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Leibniz-Handschriften zur Mathematik LH 35, 2, 1, fol. 266r

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: 0.82.

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. 265v); this page is its right half.

The machine reads it as

  1. sedalium
  2. Videmus an revertiliceat ad methodum Hudeniananoe Aequatio ista: S= v. y Y2vy -X = 0
  3. duas habet radices aequales, multiplicetur per progressionem arithmeticam, ubi prius recte fuent ordinata. Sed nc
  4. aurtu subesse. ed malum in eo est, quod recte ordinari non potest, cum exponens verus ipsius ipsius y. in
  5. termino Z y, non sit notus quia y. ipsi e implicatum est,
  6. Differentia inter applicatum lirculi e Hypertole. 2aX +X = EaK - X p 2
  7. fiet. (2a X) +X 1 Z + 2Z trax X ( 2aX ( X)
  8. Ergo Z e 4Z vC 2ax. X p 4X (= aZ X) + Zt, 9Z aX (= 4Z X
  9. Aliter a +X a 15 - ae -y e V, unic aty 1B + a - yd sive (a V + 2VS.. ( a) -
  10. sive _i 27 1vs. et quadiando 4y (4yYt vt 4v a = 4V y)
  11. qu 4a - v, 2 2a - v rato
  12. Ergo +y B -
  13. patet aute omnia fogurae differentiarum vari momt quadratorum summarir; pendere a
  14. v - +v a + a a- 4y
  15. monculo segnerhexcentid. V SV Sa jum V, ita investi gabimus
  16. Unde a - v, 2 a - v , a - 2 a + 2, sive
  17. a + v, D, a - viI ( a + yS2 a - V12, a +ry;
  18. +v 1 a p, Sa =- 4 , et vr + sat qui. + a
  19. 8ra= s.
  20. 4y H40 a - v+, inde 16yd (p BY a. V, eyo ls) 16y
  21. x 1+ 9p L. Erro Z p lv + 30
  22. Ope differentiarum inteo duas figuras commensurmbiles novae habentur quadraturae
  23. v9. a X - a 2 ay, H X. Ergo XX + a X H 2ay2
  24. Y7 a
  25. p C X - 2a, + a X p7 0, pore _X - 2a p Z fier yZ + a Z + 240
  26. gu parabola: yVZ - aZ + 2a 70
  27. differentia inter Y et y F; Y a X et inter Trax.
  28. a - X
  29. pax -X 2a = SaX + 7. Unde 2aX - X p, aX , 1Z Sin 4 2
  30. 2a-
  31. ea -x
  32. sive hax = X = aux - q p 22F.. sed nihil inde
  33. X
  34. Saa +gy = Saa-yy aequ 7. Ergo 2aa + Saa a- B y aequ. 2Z.
  35. seu Sa=- y aequ. Z2- aa. seu saatgyu. Saty. Sa-y aequ. 7+a. Z- a
  36. alscissae
  37. 7+a aequ Sa Ergo momentum ipsius Z4a. ex y. a,
  38. afigurae ex axe conjugati datur ex data Satitaus
  39. 27Zaa aequ 2+ y
  40. promentu in X
  41. sin (a -y aequ Z E + a) = 2ZZaa et fit:
  42. seu yy aequ. Z f2aa -ZZ. Et y aego Z 220a- 77
  43. Vbb + cyy + dd + e yy _. aqu. Z. fiet:
  44. bb + cygego ZZ + dd + eyy = EZ dd + egy
  45. b +2bbcy +Ccg + Z + 277dd + 2ZZCt d + 2dd eyyt ee d a
  46. 4
  47. qu
  48. = 2bbZ- 2bb dd - 2bb Cy - 2 cy2Z - 2 cydd - 2 ce y
  49. Tollamus ZZeyy faciendo +2e- 2t 40
  50. aequ. - 423 dd 4 2zeyy aequ. 0.
  51. seu eaequ-e
  52. ita tollamus alia qnvolumus
  53. Ergo

Cite

Leibniz-Handschriften zur Mathematik LH 35, 2, 1, fol. 266r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00067993:0533?run=73