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Leibniz-Handschriften zur Mathematik LH 35, 12, 2, fol. 172v

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: 0.80.

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. 171r); this page is its left half.

The machine reads it as

  1. Jureni supra aequationem ali ordinatae demissae ex curva eonica, ad ex
  2. rectam ex vertice intsa curvam ulcuque ductams, nempe abscissa cjus rectae, posita
  3. ert applicata ad angulos rectos:
  4. in Daita sectione, qinvenie valorem rectae YX ex ob curva
  5. Abscissam ex axe A applicatae angulo dato, ita
  6. cum
  7. scilice ut ratio rectarum YB ad XB, sit data C ad q.
  8. Sit AX y. ex _7(+) ZB (e) datur ZB, N
  9. erit enim YB e P2ya ea + La y + a c+(+ 2
  10. At eadem YB datur ex e, data, erit enim YB C.
  11. Ergo erit X 2ya (F) rea ec.
  12. ordinandoque erito
  13. Eritque e +n 1 ya + a yt rri
  14. poranus pu , Va res1 y
  15. F
  16. ea
  17. enXB
  18. uitin e
  19. n
  20. Nimis prolixus fit
  21. calculus.
  22. i
  23. 9
  24. In cuculo ex recta AX, quaentuo
  25. ipsa X+ dato angulo
  26. YXB seu 2B r1 4
  27. at AX 4y. XB, jC.
  28. 2ax (F) 2ac a X
  29. Cum detur YH ad YB dabitur et
  30. X4 YX
  31. YB nempe ergo et BC
  32. datur pono et X XE a - X. ergo et EF
  33. dato datur FY juncteq FY et
  34. FX, dant YX, quaesilam, 1d
  35. re apse excquamur:
  36. AX A X. YBB E XEp, a- X
  37. +B
  38. ex L YeM Ergo XBBC.
  39. Ergo YB ec o3 Y
  40. Ergo YX res
  41. L 1deC+ e
  42. YB H. 4 Ergo
  43. AYC -XC4
  44. XC B SCA Ergo Fx 9a -X4 X que quet ac = XC
  45. En
  46. set qu Data FE, datur jam FY estqu a a Aep. 8. l N - aY O + er o -rat An + 8no 4n Bah+ 2n B k - anb g
  47. Ergo YX, hoc est FY +
  48. +
  49. VX, 1) S a a - 2aX +
  50. eet qu
  51. Substituatur y habebimus YXN
  52. Sc+qu
  53. +4
  54. ent Lee
  55. + 4a - Xq
  56. Si loco a - x,
  57. X ad g+ C+ qu, C
  58. pro a ponatur b ut in alto Aqualio re maned = + 4
  59. et pro 2 ponatur y
  60. 4
  61. et )a () ZC +n ri2ya
  62. ) +
  63. Unde fiet XB7 Eya ( ran +a 44y rn
  64. et FE p
  65. ac
  66. +a
  67. 1
  68. + ay + 2a y
  69. Sc+
  70. quadrando, et ordimando tiet + 2a y +2a 1) = b 29A
  71. P A q erqu
  72. 4
  73. et FX
  74. er cum detur BC,3

Cite

Leibniz-Handschriften zur Mathematik LH 35, 12, 2, fol. 172v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068195:0344?run=74