Leibniz Legible

Machine transcription of the Leibniz Nachlass

Search the Nachlass

Leibniz-Handschriften zur Mathematik LH 35, 3 A 7, fol. 29v

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

The machine reads it as

  1. qualibet continet duas radices, seu radicum
  2. combinationem, sunt autem e combinationes numer b
  3. ab ac ad
  4. ac
  5. b
  6. Cc
  7. Xtx + abj 1
  8. X +C X tqod
  9. F ubi a + B
  10. su Nempe a+ b vocetur y. quaerendo
  11. terminum secundum. divisoris, ergut a + b = at C ) at d F btc f. B
  12. aequ. 3 a ++cd aeq. 0. qui est sumnomuum s possibilium
  13. et summa rectanguloni a + a b +3abc
  14. + eb
  15. Hinc si
  16. aequatio pro Y caret termino secundo, aequatio pro Y
  17. carebit etiam termino secundo Ascendet autem
  18. ad sextum gradum.
  19. sequationum tamen quadiaticarum inter se
  20. ducendarum ad procdelendiam aequavinem
  21. Tatam combinationes sunt tantum tres
  22. Quarum unas
  23. X + a X 4 ab
  24. in X + C X + cd
  25. itaque squ si ab + cd quaeramus, ascendetur ad aequationem
  26. tertii gradus.
  27. nam tres tantum sunt casus:
  28. ab + cd, ac + bd, ad +bc
  29. atque ita evitatur sextus gradus,
  30. ad qvem ascendit Cartesius
  31. et alii
  32. X
  33. + Ix + m
  34. X + nx +
  35. LXE + mX + lpX + mp
  36. n X pX + mux
  37. In X
  38. Comparantoedator X + GX + Y X + S aeq. 0.
  39. sit m + p aequ n. fiet: pagotam 4 + lX + hX + lh X +mh
  40. ergo
  41. Im um
  42. +n X +n + mn
  43. Ergo ln aeq. 0. siu naegu - l. et I aequ h - 9.
  44. et Ih m - 2lm rqu. Y. seu H aeqo Nr. aequ. h- 9
  45. seu rr aequ ht (4hm + 4 mm
  46. h- 9
  47. (4mh as
  48. th - +lm + amm
  49. Ergo rr + 4hs - 495 - h + ghh aequ. 0.
  50. pa
  51. uimu
  52. seu h3- ghh -4) h + 495. aequ. 0. Unde habetur h
  53. cubice
  54. est autem mm hM + tit aequ = tih - s seu M aequ. h + S+th -5
  55. et P aequ =h - hh -s et l aeq. dhtiq seu Y
  56. et naeqo Y
  57. +Sitih - 5
  58. h- 2m
  59. -

Cite

Leibniz-Handschriften zur Mathematik LH 35, 3 A 7, fol. 29v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068220:0058?run=74