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Leibniz-Handschriften zur Mathematik LH 35, 13, 2c, fol. 124v

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. 125r); this page is its left half.

The machine reads it as

  1. X = H~ 10D +, , OD. Ducantur invicem XH, X+m, X+n, fint X + lXX + ImX +
  2. X3 = 100 + 3. 100. 112G 10D + 3. 100. 11290D + 112O P LOD
  3. (Lamin) XX Llamtn), 100. 90 + 2. 100. 112 E LOD + 1120D
  4. lmalu tun, X = latlnema, 100 + 112 f0D
  5. XFl, XIm, X F
  6. Et ordinando fiet, X H Xx + luX Flum =
  7. 100. 100. 1004
  8. 3. 100. 112. 112 907
  9. +
  10. 00100. 100p es 4
  11. 00. 112. 112p (9
  12. atC
  13. 00. 00. 100a pe
  14. un
  15. Compendio sit lam + n = p
  16. Ut shnando fiet
  17. +1C4 GB
  18. 3∞00 +10
  19. cntlntum = a
  20. Quaeritur A(XFC, Xtm,
  21. + 106. 112G0) 12. 114 +12 (d5
  22. d irE
  23. + 0), L3100100 200. 100 mpE
  24. 1. 112. 12. 1123
  25. quae formula aequoenda quadrato a ad O + aq
  26. coefficienti
  27. 197)
  28. a
  29. Forw. oolmn
  30. Et pars rtionalis valoris ipsius X3+ pXX + ap X + amas partis irrationalis aequare oportebit at
  31. parti vero rationali ad + a8D. Quod fieri poterit explicando C et D) per unam
  32. et 21 = + 123. 11. 3(a + ot. 11293: 00 a
  33. 0.00.
  34. Veninmus jam ad partem rationalem. ibi non potest esse Q, nisi in 40D, Ergo ut destruatur
  35. D debet esse 100r1o + 3. H 108. 00 +3. 112. 10. 30. Ergo fit 100 = 100 112 ed 30 +. 5 ( Y. 31030;
  36. quos duos valores aequando fit 10. 10. 30. 30g = = 3. 10. 30. 00.00 et 10. 30 = 6 - 27,00.00
  37. superssupersunt aequandi termini in rationalibus ciefficientes ipsorum e, e et G
  38. ope literarum 10. 30, 15, 31, quae ex Itaque ad ad hoc, et ad tollendum terminum e, opus
  39. est aeqq. quatuor, et e arbitrariae sunt etiam quatuor, 10, 30, 11, 31. Nec videntur
  40. haec nimis prolixa. Scribamus ergo omnia distincte; et primum partem irationationalem
  41. 300 100. r +3. 00. 00, 100. 112. 112 ~∞ + 2. 00. 00100. 112. 112 p 4 + 1. 00. 04,00. 00. 112a9
  42. + 1 a 10.3]2112. U2 W2 a8
  43. + 1. 11. 31. 112. 112. 112 aa
  44. =1. 00 99, 98, 80, 00 a 8 - 1. 00. 21,90. 0087d
  45. F +1. 1V. 30. 112. 112. 112..
  46. 11 30.
  47. ( aqu0
  48. 1. MF
  49. fit 100 = - 10. 30112: 3.00 et 20 = 2=. 10. 30. 1 p + 10. 317112 a, : 00t a. Et X 00. 129 + 11311N a.
  50. octa
  51. In parte rationali habebimus, 100. 00 +3. 112. 10. 30, 9=0 fint 100 = 11, + (- 3. 10.30):00 sed prius erat
  52. 2
  53. 100 = = 10. 30. 112 : 3.00 quos duos valores aequando fit 10. 10. 30.30. 112. 112 = f - 27. 00.00. 10.30. 112. 112
  54. seu 10.30 = -27. 00.00. Ergo (.+ 100 = 9. 112. Hiac ex aeq. l. fit 27 (11100. 00.27. 11282700.00. 112 =8
  55. et ex aqu. 4 fit 81. 112. - 3. 27. 112 =0, ut oporet.
  56. tar pe g
  57. ru quae rui
  58. communem porrit poterit autem esse secundi gradus, a son a 00 a t= obi PR +000 aroB naa
  59. et ita equatio ivessi inter coefficientes trrationalium, dabit valores ipsarum 20, 21, 22. Superest ergo
  60. debet autem e esse gradus simplices, et poterit esse 204 + na, ita aequando coefficien
  61. tes irrationalium, habetur 20 et 21 sd et ex irrati habobetur 3
  62. 2 = 308)+31a fiat 3. 100. 0d = 112. 1030 = 0 seu 100 = - 112. 10. 30 : 3. 00
  63. 112ob:6
  64. in se ipso et
  65. 11.
  66. i
  67. extractione
  68. Xy = ab
  69. Fd Xx = ab

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2c, fol. 124v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068199:0248?run=74