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Leibniz-Handschriften zur Mathematik LH 35, 4, 3, fol. 42r

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

One image of two folio pages side by side, registered by the library under both labels (also fol. 43v); this page is its right half.

The machine reads it as

  1. axty =ll ax + aZ = mm
  2. ax ay = pp ax - a Z = 99
  3. 2aX = U +pp = mm +94
  4. ay + aZ = nn
  5. ay - a Z = p F
  6. Zay = Il - pp =nn +YY 2aZ = mm - 99 = nn = rY
  7. 2g = Ex tribus his aequationibus quaeramus l, p, n,r per m et in medio positas
  8. Ex aeq. 3 esto n+Y = S m + Fg n - Y = a m + = 9, fiet 2n = (S + aym 4 (S - 2) 9
  9. et 2Y = ( - 3 ) +(Z + 2)9. vel compendio 2n = =m + 8G et 2t = d m q
  10. a
  11. Ex aequ. 1 fit l - nm = 99. pp, sit l + m = à G(4) D et l- m = a g (4) ap, unde fiet
  12. 2l = (a + 4) 4(4) CL - 2) p et 2m = ( - 4) 9(+) (+ + a) P. seu compendio al - h9() kp 2m - h a h
  13. at 4, seu 2l = 2 2Km + hhr. KK
  14. superest aequatio 2d a praestanda, quae est l- pp = nn +YY, in qua substituen substituendi inventi
  15. valores ipsatum , a, P, Y fiat - Al + app + 4nn + Arr= ohinc prodibit
  16. 4Hkum 4 Khhr. - 4+ R mq h- 2hihkK + k gq
  17. atit
  18. +16 aa mm -16 ak mq
  19. X
  20. hk
  21. Afm
  22. aa
  23. aq
  24. dd mm
  25. aa
  26. ht
  27. f2 fg mq
  28. aa
  29. + 2fg mg
  30. aa
  31. aaht
  32. + TkKqq
  33. ht
  34. = 1899
  35. a
  36. + ff
  37. aa 7
  38. 2
  39. Hic videamus an liceat destruere mm, faciendo - 4KK + 16 aa + fF + d
  40. aa
  41. tihi
  42. tit
  43. =0; ubi videanas an
  44. aa
  45. sufficiat explicare f et g, quae timplicius exhibentur zerat = S + a et 99 = L - a fiet ff + d = 2s + 2aa
  46. h = 4 4 K= t - t hh = Ht +.
  47. aa
  48. ad
  49. KK
  50. 5
  51. = H
  52. et KK + 16aa = utlina +B Aaa: H 4F + f a aH aa
  53. hh
  54. hh
  55. . An aliter si itidem faciamus
  56. aa
  57. a
  58. 1 230 +316 + h
  59. Numerus eonux 10 + ub + 12bb + 13b3+ 14b+ 156 + etc
  60. quadialum 10. +B + 2. 10. 11b + 2. 10. 12bb = 2. 10. 1363 + 2. 10. 14 b + 2. 10. 15b5+ etc
  61. + 1. 11. 11 bb + 2. 1P. 126342. 1. 1B6Y +2. 11. 14b3+ etc
  62. 50. 30 + 2. 50. 51b. + etc
  63. 2020 + 2. 20. 21 A etc
  64. E0. 60 + 2. 60.61b tet
  65. aa iaa
  66. 2 + 2, et -aHK laa =- AG
  67. a F16aaH=
  68. +4 + 2aa H + at
  69. +1. 12. 126+2. 12. 136342F
  70. Aliter sunt hes aequalines Upp = mmtgu
  71. 25442a - - 3 - 99
  72. aass
  73. ll- pp = nn + VY mm - g9 = nm +rY nn -YI
  74. sit p = l5, et fint l - pp = I= tf + ff N - 1+ 2lf - ff = mm t4q nn +rY, sen l- nn err+ H
  75. rursus 2I - 2lf +ff = mm + 99, fiet l- u nntrr+ss,. 2f
  76. ubi substitu endo am rursus l = mn + gg- ff, : 2l - f = nn + rr + ff3: 2f, et fint.
  77. 2frum +2f99 -(273 = 2l nn + 2l rr + ilff - fnn- frr (f3), fiet
  78. El = 2fmm + 2599 + fnn + frr,:, Ann + frr+S = nn + rr + ff,: F
  79. fit 255mm + 2f5gg- f+ Snntffer = que nn + rr + H)
  80. Rursus ob rumq nm - gq = nn -rr, fiat r = n - g, unde fint mn-99 nn - nd + 2ng-g
  81. et n = min - 99 + gg,: 29 et r = mm -49F99 - (299,: 29
  82. Ergo nn +rr = m + gt + gt - rmm gg (t 2mmgq - 29999) + m . + g2 + g - 2mm49 (2mmag. + 2 9999); +gq
  83. b
  84. seu nntrr= f(m + 9+g)-mmgqe : gq = 00 Etsum + 2f49- 5 4 (500) = d(0ff f
  85. sit vg m + 8g199. 89
  86. +4f
  87. fin O0) + OOff+ Zs= 2H (mm 199) - 254
  88. et 13O + f = fi (2(nm +49) - Z H)
  89. et habemus m + q+ g - 2mmgus _ggH = 2fGg ((2 (mm + 44) = Z fs)
  90. quae estullima aequatio, affungens ad octaon gradu in in, g,e, et ad atum in F, quae efficiura
  91. est ud pationglibus, et ext his tu quatuor vel potrus in effectu 3 liters,
  92. bra sunt aritrarae
  93. es
  94. t
  95. = 4nn
  96. ad na
  97. M = 20 + 21b etc
  98. 42 60 +61b + etc
  99. r= 70 +71b + et
  100. l = 10 + 11b A+ 12 bb + 13 U. + et p. = 50 + 5ib + et
  101. -2+ 4

Cite

Leibniz-Handschriften zur Mathematik LH 35, 4, 3, fol. 42r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068000:0083?run=73