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Leibniz-Handschriften zur Mathematik LH 35, 3 A 7, fol. 10r

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: 0.76.

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. 20v); this page is its right half.

The machine reads it as

  1. 1
  2. sit Aequatio data X + bX cX + dX +C a q. 0.
  3. quae divellenda est in duas partes utrobique extrahibiles, quarum
  4. latera sint X + lX + m et n X + p, se de et fiet
  5. X + lx + in aequ +n X + p. depressaque erit aequatio. Est autem
  6. (2) X + lxam aequ X + 2lX + 2m X + 2lmX + m
  7. + U
  8. et IelAnX +p aequ np XX + 2np X + pp
  9. et fier X + 2l X + 2m X + 2 lmX + mn aeg. 0
  10. comparanda
  11. e
  12. + U - 2np = pp
  13. un
  14. fiet laequ b: 2 et m aequ c: 2 - b: 8 + nn: 2
  15. et rursus m aequ. dett d . b + 2np: b. Ergo paego bc: 2- b: 16 +nn: 4-do~ r. n
  16. Ergo P aequ. bce - b A8 +. bnn: - d_: pIn
  17. per compendium c: 2 - b: 8 vocemus f, et bc - b:- d Quocemus g.
  18. et sunt enim cognitae fiet: maego f + un:r et paequ g +.bnn : 2n
  19. Resta t aequatio: mm- ppaequ. e. Ergo fiet:
  20. f2 + fnn +n - _9g- gb nn -- b nt: ann aequ. e. unde n - +. b H =gbn aequ. 90
  21. dd
  22. Unde denique siet n n b nn aequ. F99
  23. sen
  24. 44f.
  25. ..
  26. Hic enrons alculi conigendi exproredentibus , aue correctis
  27. -B2 n4 +9
  28. e
  29. 1
  30. f2c0
  31. 62
  32. b
  33. =2
  34. bC
  35. n aequrisb
  36. + CC i
  37. ++b d.
  38. +4C.
  39. b+c
  40. _Vd
  41. +b c2 Et explicundo
  42. = bcd
  43. + dd
  44. quae aequatio servit ad resolutionem, aequationis quadrato.
  45. quadraticae cujuscunque. Inventa enim n per
  46. aequationem praecedentem fit:... Xex + + b +f
  47. sive, X + = B X X
  48. ag
  49. eit
  50. +M. +2C
  51. Hic adhuc errores +: nn
  52. calculi conigendi
  53. L1 13
  54. ex praecedentibus -2b
  55. Zin 2+nn aq.0 sive
  56. divis. per + n
  57. jam correctis tsds
  58. Ebn
  59. . +n
  60. bn
  61. qua aequatione resoluta, posita = esse = et + esse +
  62. habentur duae radices; posito vero = esse + et + esse-
  63. habentur duae radices reliquae aequationis quadrato. Quadraticae
  64. propositae. Quod si poras b aego seu abesse terminum secundum in data
  65. siti. n +AC N Y Cchi aequi dd. et se n X + efe aeq. 0 Et p. Mp ponendo yy
  66. denc
  67. pro ponendo y prodit
  68. nn
  69. +4f 4452.
  70. qe
  71. 0
  72. ++ Eequ 8 cc- Gebri bt
  73. =9buq. A- L. b C + b bd
  74. daq. eb. 75bc
  75. +bdt
  76. 4bc. 12
  77. 1a
  78. 1
  79. 16
  80. u

Cite

Leibniz-Handschriften zur Mathematik LH 35, 3 A 7, fol. 10r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068220:0019?run=74