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Leibniz-Handschriften zur Mathematik LH 35, 3 A 30, fol. 10r

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: 0.74.

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

The machine reads it as

  1. v. octobu 167
  2. promotus re
  3. Arithmeticae diophant
  4. habeae minorum rationatem, ita enim si
  5. s
  6. ratis seriibus ex quibjagnosci possit an aeiquatio data
  7. preter datam aequationem
  8. v. 9. X + V (3. adhnc aera supponatur
  9. ut X + 6V + X + Y + C. p0. videndum in sufficiat una imognita sublata provenore aequationem
  10. divisibilem sive rationalem ita emius ut s hoc loco fiet: X + y 1 - dy - C 113. Ergo erit yp, e+3
  11. a
  12. ergo sed ita substituendo non habebimus valorem ipsius X absoluto. Quod tamen ita assequemur si pro X faci
  13. 9+ b. fier Z + 2bZ + b + y 13. et
  14. modo, qua non remaneerd Z.
  15. eiit ergo
  16. 3V + 267 +6 +y FdY + C 11. sed hoc inutilo; hoc
  17. t
  18. X +(3. C +bC7G
  19. 1 A1 Y3a2 = et -60 = 9
  20. a
  21. ergo debet 3d = e = 6C = 9 esse quadratus. quae difficultas est aequalis curo difficitor data
  22. ergo aliter praeter aequationem X +y 3a ponamus X +Y + dY + cX +C1v.
  23. i
  24. d
  25. fier
  26. st
  27. dy +
  28. CX
  29. +C - 3.
  30. + 2d eV + 1d + C
  31. + 6.d.
  32. aequatio
  33. +b ea
  34. 9a2)
  35. -
  36. 6a.
  37. 1
  38. et X H - dy - e - 3a
  39. )
  40. bec 3- y
  41. a
  42. sive
  43. =
  44. d s - 64
  45. d
  46. = 6aY (F 9a). Quae aequatio videndum est an solvi possit
  47. in numeris quem in finem faciumus
  48. +
  49. d
  50. 2 + 2d ba
  51. + 36a
  52. d+ + 2d6a (+36a
  53. 4
  54. CH- 3a
  55. ( 9a) a= 18a
  56. 4, 3a= (0
  57. Co
  58. crit
  59. et deber dt + 2ba esse quadratue. quod fieri potessi
  60. sit ille _ d+ 2deo +co. fiet: 26ap 2 dco + co et dp 364 434 = co
  61. et fier
  62. 2
  63. + C0). et y 1)
  64. A
  65. a
  66. cas
  67. + 3a 4
  68. co
  69. u
  70. 1594 - 8, 3a + Co
  71. sed satis agnosio nos non multa hiecu
  72. con
  73. ducturos nisi quod
  74. quaestionem propositam simplicem mulide poleriu en mide
  75. ompositas quod dicissimi seroiet ad posilas rednebuda, ad simplicest.
  76. sioner
  77. Gene
  78. vera methoiu redo, in eo consisteret. ut generalis fiait substitutio v.g. data aequalio est
  79. + 2
  80. B
  81. Xy
  82. e
  83. 3. Fingatur aequatio: ed
  84. dl
  85. + Xy
  86. + X
  87. a- 1 1
  88. Va-2
  89. etc.
  90. +
  91. X.
  92. c
  93. - 1
  94. d
  95. XC -2
  96. o- 3
  97. + V2
  98. sed satius ne in in infinitum rabeat
  99. + Y∞- 1
  100. certuri
  101. efigere gradum pro X+ quo X et V. summa aeq potestates aequalis sumuntur et fiet
  102. Bat
  103. N + XC
  104. X P
  105. X
  106. -2
  107. erc. et X. v
  108. d
  109. 3-2
  110. et X
  111. X
  112. X
  113. β-1
  114. 81
  115. ata ordine; porento quaslibet mulliplicati, excepto. uno y. quod mulo affectum, quia
  116. calculum explicationios explicabimus generalem.
  117. 4
  118. Y-2
  119. (3-7 2
  120. a
  121. (

Cite

Leibniz-Handschriften zur Mathematik LH 35, 3 A 30, fol. 10r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068243:0019?run=74