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Leibniz-Handschriften zur Mathematik LH 35, 14, 1, fol. 282v

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: 0.84.

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. 281r); this page is its left half.

The machine reads it as

  1. Jam ergo ut calculum de integro ordiamur,
  2. data
  3. Sit, aquatio
  4. W X - 39 Cd +25 96 - at 0.
  5. erit ea intractabilis per regulas Cardani, quoniam a q
  6. riente termini secundi 34 cTubus 4, major est quam qb - a+ +2
  7. quadratus a q - a +, semisse termini uttimi, 2 Sq- aF
  8. Ponatur jam Ce p Y + 29 13
  9. -39
  10. +3Sq. a F)
  11. =4N3, y +3, 4, 39V
  12. y +6953
  13. et fiet aequatio
  14. +89.3 B3
  15. - 34, 2953 (6 8)
  16. +21q - a +
  17. +189313 (49
  18. +259 - aF +2S
  19. ubi sed video, a me erratum esse, in calculo, debet treri
  20. Aequatio data: Cd X - 9 q Cd , 224 - a t H quae aequatio
  21. est intractabilis per regulas Cardaniu nam cubus triens a 94
  22. qole cognita termini ul penultim est 34 ejus cubus est
  23. t2 surq aF)
  24. Cd ei
  25. (15)
  26. y A - 2 9 13.
  27. ut ante, fiet:
  28. (3, 295, Y +3, 493, ) 892
  29. 99
  30. + 2794)
  31. .92913
  32. 2 Jvig at
  33. 6qu 3
  34. =ril 279. a
  35. prtam sacisim potestates In qua aequatione si faciamus tantum, ut
  36. duae radices, 13, et 1279- a eodem signo sint
  37. ita iss
  38. affectae, quod in nostra potestate est erit signum
  39. termini secundi et ultrmi idem quod si ergo suam
  40. molem exhibent, sie affirmativa intelliguntur habebimus
  41. aequationem ex data factam, omnes radices habentem
  42. veras, quia signa alternant; et talem ut a
  43. 3413. semisse termini secundi factum quadratum,
  44. 993 sive 279, aequetur ipsi 279 cognitae quanditati
  45. terminipealtimi. Quod desi derabatur.
  46. haec aequalio cum
  47. fier ergo ex terminis ultimis:
  48. m+ +(2243 ⊓ (6 qa 13) + 2aY 279- at
  49. M12 + 160e9 s3 m + 64a962
  50. 2a279 - aFF2
  51. et signa radicum s
  52. conferatur jam
  53. hacl. ay-omne +ominay -no
  54. C fiet mn B aq s3, et ne aq S3, et n6 2ra g
  55. M 1 274606
  56. mt
  57. = 2796-a
  58. (+ 16a4 r2rg- a F
  59. 1oZ abg
  60. +279247
  61. 166
  62. O3 aq() 13 nest
  63. adeoque
  64. =, 3, 16a9 (279- a F2
  65. 2449
  66. quae aequatio est semper possibilis Ment C B3 4at79F sig 1 q6 - 1316,
  67. et erit m. 6a 43. β3 = a Sirf. at. + sug
  68. 41 221
  69. = 15, 16a9 527 96- a2 +. quae semper et postitili.
  70. 14qui utique major quam 279 - a F quadra Aebet ergo aequatiaii () termini
  71. tum a 274- a4+2 dimidio termini ultimi. Jam
  72. faciamus
  73. -0q0
  74. L adeoque 9m n p 9a93 1 279 a
  75. modoq sit masir gerim
  76. quantitates
  77. characterem portant
  78. sunt formutae quae
  79. affectionis ut
  80. sunt
  81. quae characterem.
  82. portant ambiguitatis
  83. et quarum signa pro
  84. arbitrio, aut rei usu
  85. atque exigentia variare
  86. dicet, ut radices
  87. quad raticae, vel
  88. aliae parium dimensionum
  89. Cterae omnes quantitates
  90. sunt o in differentes
  91. non portant affectionis
  92. characterem.
  93. ex terminis
  94. secundis et
  95. tertiis

Cite

Leibniz-Handschriften zur Mathematik LH 35, 14, 1, fol. 282v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068201:0564?run=74