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Leibniz-Handschriften zur Mathematik LH 35, 12, 2, fol. 184r

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: 0.85.

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One image of two folio pages side by side, registered by the library under both labels (also fol. 183v); this page is its right half.

The machine reads it as

  1. Sed cum successus videatur mirus, et pene, incredibilis; operae pretium, est exemplum
  2. ipsum Fractare speciali seu proprio calculi, ut facilius appareat si quis adsit lapsus
  3. ergo aequatio - aayy + mn XX +ac (mn) X + aa cc = 0. Hanc ut praestemus prationalter
  4. ad lustitutum nostrum, sumamus _ X: a = 100V + 10Ia,: 200V+ 201a. et y. a = 300Y + 7019) :, 200V + 201 a. Fiat
  5. + 201. 201..
  6. 1. 101. 200..
  7. aequ. 0.
  8. Ex termino si
  9. 200cC + C (mtn) 100. 200 + _ 100 mn = 300. a=v
  10. ubisi faciamus 100 mn -300 aa =v. fiet
  11. 300: 100 = Vmn : a et 200 = - 100, m+n,
  12. Ex Termino summo destructo fiet
  13. 201CC - + 101 (mtn) 201 C + 10emn - 301aa = 0
  14. fiet 201C = C - = 101 (m +n) + L Soi qu m An)- toinm + 4. 3ota)
  15. aequ. 0 ubi ut destruamus quod est in vinculo radicali fiet ,onm - 2toi mitaedoia
  16. 2. 200.
  17. quae aequatio est imaginaria, sed hoc nos non moramur, et fiet
  18. . 301 : 101 = m - n, Y-1, : 2 et fiet 201: 10, = t1): 2C
  19. Rursus ex Termino medius destruendo est 201 = (t300. 30l aa - 2. 190. 101 mn - 101. 200 (n + n) C, 1 2 20
  20. seu 100. 101 gu (m+n) = 100 (mn) (m = n) D 101 = 2. 100. 101 mn + 101. 100 (mAn: C) om + r) C
  21. opparet divisis omnibus per 100. 105 evanescere
  22. sitasrrationalem, aut ullam novam ad hibes
  23. restrictionem; sed maneat 201 c = = 101 (mtr) + L 1 (101101 qu ( m - n) + 4. 301.301 a4)
  24. Eno non licet in valere ipsius 201. Destinete
  25. sed ex Termino medio fil 201 = 2. 300. 301 aa - 2100. 101mn - 101. 200(M + n)C ; 2. 200 ∞C + 100 (n + n) C
  26. seu 201C = 2. 100 mn) 301 - 2. 100. 101 mn + 101. 19qu (m 12), :, 2 man) Y + 1e (u i)
  27. seu 201C = 2. 100. 301 armn + q (mm. + nn) 100. 101, : - f. 100 (m + n)
  28. = ∞= 101 (mFn) + L (1oi qu (Mn) + 4. 301 aa)
  29. (1430
  30. seu 2. 100. 301 a tmn = 2. 100 101 mn (4 100. 101 qusm tn) = (10B. 101 qu ( +n) = 100 (m + 1) L(io qu mg
  31. 4. 100. 30i aa mn) + 4 G00dioi mn _ 100 iqu emn. n) +(30) vitum + nn) 4 100i 30i m aa
  32. _. tot. et amn Amn 4. 30 mntnn) aa + 8. 101. 30amnumn + 101 qu (mm. nn) = 0
  33. seu
  34. = 8. (1003101. 30lamnima
  35. ioimmnn
  36. et fiet 2. 301 a =- 2. N. masma +) m id - (qu (mm. na) - 4 mmnn) nm + rn)). n
  37. F 200. 200 Cc + 200C. W n) 1009 + 105. 100 a f - 300. 300 aa = 0
  38. 00 : 100. = sf: a) - taf: a
  39. 201. 201CC + 201C 1019 8 a(, 101. 101 af = 0. Ergo 201C - - 5 1619 + 5 110199. as
  40. Ergo 200C + 100g = 0 seu 200: 100 = = g: c
  41. 301. 301 aa
  42. 2 200, 201cc f201 c. 1009 + 101. 200c9 + 2. 100. 101 af - 2. 300. 301 aa =
  43. Hs ex deniue ex permino medio est
  44. X = - = 11 + Y (i- 4. 12)) q pro 300 et pro 700 ponendo valores per 100, et 300 a = 100 Yaf 200C -
  45. fis -(2. 1009201C+201C. 1009) 101. 10099 + 2. 100. 1014f - 2. 100 1a f 301a = 0
  46. et divisis omnibus per 100 fit 201C9 = - 1099 + 2. 101af - 2. 301 a 1a f
  47. Ergo ex priori valore ipsius 201C fit (- 101 99 + ( (10i gg - 4. 10r a5 + 4. 301 a a)-
  48. sit 9g aaf = ah, et fiet
  49. 9 (101 ah + 4. 301 aa) 101 ah - 4. 3oratas, et quadrando
  50. =(2, 10199 + 4 101af - 4. 301 a ra f
  51. utrobique siet roj atigu + 4. 50i aague - (10i aatt) + 16 20i a3f + 8 101. 30+ aa h lat
  52. 10X = - 4 11 4 3 (1. 4.10. 13)
  53. aequ.0
  54. 100. 101 (m +n) C (- 1m 4 1). 20)
  55. 10. 10XX + G. 10X. 11 +10.12
  56. 200. 200.. +2. 200201.
  57. AX + IX + Z 1 = L, 11 - 12)
  58. 19XX FIIX + 12 =0
  59. rqu 411 = 10. 12
  60. seu 62
  61. XX + IPX + 1220
  62. 10XX + 10X. 11 + L. 11
  63. Aayy = 24, 300. 300VP +2. 300301 aV + 301. 301 aa1
  64. +mnXX = +mn, 100. 100.. + 2. 100. 1011. +101. 101..
  65. raesnm) X = csmn), 100. 200 .- + 1. 100. 201 .. 4 101. 201..
  66. taacC = cc,
  67. estructo
  68. Te
  69. 44 2elaa 9g
  70. ccuce
  71. seu (1019 = 4. 10i afgg + 4. 301 aagge = (10 q -(8) 101 a599 + 8 agg Saf. 10130) + rt s 3eur. B
  72. 4. Ze aavt
  73. 1o1 aatihreroias
  74. B F16. 10C a t = 32. 101. 301a f (af + 16301 af bi
  75. Sit jam Aeg ag - 4 af = ah fiet 4. 301 ah 8, 4 4. 10 afah 8. 101 30r a atratat Z0
  76. 301 aR - 101 sa f =0 videamus au res actu succedat
  77. Is vulo Ergo 201C = L 101G + 10, Cah + a(af vat)) sei 2ot toc (:2C) g+ Hatita aalsi
  78. seu
  79. 200 = 100g: C 300 300 = 100 raf ia 301 =10Naf: a
  80. Em XB: a = 100B + 101a, :, = 100(9: C)D + 1O1 C2C) 9+(ah + 4 a a f : h)1)
  81. seu 201 = 101 (: 2c),94 Hah + 4 aa (f: h))
  82. sit formula af xx + BC9X + CC, ubi pro X: a substituatur vator 100∞ + 11a, : -100G: d)v+ 201
  83. afxX = aB p0o po V + 2. 100af101 aV = 101a s1o1 aa
  84. G 109.10)
  85. F10099..
  86. 1. 10059201 _.. + 101. 201 aa C9
  87. 1. 10099101().
  88. = (2.) 10029. 201 . . + 201 201 aa cc
  89. 100. hocas
  90. n 100. 101 39
  91. ubi 20+ postea etam expli
  92. Sed hinc ortur absurdim
  93. nam si 301: 101 = taf: a
  94. fiet 301: 101 = 300: 100
  95. quod non licet. Itaque
  96. res non procedit.
  97. ta y esset in ratione data
  98. ad X, contra hypothesin
  99. C9X=
  100. cc =

Cite

Leibniz-Handschriften zur Mathematik LH 35, 12, 2, fol. 184r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068195:0367?run=74