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Leibniz-Handschriften zur Mathematik LH 35, 12, 1, fol. 104r

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.

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. 105v); this page is its right half.

The machine reads it as

  1. de Roductione Sexti gradus ad Quintum
  2. sit aequatio X + bX + CX + dX + eX +fX +
  3. ex
  4. os
  5. sit Ket b sit X+AX+ SX
  6. si X L HX+ A X L1X4 I4X +15X + 16=0
  7. 240 n
  8. suciessit
  9. formetur formularcubica sexti gradus generalis; facta
  10. ex cubatione hujus 10X + FIX + 12, quae dabit
  11. 10X 12O. H X = 3. 10. 12X + PIX
  12. + 3. 10. TI X + 3 222 + 3. 10. 12 X
  13. +EBX +3. =1. q2 X + 311. IX + 12
  14. articuli
  15. Farmula 3 addatur utrique later aequationis 1. fiet inde ae
  16. firuula vel aqu+. quo est aequ artic. 4. Cujus pars sinistra
  17. aequanda est cubo generali alteri ejusdem gradus nempe
  18. excitato ex aquatione hujus formulae, 20 X F 2IX + 22
  19. ex
  20. fursus
  21. cubatione quae dat fiat
  22. 2
  23. 20X + 3.28, 21 X + 3, 20. 22X, + 2I X
  24. 3 20. 21 X
  25. + 3. 20. 22 X
  26. foe (5)
  27. E)
  28. + 2t X + 3. 25. 2 X L 3. 21. 22 X + 224
  29. et multiplicanda esset artic. 1 per aequatio
  30. in l. per form 207- 10 deinde addatur ei ab utroque
  31. per
  32. latere formula ex 3, fiet equatio in artic. (6) quae incipiet
  33. 3
  34. 28 X + 20
  35. = 10
  36. X ere 10X + 310. 11 X ete
  37. quae ut sit utrobique extrahibilis, cum sit in latere
  38. dextio, debet comparari sivistrum, cum form. 5
  39. + 3,10.11.
  40. sed video nos tantum habere literas arbitrarias sex 10, 11, 12
  41. 20, 21 22. imo revera lantum 5, ob laves notas, quia omnes
  42. termini in arbitrarias ducuntur et ideo cum tamentermini compa
  43. raudi sint 7. Res igitur hac methodo non procedit. Et
  44. tamen aliunde judicare mihi posse dibvideor, debere
  45. procedere. itaque Methodus hoc sb succurrit, aequatio 1
  46. mulliplicetur per _(220= + 20 X + 31 X F 32X + 33.
  47. ut ffiat aequatio L3) graduum noven. 110
  48. ibus (
  49. et proformilis cubenter formulae () 10 X3 + ( 1X +. 12X + 13, quoal mbus
  50. quaeratur (4) imbuforinntae (6) 20X3+ 21X +22X + 23 quaerata () cabus
  51. cubus ponatur ab cubus ex 4. addatur utrique parti aequationis ex 3. cuius latus sinistin
  52. dextrum ideo erit cubus, simistrum erit aequandum cubo ex 7. Habemus terminos aequando
  53. numero 10. arbitiarins vero habemus , in effectu aequi valentes 10
  54. et comparatio procedit.
  55. 10E
  56. verte

Cite

Leibniz-Handschriften zur Mathematik LH 35, 12, 1, fol. 104r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068194:0207?run=74