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Leibniz-Handschriften zur Mathematik LH 35, 14, 1, fol. 133v

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. 132r); this page is its left half.

The machine reads it as

  1. Ergo aequatio
  2. sit intractabilis.
  3. t aequatio sexti grabu exipsis habebit quatuor 2
  4. Tubica
  5. Aequatio plana assumta habet duas radices
  6. voles; aequatio ergo quadrato- quadintica habebit religvas du as
  7. radices reaes, duasue alias imaginarias.
  8. idendum jam an omnis aequatio quadrato-quadratica quae duus tantum
  9. taabiem
  10. an vero revocetur ad tiradicalem. Utroque modo lucrabimur, nam si revocatur
  11. in triradicalem poterimus aequationem duas medias proportionales invenir
  12. per trifectio nem anguli, duplim, si ad ractabilem, poterimus trisectionem
  13. X= + bX + C
  14. + b2).
  15. x b2)..
  16. N= - ( X ∞ qu
  17. ∞b X
  18. b3.
  19. X+ X +CX2 - ebX - 4
  20. -12.. - 86.
  21. =e b.
  22. qN Yx +5)
  23. b11 1) se - d - q
  24. vel
  25. assumta est, tractab
  26. anguli invenire per Mesolabum
  27. X + bX +c
  28. X X +cX
  29. Ci
  30. ed p L-)
  31. u
  32. C - d -
  33. 2
  34. unde et -d ac- 9C = 25 5 1Y
  35. ubi memorabile est nanc calculum
  36. sic terminari, cum iderus cale
  37. quaerendo y. ultimo lodo
  38. terminetur in cubicam.
  39. ung
  40. unde generalis habetur nota, in aequatione quadrato- quad ratica sacundo
  41. -
  42. L d2 62
  43. termino carente, non nisi duae sunt radices reales
  44. quandocunque signus terminorum tertis et ultimi
  45. cont Tertii Termini signum est affirmativum
  46. compludiosioris calculi causa faciamus
  47. b
  48. 4C,b2
  49. = c2b0
  50. traectabilis. Generaliter ponendo ex tore terminum tectium fict,
  51. Aliud exemplum: ponendoque dYC4 teb
  52. erit terminus tertius p0. mamente secundo
  53. unoc term. quartus e (F eb3 - cb - b3
  54. eb) et altimque erit:
  55. bt - 206 - ebce
  56. ubi rursus sibicae
  57. productae terminus
  58. penullimus resula-
  59. ater fiet affirma.
  60. tivus, Acredibile
  61. Follatur aequationis ciusmo quadhaticae generalis tertrinus quantus
  62. cini tertius, faciendo X 4+ pX2 +
  63. frei: N2+ ay
  64. ultimi signo contra existente negativo
  65. quae revocaxitur cut cubicam hanc:
  66. quae aequatio reduora dat quadrato
  67. quadraticom A Xh N. X
  68. ulus
  69. u
  70. q
  71. X +
  72. + +BY + p+
  73. + py exEY +3 pB Y +B
  74. excitatae
  75. ss v. et
  76. esse nactubilem;
  77. VFap etp
  78. + c2b4
  79. b
  80. W0 X ++C W
  81. YW
  82. Unde lubica:
  83. quae aequatio semper +tCb
  84. + b X
  85. 2 + C X
  86. 2
  87. + b. X3
  88. 12
  89. 1
  90. ... + eb..
  91. d ab.
  92. Unde fier subica:
  93. Uende per Tubica:
  94. est, etim cum sic
  95. negalivus, tamen
  96. aequationem (ubicum
  97. 10 cd. X +4C tsd +ocd, W0 etc
  98. +4 eb
  99. ate
  100. D
  101. eb2

Cite

Leibniz-Handschriften zur Mathematik LH 35, 14, 1, fol. 133v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068201:0266?run=74