Leibniz Legible

Machine transcription of the Leibniz Nachlass

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Ps. 2, fol. 133

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: 0.81.

Original at the GWLB · Page image · Annotations (IIIF) · Download text

The machine reads it as

  1. P’ mjo
  2. RCNO
  3. +des
  4. Dec tont
  5. adIX XpI
  6. IMOT qua
  7. eOGVEMM
  8. X + PX
  9. ralereaet
  10. rajus qu
  11. amlibet 1.
  12. ideoque
  13. XX, de
  14. (M XX.
  15. 1X. 1
  16. BebIIa
  17. O
  18. IIndet
  19. AE O U A Y L O H U M.
  20. cet, lixx aequatur iplimm, hoc est, x m, candem xtore aequa-
  21. lem iph : ac per consequens, situerine terminihim _== 2 qua-
  22. les, eric una radicum aequationis propolica ae qualis lingulis iplo-
  23. rum; e E inxquales tuerint, neuera duarum radicum aequatio-
  24. nis propolita poterit esse inter illos duosm e. Fodem modo
  25. pertranspolicionem eAt x+ =n X Dmmx x -p+. UInde Cimiliter
  26. dilcimus, si x3 aequatur ip(i n3, hoc est, x ∞ n, Fore ctiam
  27. X X D n hoc CA, x ∞ . Ideoque sihi terminin el fuerine
  28. aequales, una ex radicibus aequationis proposiea aequabitur sin-
  29. eulis corundem terminorum; sin rero inaequales fuerint, nul-
  30. la radicum aequationis propolitae inter illos duos constituta crit.
  31. exaterea per cranspolicionem eAtxt. L p+ D mm X X L n3 X, ideo-
  32. Que mmxX Ln X majus quam x+, _ mmX F n3 majus quaim X3.
  33. Porro, (i propolita aequatio est realis, erit n realis, et aequalis,
  34. vel major, relminor quam n. Si tuerie aequalis rel major, erit
  35. mm X. L nnx majus quam x3, CE m m: F nn majus quaim X X, hoc
  36. est, xminor erit quam V mm- Lnn. Si fuerit X minOr quaIm n,
  37. minor etiam erit quam V mm- L Bn. Guare patet, quamlibet
  38. radicum aequationis propoliex neceslario minorem esse quam
  39. mm. Lnn. Denique existente x +-L p + ∞ M I X X L n3X, exit
  40. Timilicer mmxx Ln3 a majus quam p2. EF quia inventa eAt
  41. Vmm. +nn major quamx, erit conlequenter mmx V mm. Lnn
  42. Majus quammm XX, ideoque mm X V mm LnN, L B3 XajuS
  43. P
  44. quam pt, ee xmajor quam
  45. mmrmm Lnn. + X3. Ouare inven-
  46. cus est terminus unus major a alter minor quam quaelibet dua-
  47. rum radicum aequationis propolua. Atque ita modo seguenti
  48. capice obterraco propolicione seprima demonstraripocest, quod
  49. x major est quam minor horum cerminorum n et in mn. L. n3

Cite

Ps. 2, fol. 133. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/175906937X:0157?run=74