76. et x = -dZ + nn : - nn: d
  77. am + 2 ab mm + zascemtad

Cite

Leibniz-Handschriften zur Mathematik LH 35, 6, 6, fol. 16r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068051:0031?run=73