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Leibniz-Handschriften zur Mathematik LH 35, 3 A 3, fol. 1v

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: 0.77.

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. 11r); this page is its left half.

The machine reads it as

  1. mde. Amul +
  2. -n + = n m = K m + m
  3. 314
  4. rugo 2 + 3 + In- Imo + 1t = 2 nene + 3 (1- Inq +1- m
  5. m
  6. 17
  7. mu
  8. + 4
  9. X A PX + gX +r nqu. 0. X equ. a + b + c; composita ex radicibus aequationis
  10. a +V a d aequ. 0 cujus cndices a. b. ct. Est t
  11. Est autem a + b++c aego β et ab + aC +bC aequ) et a aequ d
  12. X aequ si Xrgo a +b+ C. et sint a. b. c. radices quadratoquatuaticae patet
  13. id quod in ipsis est ratione quod est in X latere non in a. sed in ab eodem modo
  14. quia X aequ a id est quia pr aego a + 2y. rationale ipsius X erit intry.
  15. item X aequ. a + 39X = 3Z, patet in ae nihil esse ntionalitatis. ipsa autem intantu
  16. est quantitus irrutionalis ex parte
  17. nimirum in quantuma in se continet Z seu abc.
  18. non curducitur xin y ducitur a + b +C in ab + ac + bC. Juri ain ab, dut
  19. ab quod necessario maned int irrationale si a et b. inationali Hinit videtur dn quantum
  20. eodem modo ac. sed abc. dat aliquio rationale ipivora non nnsi in quantam
  21. partibus constant rationalibus. ita ergo delepminari polerit quid si
  22. sit in Z rntionale, et ita porro. sed haec paulo laborioseta quam
  23. par sit
  24. X + bx +c
  25. +Cx3 AcpX Cq)
  26. +bX alex +bq
  27. X + p X + 9
  28. (1)
  29. X + pX + q aequ. 0.
  30. Xaequ. a + b
  31. Ducatur aequ. 1. in formulam: X +BX +
  32. Ponatur in aequ. 3. baegu. p et cpagubu.
  33. fire Tex sp Cagu. 9. per 4. et luo aequ. 3. fiet:
  34. Quaeritur aeqquatiotalis:
  35. fiat. X-
  36. .......
  37. X + aX ta X+ 1ax
  38. +10 ab +21 8b..
  39. X + AX + q. ex sitt : X + nX + n aequ n - 9.. sei Xaego Yn. 9 - n
  40. 2
  41. a ta b + ab
  42. X _ + PX +g. fin: X aequ 14 + Y4. P + V. 4-4 aqu. +
  43. Nm sit Xago a +b. erit X equ a + 2 ab X, seu X - 3abX - a rego
  44. fiet pago ab. seu abaequB et aequo 4. Ergo a aequ B. et fiet
  45. P
  46. B aqu. 4s
  47. 2763
  48. i
  49. aadeous 62 ago 4
  50. n
  51. b+ 4b3 = P seu b+ qu + 4 ago P+ qt
  52. +n Y + m + l. aqu. 0. fiat aequ X- _ fier
  53. Y aequ = X - 3RX + 32 y - n
  54. n’y aequo.
  55. +my
  56. +
  57. y
  58. 27
  59. nX - 2n X + n.
  60. + m X = m
  61. =Etx + 213 equ. 0.
  62. + m.
  63. =ma
  64. 27 4
  65. +X. pX + 9 XapXrgH-r
  66. ppiin
  67. A - pA = qXL AXHA
  68. X +AX + A2 PXDpA
  69. 1X + pR + q++Y
  70. A3 - pA = 9A = Y
  71. p
  72. saequ. o
  73. +p. .. +9.
  74. H X +
  75. Gaxq
  76. 114
  77. (5
  78. +a b aepu. 0
  79. 9X X X +29X. pX X +9. aequ. 0
  80. e
  81. 16) a
  82. a + ab + b
  83. 1= b
  84. -ab - ab - b
  85. fiet
  86. Y aequ .n +
  87. un
  88. XD +AK AX A
  89. pX +pA
  90. mu

Cite

Leibniz-Handschriften zur Mathematik LH 35, 3 A 3, fol. 1v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068216:0002?run=74