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Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 211r

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.

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The machine reads it as

  1. X + sp X + aqt taa X + as xx P a t X av = 0
  2. fiat X + pX + agX t aar X + aSXX = ee x + aa fx + a’g XX + a FX + av
  3. +cex + aa fx + agXX
  4. id jam agitur, ut utraque pars sit extratibilis quadratice, seu ut quadrati sint
  5. tam XY + pX + agXX + aarX + cs, quam eex + aafx t aegXX + a EX + av
  6. identificetur eex + aa sx etc quadrato e re ab ext D X + aac quod
  7. + ee
  8. aaf +ag
  9. + aa dd XX + 2 acdX + acc eex + aaf X + agxx + a tx + av
  10. est ee X + 2 a de X + 2aa cC X X
  11. fiet C = Iav et d = at: tav et proinde habentur, c et b
  12. et f= 28 C: a
  13. sed video, si jam ad alteram accedamns
  14. cum quadrato aequationem non esse sufficientia dta arbitrarias.
  15. et g- 2a 2 ce + dd,: a
  16. qu (Exh+ ad xx taaexta )= CexacdX aacex r x
  17. An sic (X + X + agX t aar X + a sXX + a tx + a v = 0
  18. (melius.
  19. Ergo
  20. +aaddx aedex+
  21. IEX PaeS_ta
  22. 4CX
  23. u Eai radxe aa et
  24. siet exX ACx + aepXE+ aaqX + aCYX ta C
  25. ab X+ abpx t aabqu + abrx absxx + ab1 x + abs.
  26. CCx + 2acdX +. 29a CeX + 2a cfx
  27. +a DX +radeX + 2a dxX
  28. ta ee XX Y 2efX + a ff
  29. = CC X +2acd X + et
  30. dat
  31. extracdXt2aa cex
  32. Hoc latus sinstrum aequandum erit quadrato a yX + DXX +. H X +
  33. Habemus com identificatorias septem, artatrarias autem quantitates novem
  34. nempe c, d, e f; ), d, H, et praeterea b, quo multiplicavimus
  35. aequation
  36. datam aequationem V = N(ab YCC)
  37. B = abp + 2scd,: 2 s (ab + CC)
  38. p = Abs+ S
  39. H = abt +2ef,: 2 165 + s)
  40. supersunt tres aequatiores, ubi hi valores sunt substituendu
  41. quadratum a Vp + ADXX + aa HX + ae est DyX + 2a]BX + 2 a a V HX + 2ay GX
  42. + aa bD XF + 2 BDH + 2at BGXX
  43. sit jam _ ex ipsis X, aabe bg. +rce + dd = VB Ab L + Zs) s a 4 cd
  44. 1bs +
  45. +s
  46. ex ipsis XX sit bs. + 2df. + ee = (lp + 2cd)(,d ab +ec
  47. + qu (bt + 205)
  48. 4, b5 +fs
  49. Si fierent A = 0, et H =0 mullum contraheretur calculus
  50. 5)
  51. et fieret bp + 2cd =0 et bt +20f20 et bf + 2df = bg + 2ce + dd =0 et bs+2df + ee-
  52. quibus quinque s aequat ombus
  53. et superest br + 2Cf + 2de = 2 +(ab+ cc, bs+ )
  54. 22gcd. p +28 - - 29 cf: + + 2ce + dd =0
  55. 2ot
  56. =29ef - 2tce = tdd, fit
  57. = pee
  58. 2scd = 2Bd5
  59. sed rmrsus d = X Ps c.
  60. pf.
  61. et = et et = pe
  62. in irrationali sunt b, c, f. Et
  63. b = -2cd, : p = 2 ef: t, fit cd: ef = p: t
  64. solvendis inveniendae essent literae c, d, e, f, b
  65. extra irrationalem sunt d et e
  66. = 25c0: p +2d5 + ee =0
  67. 2sC - 2p f et fit de=
  68. f - 2tC = pe
  69. +d
  70. 0+ - 29f -2tc
  71. seu C = 2f, sc - ps,: Ct et d = 2C, 9f - tC,: P
  72. +
  73. 2SC -2p5 et fiet
  74. 20
  75. sc pf, et et
  76. p.
  77. g5- tc
  78. =p
  79. Habetur ergo F per aequationem
  80. A Sc- ps
  81. quarti gradus. et d habetur per F, Et cum de etiam habetur e et d per f et
  82. 4
  83. et
  84. B
  85. C4
  86. F: C
  87. =t C
  88. seu fit
  89. 9F - t =
  90. ut C, etsi habeatur
  91. tostat ut hima aequatio br + ECF + 2de = 2 1 (ab +CC, b (+ fat - tC, sc- ps, Ys: AtC
  92. seu dd = _ 4, q tc, sc -pf, (F: C): Et, ubi pro f: c subiatri+ est quantitus inventa
  93. = PF. fit e = +C, : pf) d = 4, 9f - tc, sc - pf,: pt d. Ergo dd =
  94. porro ee = dd, sed et = -d sed Hinc sequitur etiam fre si D = - 1 fore etiam F=
  95. sed ita hunc valorem conjungendo, com aequatione in qua f: c assurgit ad quartum gradim
  96. orietur nimua dete minatio, itaque non licet cere D simul et q facere aequale ihilo
  97. Relior erit depressio, si fiat ab +ce =, b(+ f vel saltem si ambae sint in ratione
  98. constanti e
  99. ita enim cessabient, e exaltationes ob irrationplia, nis sublptis
  100. + at un xX L 2an9X + à 55
  101. + qu (bp + 2cd)
  102. 4, ab +cC
  103. superesttertia aequatio
  104. es
  105. sis
  106. 9 terse B
  107. pt
  108. ct

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 211r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0417?run=74