Leibniz Legible

Machine transcription of the Leibniz Nachlass

Search the Nachlass

LBr. 695 · Oldenburg, fol. 38v

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: 0.81.

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. 37r); this page is its left half.

The machine reads it as

  1. Formula plena
  2. inferior
  3. X
  4. Valorassumtus Radicis
  5. M X +b M
  6. X
  7. C mn
  8. = m 6F0
  9. X X + b v X 4 - bm
  10. Aequatio factitia
  11. Aequatio factiti
  12. ordinata
  13. Aequalio
  14. X
  15. LC mn
  16. rnor
  17. +b2m
  18. X
  19. Fc a mn.
  20. X + PX
  21. inn
  22. = b2 m
  23. +
  24. im
  25. quae aequatio resolvenda, ut comparetur factitiae, hab singuli termini singulis,
  26. resclvenda
  27. fiet: +b a m. + C mn 1) p. et pocendo
  28. et
  29. + b 2m3
  30. n3
  31. =ba mnrm H9
  32. Quarum duarum aequationum ope quaerantur m et n,
  33. m in p p
  34. n’∞ mnB pm
  35. 9 13 et 9 - n2 + mn s pn
  36. et mM n3- 4
  37. n - p
  38. m3 + n e 1
  39. et ut novissima aequatio
  40. sed ita ut aequatio novissima, secundum quam alter utra earum (nam perinde est)
  41. invenietur hanc habeat formam: M.. M
  42. epe quantitatum pro arbitrio assumtarum
  43. X
  44. b et c
  45. .. 0 quod effici potest
  46. ponendo enim + b - 1 10
  47. sive b H 1 item = b 10 seu bp - c, sive C1 = 1.
  48. me - 4 mn B p
  49. statim inveniuntur.
  50. L X b (. m. N C X
  51. C lo. In. m
  52. e
  53. tunc fiet:
  54. et m3+ n. n4. Unde re gula Cardanicae
  55. a l. m. n
  56. e em. en. Ben s
  57. lmn
  58. radices irrationales posse
  59. Certum est huc methodo inveniri
  60. debere; itaque tarotum quaeritur
  61. quae eligenda sit eliminandi via.
  62. In hanc rem proeclara habetur
  63. ratio, quia enim necesse
  64. est omnes a vias pro
  65. altioribus necessarias, incipere
  66. Jam tum in inferioribus, ideo
  67. enumerentur viae omnes
  68. in destructiondem in inferioribus
  69. quadrotica e cubica,
  70. qua cum sint parcae
  71. scilicet et quadratu- quadra
  72. fica quae cum sint paucae,
  73. ex apteris illas quoque reperiemus quae
  74. in cufi nitum progrediuntur
  75. Aequatio data resolvenda X3 X pX +9. 10 careus secundo termino compendii causa, quia is semper
  76. tolli potest. Huic ut similis facile resolubilis
  77. construatur, sit formula plena inferior
  78. C
  79. nn
  80. M
  81. -8
  82. e
  83. mu
  84. .
  85. M..
  86. n
  87. 1
  88. quae multiplicetur per valorem assumtum
  89. n- 2973+ 9
  90. X H in + H sine X - m f0
  91. e
  92. ..
  93. =c
  94. l. m. n
  95. -2lm...
  96. C3 Cm.
  97. =36 Imn
  98. f, Vmn
  99. re lmn,
  100. et m
  101. N- 2pn + p
  102. tnrin
  103. +c. 11
  104. ter tm
  105. + F Imn
  106. c
  107. pemn

Cite

LBr. 695 · Oldenburg, fol. 38v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/DE-611-HS-860722:0076?run=74