Leibniz Legible

Machine transcription of the Leibniz Nachlass

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Ps. 2, fol. 283

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: 0.79.

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

The machine reads it as

  1. M
  2. e
  3. CH
  4. I E B. TI. C AL. LLL
  5. Fxempla reductionis aequationum ad formulam
  6. Theorematis XII ex XIII.
  7. Si xquatio (Ic yy +
  8. b X
  9. ∞y -L = -6, CrIC y ∞ Z
  10. b3
  11. e
  12. -
  13. =c, eoque substieuco in locum
  14. iplius y, atque ejusdem quadrato locory, sublatisque iis, qua le
  15. invicem destruunt, erix y bbX 2bc∞
  16. aat
  17. Et Facta congrua transpositione,
  18. y
  19. fX a
  20. 66∞-
  21. FXX
  22. e
  23. bb2X
  24. a a
  25. + ex 1
  26. 2bc∞
  27. Ld d- f.cc, hoc est, mulciplicatis omnibus aequationis terminis
  28. per aa productoque dirilo per fa- L bb; ut quanticas x x ab (que
  29. Fractione remaneat, fet
  30. a422
  31. (a BG∞ X X
  32. Deinde aTuptOV~X. 1
  33. aa Cx 2abcx aadd aacc
  34. a ac = 2 abc
  35. fa + bb F fa + bb
  36. 2fa = 2b6 Ut terminus quoque
  37. quationis, in quox unius dimensionis reperitur, plane cranelcat,
  38. habebitur X ∞V = a a c -2 ab0
  39. 2fa = =bb. uo substituto in locum ip(IIISX,
  40. atque ejuldem quadrato locoxx, ablatisque iis quae se inricem
  41. tollune, reducta erit aquatio ad Formulam requi(ItaI. AEVeTO UE
  42. trat aquatio
  43. a e 2 abc
  44. fa.L bB Scribatur 2B, IEa UE
  45. +a + bB∞ X X 2 B~ a a d d + a a cc
  46. fat bb. Tum 2u-
  47. aa Z2
  48. PEov ∞x. F hleux∞ V - h, eoque substituto loco x in aequatio-
  49. nC, ac ejusdem quadrato lOcOX N: Crie
  50. ad d = a a cc
  51. aa2 2.
  52. 5a +- b
  53. 3 VV - BB. L
  54. fa. bB. Unde apparet, ance omnia hic esse consideran-
  55. dum, ucrum hh sic majus quam aad d + a acc
  56. fa-fbb an contra. Ei enim
  57. majus siE, erit casus Theorematis Z II; SIn CONETa, erit ca(US
  58. Pheorematis X III. Ponatur itaque primo majus, ac proinde a-
  59. quatio formula Theorematis XII. Et constat exinde Locum
  60. quaelicum Flyperbolam esse.
  61. Ad cujus peculiarem determinationem esto in apposita FISUITA
  62. ipsius x inicium immutabile A punctum, eadem que x in linca A F.
  63. ab A versis P indetinite se extendere intellisatur; sitque angulus
  64. n 2
  65. que

Cite

Ps. 2, fol. 283. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/175906937X:0307?run=74