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Leibniz-Handschriften zur Mathematik LH 35, 4, 3, fol. 30r

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: 0.80.

Original at the GWLB · Page image · Annotations (IIIF) · Download text

The machine reads it as

  1. 3 dividatur in bina quad rata xx: hh et yyenh
  2. Niha hac
  3. 3th B = Xx+yy unde hh - XX- hh + gu sito. si
  4. sit Xth X sera)h Y Fh_ (Pia)h sint h = P ( L) + f(y -h)
  5. eton aaas leaa as sed ita connescit h, explicatis X et
  6. et
  7. IhR-
  8. piat be
  9. X =eh +C y = fh + d
  10. Y
  11. 3hh = eesh + 2ehc +cc + fl, 2fhd + dd
  12. ac
  13. sit cc + dd = lig et fret 2h = eeh + 2ec + fth +bd, et cetdd
  14. a
  15. =
  16. na
  17. ea
  18. 2ec +2fd + ag = cc+ dd
  19. haque ee-5s
  20. 99
  21. aa
  22. Ergoe et fngu possunt esse maiores quam e
  23. in erant D vel 1. si sint ambae a fiet vel ifiet
  24. h= rec +sot 2et 2d + ag 2c+ 2d+9 et fit rc+ rd+9- cctdde: q
  25. sit aq = 3aa - eo ff fint 2ec+ 2fd + 3aa - ee- f = cc + dd. sit
  26. 3aa ef fint c 3aades2cd+ mm, et fint
  27. m = c + d + e +f. sit 3aa = - 2ef - 2cd 2ef
  28. seu cc + dd + ee +s D 2cC- 26f2d + +2cd - 2cf- nm
  29. 3aa -2de + 2ef + 2cd- 2Cfmm, fint
  30. fia 3aa = 2dC 2 2cd +2cf+2de- 2ef - mm
  31. fietue c+d - e - f = 4m sint _ d et f = 0 et fiet
  32. ramsit f20 et C - a = 1 sint V,d, 1. C = 3aa tmm
  33. fiet d = _m + e+f - c .= 3aa + mm - 2cf + 2ef, : 2e = 2C
  34. Et =M F e -C) +2 qu (P-c) (2f (8- C)) = 3aa + mm (+ 2f (e- C). Hinc potus
  35. sit e-c = l fiet 2lm + 2ll = 3aa + mm, seu
  36. pimi
  37. Cl- m)
  38. inm + ll + ulm = 3l -(3aa sit a(l - a) = b () fiet
  39. a l- m = 3l+ 3a, b. fiet M = - 3bl3 ab + al,: a = bl+ aa- al
  40. seu = 3bbl - 3 a bb (+ abC) = (ab1) + a = aal seu l = a + 3 abb, :, aa = 3bb
  41. sit m = C3bC+ (ac 36) - 38eb + 9ab + a + 3ac bb - 3a b - 3 ab 2 aa - 3bb
  42. a
  43. seu l= - a3 = 3 abb3 :, 3bb = aa et m = 3, b 3 ab, ab + 26b =2aa,:, 3b6.
  44. seu m = 6ab3 -6ab + 3aabb, :5 aa - 3bb
  45. a
  46. Ihh = xxtgy sit X = eh: a +C, fiet 3hh = eehh + Z ceh + aacc aay1: aa
  47. f20 fit D =
  48. sit cet gy = hg, fiet 3h = eeh +Z ace = ag,: aa. unde h= 24_e + 9, :, 3aa - ee
  49. 5
  50. C
  51. sit a9 = 3aa - ee firt 24ce + 34 lec = cc + yy
  52. siet +3aa = c+ 1gy Cc + ee 2ce + gy +2Cy - 2Cy = Mm = 0
  53. et h = CC+99,:
  54. +rcg- 28y
  55. ( C + y - e = m et 3aa = 2Cy -2Cy - mm
  56. sit c- = l Aet Hy=m et zaa = 2l, mm. unde
  57. Ergo
  58. tollento y fit y = m -l et 3aa = 2lm - Ell - mm seu l-3aa = mm + l -2lm
  59. nem
  60. 30a mm - Ely = - zaa nm + yy -ily = ll- 3aa
  61. sit me m =n + a fint nn +gan taa - Ely =. Zua +H = 3aa - ll - 2
  62. nn ll - 2lm = 11- 3a a
  63. 3+ pp = 49 3=99 - pp
  64. qu2 qu1
  65. nam -um sit est _ qu (m- 1) - U 3 3 1
  66. 4+ p = 3 q. p = 1 sit q e 1tp = 3- p p = 1
  67. M a +n
  68. 20

Cite

Leibniz-Handschriften zur Mathematik LH 35, 4, 3, fol. 30r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068000:0059?run=73