Leibniz Legible

Machine transcription of the Leibniz Nachlass

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[Ps. 1], fol. 135

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

The machine reads it as

  1. Cadu
  2. 2dC
  3. tOn
  4. ce
  5. Get
  6. Dec
  7. eden
  8. e
  9. e I
  10. alc
  11. cerm
  12. se
  13. ec 6
  14. tiori
  15. trabe
  16. S
  17. den
  18. renlio
  19. oTIne
  20. 1
  21. a
  22. NV O Y A B R E V E S.
  23. 33
  24. ee iplius cubum y. pro x3, atque mulciplicando secundumtermi-
  25. num per h, certium per hh, d quarcum per b3; eandem consecu-
  26. curi simus aequationem. ut ex demonstratione superiori tacile est
  27. colligere; e omnes quidem termini x que multas habebunelite-
  28. ras seu dimensiones. Lc tantum de operatione per literas.
  29. Ouod autem spectat ad operationem, gux fc, cum radix inco-
  30. nita per numerum aliquem est mulciplicanda; ipla cidemr de-
  31. monstrationi innititur.
  32. Fsto eadem, guae supra, aguatio: X3 = CX X d d X = b3 ∞ 03
  33. ee oporteat radicem incognitam x mulciplicare PeF 3. SupPOna-
  34. TULy ∞3 N, CxIEGuC ~ X, e ∞ N =, NCCHOH, ∞ ∞ 3. Oui-
  35. bus, ue supra, substicuris, Aet 13 -cY 2 1 d27 -- b3∞O. AC
  36. proinde multiplicato totOper 27, exturg et y3 = 3cyy L9d dy
  37. 27b330. Oux aequatio etiam invemIEuF, Si in aequatione
  38. propolica substicuamus y, quadratum ejus ry, de ipsius cubum ys,
  39. loco x, quadrati x 2, _ x3 cubi; atque deinde secundum cermi-
  40. num per z mulciplicemus, certium per 9, ee quartum per 27, cx
  41. praelcripto hujus Geometriae. Oua quidem operatione termini
  42. omnes, ob rationes supra allataS, aeque muleas dimensiones ac-
  43. Quirent.
  44. Idem intelligendum est de exemplo in hac Geometria pro-
  45. Polico, X3 = ∞ x V 3 + = X-
  46. e
  47. e
  48. 2, V3 ∞ 0. Etenim suppolitO
  49. y∞XY 3, erit ∞ X, e = ∞ N =, neCnON γ ∞ X3. Vnde
  50. siin aequatione propolica substituamus quadratum ejus
  51. _ iptius cubum v in locum x, quadrari x 2, e cubi x 3; inre-
  52. nietur 33 - γV3
  53. 261
  54. 27V3 27V, 00. Atque adeolcocum
  55. mulciplicemus per 3 V 3 habebitur y 3- 3yy. L 5y - = 30.
  56. Fadem nempe aequatio, qux obrinetur operando juxta hujus Oco-
  57. metrix methodum, quemadmodum supra fuit ostenlum.
  58. Non secushiet demonstratio, (i de radice incognita per quan-
  59. cicatem aliquam cognitam diridenda asatur. Proponaturnamque
  60. RquatiO X3 = CXX L d d x b3 ∞0, Cieque x diridenda per B.
  61. Sup.

Cite

[Ps. 1], fol. 135. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/175905688X:0157?run=74