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Leibniz-Handschriften zur Mathematik LH 35, 12, 2, fol. 178v

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: 0.78.

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. 179r); this page is its left half.

The machine reads it as

  1. sit eadem sectio conica, in eodem plano aliter popta, nempe
  2. LY, priorem AY secans in Y. sit novers vertex Axis LZ.
  3. priorem secans in M ex L in AX agatur normalis LN. et fiant
  4. AM, LM, MN, NL, +LZ, a Z Vagus N AX XY. AB BC
  5. 5
  6. m
  7. n,
  8. Etprius
  9. secet ZY, ipsam AX in Q., erunt triangula , MA L, MZ Q, YXq simitia.
  10. Est autem Z M = l - Z ZQ = v - QY et qY = yl:m p. ZQ = v - yl: m
  11. QM = Z M, l: n fit q M = l. Z l: m YY = X Q = yn: m
  12. _ZM: ZQ = m: n Ergo l- Z:, v- ytm= m: n.. Rursus
  13. AX + XQ + ZM = AM, fiet X + yn:m + (L. Z)lim = B, Ex his duabus
  14. aequationibus habemus l - Z = vm:n - gl:n = pm: L = Xm: L - gn: l.
  15. seu v = pn: l = Xn: l + y (l- ua, :Ah) n: m, -) m: l seu B2 (p. X) u tym, : l
  16. Et ex aequ. 2 fit z- Xm: l + gn: l +l - pm: l p = m -9, et
  17. l - pm: l eit l = mn + gm, : l = nn + gm,: l, sed relioquendo p, fit
  18. Z= _ l. + gn: l - (p- X) m: l
  19. est generalis pro quacunque curva;
  20. Et dic quidem Calculus
  21. jam habuimus 2YX + LXX = Gy et (bersu +(14Y) xy = rC + = CX
  22. Et ob novum Conicaesitum, habemus 2rZ + 7 22 = vn. pro quo valore
  23. in qua aequatione pro Z et v, substituamus valores inventos, aeq. G et 4
  24. fint 2nl F Ergn: l - 2r(p. X) m: I + ell fr yynnill f Y (ep 2pX + XX) mm: V) 2Xay (2 7 (p. X) M fer y a m . )
  25. aequ. ponn.l - 2px nnill + Xxnn: I + gymm: I + Epyn L + Epy n. l - 2X7 nm: I
  26. seu
  27. Aequationes 6
  28. XX - 2 panu -rpua X rm By + px ru. 1
  29. mip. s. 99 p naxy
  30. e
  31. =20a X Agll. 9 - 2il
  32. H2r mapX
  33. non X aG + EU
  34. tirumpus Fuptum
  35. +umupus
  36. Aequationes 6 et 7 quae libet multiplicata prius per constantem arvitrariam ett
  37. addantur in unum; et aequatio inde resultans identificetur
  38. aequationig. ita invenetur situs novus Conicaedatae
  39. Termidentilicandi sunt sex, nempe XX, yy, xy, X, y, 1
  40. AYbitravia sunt, l, m, p, Y, E
  41. itaque verlor ut res succedat
  42. llites
  43. Sed ita una arbitraria deficit
  44. +p+G( + +B = 0 = aequatio ad est Conicam datam +r, sum najiat
  45. + Z mm. un ZZ 1 + 2 mA7 sB cirx a1, 12r p F 2it - 0
  46. +r un nom ur Hix mui
  47. Zflo - 2+ p2+5
  48. qu
  49. t
  50. aa
  51. +22 m trrnt
  52. TEl. 1
  53. +Z1 l e fy =
  54. s t- e y f, X0 + X3
  55. roo + +d +9n + ah =0
  56. Zt x t _ vo + gv + 79g - gg - . f- ah
  57. 23= 1711
  58. fit 2EErpEes
  59. pZ
  60. = a. v - - 29 +3 (1 52 = a1)
  61. AN, H

Cite

Leibniz-Handschriften zur Mathematik LH 35, 12, 2, fol. 178v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068195:0356?run=74