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Leibniz-Handschriften zur Mathematik LH 35, 13, 2b, fol. 123v

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: 0.78.

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. 122r); this page is its left half.

The machine reads it as

  1. formula trium radicum aequata quadrato
  2. indeterminata saltem e vinculis liberata
  3. ciples aequalitas pro Eredeterncinatis
  4. Xta L2MNP X+ b = LM X
  5. 2
  6. X+C = LMN
  7. N4D2922
  8. et Xta, in X +b, in X+C = L+ M N
  9. LX
  10. 2
  11. L2MNP - a X = LM N 92 - b X = LM N R - c
  12. e
  13. Ex valoris t 6 et 7 fit L= b -c, M NE= M N R
  14. ex valoribus set 6 sit LZ a = b, :, LMNp - M N92; quos duos ipsius L
  15. s
  16. (10)
  17. valores aequando, fit: L Mb-c= Mq a - b = NR a - b
  18. et
  19. e
  20. mgmic +MgaCM
  21. et exaquo fit L = MZ a = C = NR a b,: v b.2 qnem valorem aequando velori 8
  22. fit: seu faciendo p = MN B fiet L = , M Q a- C - NR a - b, : M N b-C5
  23. 12)
  24. quem valorem aequando valori B, fit x bc C
  25. (14)
  26. et
  27. 4
  28. oe CaNR a m
  29. fit _MN5 b-C= a + a MZ
  30. +b
  31. sit s sit 5b-E = HZR et ex aeg. 15. fiet:
  32. 5,
  33. + b- a N R + a -c M
  34. (17)
  35. +c
  36. 16)
  37. O
  38. 2
  39. quae ut sit extrahibilis fieri -2a +b + C - H = 286a 2 b-a, a- c
  40. quae unica est determinatio hicassumta restri
  41. potest.
  42. seu H = 1 -2 1b - a, a -c 2a + b +C (adeoque rfiet denique
  43. (19)
  44. 2
  45. = 0, adeoque
  46. Sb-a NR Ya-C MZ
  47. ctio
  48. seu M = - Nb- a NR:, ta- c2. Egregium, si verum, nec video ubi
  49. locu
  50. N
  51. 10)
  52. error haerere possit Notandum minon curare itrationalitatem
  53. in quantit atibu determinatis, modo indeterminatae e vinculus
  54. b Em
  55. bua NRG. a -C.D - fLa N R: Ya- CZ
  56. sed ita fieret L= b cri0 quod est aslrdum; seu con saltem
  57. ipenerationem est
  58. nectire
  59. liberentur seu L= , b-CK K L N aR.
  60. permista. Licebit venire ad aliam; si scilicet scribamus pro1b
  61. L2 (17
  62. tia
  63. b= a F st N R + a =C Ny + + -2a +b + C- H ? MN
  64. et
  65. (10
  66. a
  67. ffA
  68. et fiat Nb-a +ff, a - c = - 2a + b + c = H. seu H = e-2a +b + C - 1b- a + ff, a-c
  69. e
  70. fNB ita quaesitum consequi-
  71. 18
  72. 2 (26)
  73. mur sine restrictione, nisi quod supponimus ad usum nostrum f, adeoque H. esse constantem
  74. et siet Yb- a + NR + raC M
  75. si fponitur = a reditur ad calculum priorem g Ex 2 fit M= F∞r. atnR
  76. a
  77. Et ex per 21 fit L= b- 19
  78. -2f 1b.q +f + b.a
  79. quc
  80. ba+ NR tanc Z
  81. 12c
  82. NdR+, 2F + b - a- 25+b- a t H = ta-c f- sb _+
  83. ex beta sed hinc video in valore ipsius X quaesito ex 84. 7 per 21. 12
  84. seu L(22)
  85. -c acc
  86. evanescere literas omnes inde incognitas praetert, vel ergo quaesitum
  87. obtineri nequit, ()
  88. vic cenerali calculo samus Quo substitulo in aeq. 6 fit
  89. usi) vel opptet fess inde
  90. erunnata erv. sign. C

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2b, fol. 123v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068198:0246?run=74