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Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 158r

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: 0.82.

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. 159v); this page is its right half.

The machine reads it as

  1. CXX. XV, y CB, a xy = aa dus = - aa dx: XX
  2. faxdx rdydu = dx SCa +tX) xx videamus an X + a aliqua
  3. arte sic explicari possit, ut quadratice extrchibilis reddatur, et generalioris calculi
  4. causa scribatur 1(X + C) = av
  5. Fiat X = Jam Nan erit XX = am +2 a Imn et X = aamm + aam Ima
  6. an
  7. et + aC= aamm +bnamn + 4 aam Imn
  8. (
  9. un
  10. Assumatur av = ap + fV sint Xtac = aapp + 2asp ima. Hunc vala
  11. es
  12. un ac
  13. rem priori identificando, fiet iaequatis irrationalibus, fp = 2a m
  14. Htnm
  15. et aequatis rationalibus aappfsmu = aamm +buamn + aec.
  16. Multiplicetur haec aequatio per ff, fiet aaspp + n=frum +6 af mntaffc
  17. nu
  18. et proffpp ponendo valorem daamm +8aamn, fint 4a um +8amn+ f mn=
  19. ausfrum +6 aaffmnt affc vel (4a- aas5) (mm + nn) + (8 6aas ) mu-asp
  20. nn
  21. 84+5 6aa mn = a affC. Et procedet Extractio
  22. 4a- aaff
  23. a parte sinistra, si sit 842 + ft -6aaff, :, 4a -aaff = + 2, quod
  24. seu mntun +
  25. 44 - aaf
  26. aggredi possumus, quia f est arbitraria fiet 8a + f - 6aaf = + 8a 2aasf
  27. quod si faciamus + ~ + fiet ff - baa =- 2aa et ff-4aa, et
  28. fiet (8a +164- 244) nn = affC, quod non licet. nam
  29. evanescet mn Ergo fiet + ∞ = et prodibit 8a + f - 6aass - - 8a + 2aaf
  30. seu f + 16a 8aaff. seu ffe4aa =0 a1
  31. et reciditur in absurdum prius incongruum
  32. Sit x = Um + In ert X taC= Umm blm +Au mn
  33. un +aC
  34. siat av = _ ell + q Imn et fint x t BC = ce (4, ggmn + 2e llgimn, et
  35. erit q= 2 al. e 2tarn 22a,mtn,: e, et prodibit aequatio:
  36. Umm +CIImn = ee (4+ aaa (mm +2mu) nn
  37. i nn
  38. +aC
  39. Fingatur
  40. et ob mn-
  41. aa
  42. ee in
  43. e
  44. eel, fint ee (= alleell + aC, sed hoc non licet fieret
  45. e da
  46. 4aa
  47. aa
  48. aua
  49. enim c=0. Atiter et ouum taec
  50. aa
  51. 2- aamm tbnamn rquam nm
  52. Xtac= in raC
  53. (psam + qan) ppam tepgarmu
  54. Y= tam1 tan
  55. quam
  56. taa (mmrnutimn) ma =aulma fiat am +n) = C
  57. a
  58. ee
  59. ta
  60. ac aa ( (mn) + uc = ee 10) (mta) non liaet
  61. aa
  62. aV = ar + qsin auvn = aatraguema + 2argtmu
  63. c
  64. fiet
  65. ee
  66. Au(mn): 2ar Y = 2ll (m +n): ag
  67. fit
  68. qusmins +ggmn = lln
  69. =El (m+n)= ga ac
  70. aC
  71. et 4 ( qu (mon) = U (
  72. ac

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 158r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0313?run=74