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Leibniz-Handschriften zur Mathematik LH 35, 3 A 23, fol. 5r

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: 0.83.

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. 4v); this page is its right half.

The machine reads it as

  1. fiet: abn
  2. tvv)
  3. - nv 3b.
  4. in
  5. sonendo iam + V
  6. a aequ. vb +np b
  7. fiet: +ps
  8. = vb
  9. nx quod non procedit
  10. 13
  11. sed ponendo a cego vb +b fict. Fu )b = io3 et sublatis tollendis nVB+VB -n
  12. nv
  13. +vr
  14. =n
  15. debet ergo nv + 1. - n esse po et nvv + vD = n 10
  16. unde exhis limitibus inveniri debet valor ipsius n, quippe integer;
  17. . et inp vv debet
  18. 1-vV
  19. autem latere enor in calculo foret enim alioqui n aliqua fractio.
  20. Resumamus. Primum quotienlem l constat esse aequ. V. per aequ. 3.
  21. singamus
  22. Dquaeritur m. est autem +1 + mD b pima. poms a aequ vb
  23. fiet: + + m p inv quod per se patet nec quicquam docet; ponamus
  24. a aequ vb +b fiet +1 + mv p mv+ m. quod fieri non potest
  25. Rursus sumatur m+1. loco m fiet 1+ mo + vp mv + v +m F
  26. firi 0 p1. quod absurdum est. Itaque ipsa hujus ratiocinii funda
  27. menta nondum satis constitui Utique manifestum est tmobpima
  28. Unde a r 1+ mv b supra a p. vb. Ergo F) in + x. quod per se patet. A
  29. rusus im + 1a H 1+ mo+o b. Ergo in ap 1 + mv +v. supra ar, vib b
  30. n
  31. v+ 1
  32. m+ 1
  33. Ergo Y +1 + V, quod etiam per se patet unde video hinc
  34. nihil duci redeundumque esse ad ipsam aequationem fundamentalem.
  35. im +1
  36. Habebamus per aequ. B aequ on +a- b
  37. va
  38. vbb + ab
  39. per aequ. 9. aa equ DD + vbb + b vV +
  40. bb
  41. jam porro examinemus.
  42. aa
  43. aa
  44. aa pronova divisione Itaque aequationem
  45. vbb + ab
  46. C13
  47. 1. multiplicemus per bb. fiet: b + vaa b3 aequ. a bb B
  48. Lb
  49. substituatur onter ex aequ. t fier: b5 + va Marab aequ ae bb.
  50. ergo q aa aequ a bb + vua maltiplicetm aequ. 15 per B. fier:
  51. per V fici a vbb + a b aequi b vaa b) + a- ab
  52. a6b (va B3)
  53. va
  54. Ergo et B b cp. pro b ponatur b bb et pro B valit ex aequ. 1. fiet:
  55. a bb et pro t vaa b ex aequ. 1. valor ipsius B3. frei.
  56. (16
  57. b+ va = Wvab a qu abb. Et multiplicando omnia per v.
  58. vel retinendo aequo 15 fie et efficiendo ut nanciscamur
  59. in ea v bb nab nam oqu. vel retinendo aequ. 15.
  60. et efficiendo ut nanciscamur in ea vbb + ab. fiet
  61. mulliplicamus prius aequ. 1 per v. fiet Vb + vvaa b aequ. vab
  62. addamus utrobique at babum purte
  63. et valelem a- b a ab alteratiet
  64. per aequ
  65. va
  66. a5- ba
  67. ab as
  68. et quia unus in est terminus purus. ideo fiet: aa aequ. va rbb tab + b’ a - v b- v ab
  69. varbl vbbab
  70. Ex aequ. 16. ita procedemus: vb vva ab ab aequ ae vbb (v al b + va b
  71. ergo aa aego av vbligab + a vbb = va Bbb - vl5 - r2 a rbb
  72. vnas
  73. a vbb +ab
  74. b
  75. + a = v b insto
  76. =m a +mb B
  77. in a.
  78. Isomi
  79. ph aqu5

Cite

Leibniz-Handschriften zur Mathematik LH 35, 3 A 23, fol. 5r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068236:0009?run=74