Leibniz Legible

Machine transcription of the Leibniz Nachlass

Search the Nachlass

Leibniz-Handschriften zur Mathematik LH 35, 3 A 3, fol. 12v

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: 0.83.

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. 13r); this page is its left half.

The machine reads it as

  1. Murficas esta habent usus pro problematis uniformiter
  2. compositis inveniendis ex. qu. quae
  3. sit problen, X+ y + 93 (1) C B
  4. Jl. X + y4 Z M
  5. fiet Cn m p - 29. Ergo q n m et
  6. fier r El + 3N- 2n ni et fit:
  7. et fiet X - n X + : n X -
  8. et
  9. 212+3n2 3nm2
  10. Xryt ZF n.
  11. l7 p = 3p9 + 3Y
  12. 0
  13. m
  14. N L3p 3uni
  15. Si aequatio fuisset X +y3F 13 et X+ y pi m fei 4B( p
  16. (11
  17. m 1 p - 24. et l3 p p - 3paet et quia 47 p - m
  18. 5
  19. fiei 21 i p 3p p + 3pm, seu A p3- 3m P+ 2l0
  20. Res ergo redit ad has tres aequationes: _ pX + 4 0
  21. et X - pX +q0
  22. s
  23. 15
  24. et p - 3m p + 2V 0 et qH p= m
  25. quid si et ita. sit aequationes X+y B B, et xcy m
  26. ascribamus X+ y 1Z2p 12+3 X+ 4Z m +Z denique Xry+ Fn
  27. et faciendo n.B compendii causa
  28. Hini etiam innumera problemata Methodi diophanteae
  29. nullo negotio solvimus: ex. g. X + + ZHB. X+ y + Z F
  30. invenire bres numeros ita ut summa cuborum cubus, et summa quadratorum
  31. quadratos assumatur certia aequatio x+y +Z i n manentibus
  32. et n aibitrannis, fret. habebitur aequ. g. Quam si aequemus
  33. arbitrariae divisibili X3+ B x + bd X + cd po
  34. faciendo dp. n b p 212 qn + 2nm B _C n - m - 2c
  35. habebimus bp - 213 +313 -3nm -6Cn 3Cn - 3Cm = 6c
  36. 2(3- 3n’ + 3nmi
  37. ubi faciendo bgo. seu 13 3n - 3nm - 6cn. set n
  38. fiet d - d fiet dgi n et fier dp n n 2c
  39. fier dp - n. et n e 2C + m. et posito mp C+n.
  40. fier nH 2C + e+ NBren et n, 2+ C. et dp
  41. no rete
  42. 2e
  43. et Fo qui posito
  44. fient X
  45. 7c
  46. c
  47. =c’ esse quadratum seu - C B S. _. 154C
  48. erit de,
  49. + 2L
  50. + f
  51. e
  52. e
  53. sed in eo jam male quod sic +f et
  54. concurrunt unde aliquis terminus est
  55. regativn unde non lice facereto
  56. quia omnes tres radices aequationis u sunt rationales
  57. videndum potius
  58. us
  59. Hinc nihil efficitur comparatione
  60. quomodo aequ. 9. dividi possit, in duas
  61. ex. g. pontudo X n fieret
  62. Sed jam video
  63. non magni hnc subsidia resci ad diophantea
  64. satius erit ex aequ 40 I1q inveniore aequ 1. 2. facere
  65. aequ. 10. 11. faciendo Lp 1 Z et MB
  66. pro l re. m ponendo L. M. et faciendo L (3Z3
  67. . et M m- Z
  68. (19)
  69. (20)
  70. (21)
  71. fiet ph- 3M p +1 Pp0. YB p - M. X pX + qu
  72. i seu p - 3m P + aB 10 et q p = m +Z et X px + P nirp( 2)
  73. +337
  74. -2
  75. et et si aequ. 22. 24. rationales solutum est publema
  76. quaerantur conditiones generales aequationis cubicae et
  77. quadralicae ut sits ralionalis. illud dubium an si
  78. irralionalis etiam x irrationalis. Imo necessamu
  79. X+bX+C
  80. de + 1+
  81. +CX

Cite

Leibniz-Handschriften zur Mathematik LH 35, 3 A 3, fol. 12v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068216:0024?run=74