Leibniz Legible

Machine transcription of the Leibniz Nachlass

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Ps. 2, fol. 139

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: 0.73.

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

The machine reads it as

  1. le i d
  2. eropolta,
  3. CMINS. DEE
  4. u equaler
  5. 2 ln loco
  6. habere
  7. de consta
  8. oY
  9. DA dr
  10. i
  11. racta XGL
  12. quabiur (in.
  13. Ie necellarie
  14. 11, de Gt.
  15. Oeud i 1
  16. dC prent
  17. ell.
  18. 15 Gu 21
  19. a.
  20. jor qua
  21. 2Idcem
  22. 1 L1
  23. D ex hul
  24. Inorem et
  25. nulto min
  26. (N + P.
  27. Es
  28. one denio
  29. AE C U A F E O ET W H.
  30. Prop. 4. Xt - L l ∞3 X -. n3 X pt ∞0.
  31. Pextranspolitionem est xt L l X3 ∞ p+ = n5 x, ideoque Im2-
  32. jus quam x. Fodem modo est xr L n3 X ∞ p+ = lX3, ac proinde
  33. majus quam x3. Similiter est l∞3 - L n3 X ∞ p+ = x +, _E per COn-
  34. Sequens pmajor quamx, _ p. x majus quam x+, aC lp P a majus
  35. quam lx 3. Sed per cranspolitionem propolitionis est quoque
  36. X= + l ∞3 f B3 ∞ ∞ pF. QuarC P3 X F IPPX L B3 X MajuS CrIE quam
  37. pr, de X Major quam pr. L. Ipp L. n. Et sic inrenta est radix X X
  38. quationis prOPOCIX major quam p, f. Ipp F 153 at minor quâm
  39. m. Y C. ep.
  40. Prop. 5. Xt - lx3 X, + 13 X + p+ ∞0.
  41. Pertransposrionem est n3 ~ - L p, ∞ L X3 = Xuy ideo que l major
  42. quam v. Deinde eA xt - L pr ∞ l∞3 =n3 N, GuarC CFIE X N ajuS
  43. quam7, hoc elt, xmajor quam V =. Sed est quoque at L n3 V
  44. ∞lX3 =pF ideo que v3 majus quam7, n major quam V C. .
  45. Duareinvenimus, quod quaelibet duarum radicum aequationis
  46. propolix necessario major est quam V de V C. , at minor
  47. Guaim lo
  48. Prop. 6. X t - IX 3 X - B3 X F p+ ∞O.
  49. Per cranspolitionem eAt xt L pF ∞ n3 ~ - l ∞3, ideoque, m 2-
  50. JuS quam XX, hoc est, _ minor quam V. Deinde eA xt L LX3
  51. ∞n N =pr, ideo que xmajor quam . Praeterea eA l X3 L pr ∞
  52. M3 x = XF, _ idcircO n3 ajor quam X3, hOC CA, X INOE QUAMIH.
  53. Eroo invenimus, unam quam que duarum radicum x aequationis
  54. propolica majorem esse quam, at minorem quam V de M.
  55. PrOBo

Cite

Ps. 2, fol. 139. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/175906937X:0163?run=74