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Leibniz-Handschriften zur Mathematik LH 35, 12, 1, fol. 115r

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: 0.86.

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The machine reads it as

  1. quens
  2. 10
  3. Frgo coefficientia e homogeneum datum propositae coefficientibus dt homogeneo dato
  4. Canonicae in excessas ec defectus habitudine contormia sunt:
  5. Scent igitur Aequatio proposita e Canonica aequipollentes aequali scilicet radicum-
  6. numero praeditae.
  7. Sed Aequatio Canonica de Eriplici radice p. 9. r. explicabilis est.
  8. Explicabilis est igitur Aequatio Communis proposita de radice triplici, uet est
  9. enuntiatum.
  10. X1O A.
  11. Ex Demonstratione praecedenti manifestum est AEquationem communem
  12. - - - --- aaa - 3baa + 3cCa - - + ddd... in quâ.
  13. C
  14. = vel L d........... Requationi Canonicae supra ex positae non esse
  15. aequipollentem, ac proinde de radice triplici explicare non posse . . . . .. Unde pa-
  16. tet condetiones ab Harrioto expressas nempe b. = c. et b = d. non sallicere ad
  17. arguendam Aequationis communis propositae cum superiori Canonica de tribus
  18. radicibus explicabili aequipollentiam, iisdem enim manentibus fotest esse
  19. C= = vel = d. -: . - - Secus in nostra suppositione, inquaposito b = c. EsC= a.
  20. necessario quoque est b = d. adeo ut duabus illis conditionibus positis haec tanque ne
  21. cessarium consequens omitti possit.
  22. Exempla Aequationum in quibus
  23. b = c. 8 b = d. e c = -d.
  24. 1. aaa- 13aa + 48a -- 64... a -
  25. 2. aaa 1416 aa + 48a - -64... a =
  26. 3. aa a 2 6= aa + 12a - 8... a=
  27. A. aaa = 93 ad. + 12a - - 8... a=
  28. Exempla Aequationum in quibus
  29. b 2 c. e b 3 d. e c L d.
  30. 1. aaa 10aa L 12a - = 27..
  31. 2. aaa 212aa + 26a - - 60.. a
  32. 3. aaa ~ 12aa + 16a-55... a-
  33. 4. aaa - 18aa + 35a - - 48.-. a
  34. Exempla Aequationum recipro
  35. carum in quibus itidem b = c. et b =
  36. esC = d.
  37. 1. aaa2 6aa + 1a - - 6.... a =
  38. 2. aaa 2 12a a + 5a - 60.. a
  39. 3. aaa 212aa + 4a - - 48.. a
  40. q. aaa = 12aa + 3a - 36... a=
  41. 5. aaa r 1Zaa tZa = 24.. a-
  42. 6. aaa r 12a4. + 1a = 12... a =
  43. a
  44. e
  45. 12
  46. 12
  47. 11. aaar 18aa +7 a = 12
  48. 12. aa a r 18aa+6a -
  49. 13. aaa 2 18a4. +5a-
  50. 14 aaa r 1844 +4a -
  51. 7
  52. 15. aaa 18aa + 3a - - 5
  53. 16. aaa - 18aa + 2a -
  54. 17. aaa r 18aa + 1a -- 13... a
  55. 1B. Hae 17. reciprocae Aequationes aequipollent
  56. huic Canonicae reciprocae de radice simpli
  57. ci p. explicabili. aa a r paa + 99a = - p99
  58. ret enim in
  59. hac est . . . - 99 -- p99... sic inaequation
  60. nibus quoque expositis singula homogen ea data
  61. constant ex ductue coefficientium. . . . Qvamobu
  62. rem si in Aequatione communi praecedenti.
  63. aaar 3baa + 3cca - t ddd.
  64. fucerit. . - 36)- ddd... ae quipollebit.
  65. et d Lalblucae receprocaenipsad 8b. em
  66. racix dequationis Communis proposctae expli
  67. catoria radici a. de quâ quaeritur aequalis.
  68. Vide atuer 6. prop. Sec. 2. et 18. prop. Sect. 4.
  69. 7. aa an 18aa F 11 a -- 198... a = - 18 Prax. Anal. . . . et ea quae paulo superices ad
  70. 8. aa a - 18aa + 10a - = 180... a = = 1E
  71. 9. aaar 18aa + 9a = - 162... a = - 18
  72. 10. aaa 18aa + 8a = 144...
  73. Vietam de ambignitate Cubi multipliciter ad.
  74. fecti annota sunt.
  75. Definit... .-
  76. Sec. 5. Pras
  77. Anal.
  78. Proposit. 5.
  79. Sect. 4. Pr.
  80. Anal..
  81. +Prop
  82. Sec. 5. P.
  83. Anal..
  84. 0
  85. d
  86. e
  87. 1E
  88. 3CC
  89. 36.
  90. Proposcta Requatio de

Cite

Leibniz-Handschriften zur Mathematik LH 35, 12, 1, fol. 115r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068194:0229?run=74