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Leibniz-Handschriften zur Mathematik LH 35, 2, 1, fol. 233v

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: 0.87.

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

One image of two folio pages side by side, registered by the library under both labels (also fol. 234r); this page is its left half.

The machine reads it as

  1. uli
  2. Inquiramus nunc in Curvas figuris cognitis, ut Triangulo,
  3. Parabolae, homologa si
  4. Trianguli aequatio est. X = y.
  5. X = fied. YX = a = y et posito pro X posito a + X,
  6. fiet a + X + 2aX - _ = y, = 2ax + X. Ergo
  7. Figura Quadrahix Hyperbolae curvam habet Triangulo homo-
  8. logam.
  9. Intimei Jarabolici aquatio est. X ax. X - y _ X = y.
  10. fiet regula nostra: X = x - a = ay. sive
  11. Xa = ay, et pro X posito a +X, fiet 2ax + +
  12. a + 2ax + X, D = a + 4aX + 9aX + 4a X + JaX +X
  13. sive a + 4ax + 6aX + 4 aX + X g = ay.
  14. et hujs figurae quadratrix curvam habet Trilineo
  15. differentia
  16. mege mologam. Ipsa figura autem videtur esse ex
  17. necculu
  18. Hyperboloerdum genere Unde ficret a + x = B ay + a
  19. sive pro a =+ X posito X fiere: = X = ay + a
  20. vel X = Y + a = y + a, a-7
  21. n naz n. 2y
  22. vel SX = a = ay ut aute.
  23. aetema eodem modo omnes quoque reliquae paraboloeides
  24. tractari, possunt, sumenda tamen in exemplum compr
  25. sita X=ya+X y haec tractatur non ut Trilineum
  26. sed ut Hyper parabola ipsa, fit enim sax y.
  27. atque adeo a fit enim tatus curvae homogeneae:
  28. t
  29. a
  30. a3= Et quadratum ejus
  31. A = Z, detrahatur 1. fiet
  32. a
  33. a
  34. 6-a - 3
  35. vel - X unde figurae X- a - y habe uadialri
  36. demva huic paraboloedi homosoga. Figura autem
  37. ista dabit X- a - ya
  38. paesitum. Io in
  39. cujus quadratura dabit
  40. In simplic. parabola aX y = aY. unde
  41. y= ax seu 3 = X, hujus quad. a = 0
  42. a vg
  43. cudi addatur
  44. Vax - a vel sax = y. Et huju nimirum ipsius
  45. nambola quadratix figua tunum habetio parabolae
  46. si a +Y = n
  47. ergo a- yF 13)
  48. ( a
  49. 20
  50. Ergo nitia huc dimi pt
  51. quare Geomenrice
  52. describi potest

Cite

Leibniz-Handschriften zur Mathematik LH 35, 2, 1, fol. 233v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 44). https://leibnizlegible.com/page/00067993:0468?run=44