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Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 31r

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. 32v); this page is its right half.

The machine reads it as

  1. Minimam ducere ad ex puncto
  2. dato ad sectionem Conicam
  3. communis
  4. it sectionis conica aequatio quead etas fi potes arcu
  5. e yy = 2aX + (a: b) yy, posito ex A vertice AXcesse X, et Xtss
  6. et ordinatam normalem ZY esse y. d per verticem A ducatur axis.
  7. inclo curvae
  8. secundarius A, et in eum agatur normalis Y ex fiet A AL: L8=
  9. tL: LX et AB+ LX = X fit A) = X - LX = LL: LX, et fiet
  10. X. LX - LX = LG. Y L LX LY gy Y1 y. unde
  11. X. LX - YL + gy = LG. Yt fit LX = L8, L - yy+ZL,: CX
  12. ) AG: L: AL = YX: XL, YL seu y
  13. GL + YL - Y e XL: y = gL: AQ HL: y = 8L. AL
  14. AL = X - XL = QL y. YL XL = (GLy: XL) + X = y8L: AG. seu
  15. AL + FXL = X
  16. X . AG. YL = yYL L + yA. ) seu L = X AP. YL: y (MLF AG) GY. VC
  17. + (DVa
  18. XX + y y AC
  19. AG. AL = AD: L = y: X - G+ GL
  20. Y s +L = Y -GL - gu Expriore sit . Ae
  21. Ex priore aq. pro est fit AY - 8Ly = A A(B + GL, et aequando
  22. AQX + QL y - 2A8. Q LXy = A(P- ACL
  23. ex priore essust (L: A8 = 1(9Y - 92 - y 7) yy L. 18 - 8Y 91 8. 97 est yy
  24. primum trans trans ordinatam pro coordinatis ad axem primarium substituamus
  25. coordinatas ad axem secundanum pereundem verticem transcuntem sit. in
  26. Vertex A s abscissa ex axe AX, ordinata ad AxemXY.. Axis semodarus
  27. rvae
  28. exis secundarius A, ad eum ordinata Y8. ob datum angulum ad A
  29. unctum
  30. datar AB: _L. F vocentur A X, X. XY, y. AG, F. C
  31. rm lum ad A, dabitur AB: LAL = a b b: c: Reb
  32. qui sl datum
  33. dAL
  34. AL = 8d: b R YI = yd :b LX yc : b aYL = yd: b
  35. Honc quia GL+ YL - W, fiet 3 +dy = b W seu y - bu -c8,. d
  36. et quia AL+ LX = x fint de +cy = bX seu ddg + beto- cc g = bd X
  37. seu bb + set - bdX son X = W + b, :d
  38. y = b0 (seu B ) fiet y = bW (seu YAI) - e C seu MX)
  39. X= CW (seu (N) bg (seu AL)
  40. qui valor substituendus est in aequatione data ead Conicam
  41. 2CX + yx = yy. fint 2ab
  42. 2bh + 26Z
  43. lb. Ce - (eb si eili
  44. rou. + bb 9 2 be 9W 18
  45. - bb W0lv Cc be 8W
  46. +2CV
  47. abe sqa ) gro tii i ytbr . ) u
  48. 19
  49. bb+ cc = dd. ob triangula
  50. eXt: Y L= +(
  51. similia AGL et YXL fit P: GL - 9c. b Cer CY AL- g d. b
  52. ec Le
  53. eYZ, v. fiet 8Y = AG+ Z, seu eua
  54. et A4 = GH+ HZ seu 8 = Z+ h, erit
  55. 2CW =
  56. 2b9 =
  57. 2c9
  58. 19 q d
  59. haec aequatio identificetur sequenti generali 5)
  60. ab + mZ + nv + p ZB + r 77 + 5 v0
  61. foret prolixior justo, ideo
  62. faciemus v- id-g et
  63. o sed quia is calculus
  64. in hac pltima aequatione ftus Comissa penultima quasi nunquam caliulata esset
  65. mk
  66. metnu
  67. ip asho abto
  68. 4b
  69. e a late
  70. W - v+ g
  71. et de
  72. sit eg= q af
  73. ee = bb +cc
  74. in

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 31r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0061?run=74