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Leibniz-Handschriften zur Mathematik LH 35, 4, 7, fol. 5r

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: 0.82.

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. 6v); this page is its right half.

The machine reads it as

  1. Unum adhuc exemplum ad ducere operae pretium erit
  2. cum radii
  3. rationalis in Car irrationalibus Cardanicis latens est falsa
  4. sive negativa; quoniam variatur nonnihil calculus et video raph
  5. Bombellum, analyticum certe doctissimum egregium certe artis
  6. analyticae magistrum, hic haesisse: nam ut supra dixi radiles rationales
  7. veras extrahere potuit, falsas non potuit. Eadem est difficultas
  8. Exemplum esto: X - 12X - 9 cujus aequationis radix salsa est, a, - 3.
  9. ex regula
  10. erit C. X H
  11. a
  12. a
  13. 10 2 N 175 + A9 = Y - 175
  14. et opus ergo est, et ostendamque hanc quantitatem facere = 3. quod ita
  15. fiet resumta formula superiore, et pro b ponendo - 3. ac pro ac
  16. faciamus
  17. Sumendo 2. Ponamus XF - 3 + s - 7
  18. = + - 2 id est
  19. X p - 3. Unde cuband binomium, pariter. 2 + f -g, ac residuum,
  20. - 3 - - 2, habellamus primum ex binomio: - 27
  21. +3, 3, 21 63
  22. minus; nisi aut immenso labore omnia pertentet, aut singulari quodam et quoniam, ut postea dicam utile est, c de inveniendis ope
  23. 1(-343
  24. 54
  25. 16.4
  26. l-9, 8
  27. irrationalium, rationalibus cubicarum aequationum radicibus agitur, efficis
  28. ut secundus terminus penultimus sit exacte divisibilis per 3. et ultimus
  29. per 2. ideo quod consequemur radices aequationis propositae multipercando
  30. per 3 cum defectus est in penultimo, per 2. cum est in ultimo,
  31. et per 6 cum est in utroque
  32. falsa
  33. Exemplum esto X X - 48X - 72 0. cujus radia est
  34. Xp - 6. erit ex regula
  35. XH 1B 36 + s - 2800 + 16 36 - + - 2800. ostendendum
  36. est ergo harum duarum irrationalium summam nihil aliud facere quam s
  37. . Quem in finem ponemus X , - 3 + f-7 - 3 - + - 7
  38. C
  39. O
  40. B ∞
  41. sine XH N + B, vel Xp, 1C + 1C B73
  42. Resumta ergo formula superiore qua erit
  43. A, b+ l-ac 8 b - Y- ac f et p
  44. ac nunc pro b substituendo 3 et pro ac sumendo 7. erit
  45. A.
  46. sive summa inita
  47. -27
  48. 13, 3, 7163
  49. 36
  50. 343
  51. +Y, + 6, 49, 912646
  52. - 9, 81, 7 r, 5103
  53. + Y - 2800, ut propositum
  54. eodem modo ostendetur esse B
  55. esse ) 36 -. Y - 2800.
  56. eB
  57. EXBAE
  58. BECL.
  59. EIANAODELS
  60. hufo ex estar Ergo cum ex regula Cardani sit X
  61. (.4
  62. omon
  63. XH (036 + f.2500 + cum ergo sit X (B-6p, 1( + se Y,
  64. erit X H 1336 + l- 2800 4 + (5 36 - Y - 2800, ut regula Cardam
  65. praescripserat, quod spendendum proponebatur
  66. - 64 4
  67. fiet ac p
  68. sive ac
  69. 31
  70. 81
  71. 15
  72. 1c
  73. +2
  74. 73
  75. e
  76. +2
  77. 18
  78. +981 1458
  79. 378
  80. 123
  81. t3C
  82. 427
  83. 3636
  84. 5
  85. 4
  86. 5103
  87. 5446
  88. 2646
  89. 2600

Cite

Leibniz-Handschriften zur Mathematik LH 35, 4, 7, fol. 5r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068004:0009?run=73