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Leibniz-Handschriften zur Mathematik LH 35, 13, 2b, fol. 89r

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: 0.79.

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. 88v); this page is its right half.

The machine reads it as

  1. 8
  2. in Ellipsi sit semilatus transversum CA, q et semilatus
  3. rectum S.R (posito esse focum sit Y+ itique posito puncto
  4. quocunque P, Sit AB, X
  5. gy = 2YX - Z XX
  6. s
  7. BP, y, fiet
  8. Hinc habebitur (V, nam X fil q, et prodibit
  9. eV = 2Yq = rq = rq sit XC A, a CV
  10. semiax Is conjugatus CV, sut a, fietqus aa = rq
  11. SV = CA, nam FV + S VS = 2 AC
  12. A5. q.
  13. AB,X BP, 7 S Si S+ sit 1, fet N =
  14. = 1g9- aa vet Yqu- qu A5 = 9+ 14q - qu
  15. Si AS sit X, SR erit Y. Nam Si SK, s 3Y9 Er 1gq- qu - F 49 - 1 q uqu. qu
  16. fit X A5. Nam
  17. pro tangente Lydu = Erdx - frxdx fit dy: dx = Y - ZX,: y
  18. = Y 49 + YqV = XY
  19. DS, sit normalis ad curvam in p. jam AB: BP = dy: dx. Ergo
  20. BB = gu: dp = 2 )X = Y XX, :, - = X - xCir q
  21. 22X - XX 3:, 1 - n AB - BO - x = 2X - xx - x + E 3 : 1
  22. = Y = =X
  23. seu AB - Aqui, q X AB: BB = AT: BP - b: y unde
  24. d
  25. t = EYX YKX: 4qXx: F = y qX(:q. X) : (29X - xx (: q. X) seu
  26. B
  27. seu
  28. 4, et 2rggX - YgXX, :, 499 - 4xq + X
  29. siu A4 CA rA. C et ordinando XX CHArq) 4 -(2r94 + 49HF) X + 499 lt =
  30. + = 4y_: fg - X)
  31. aequ. 61BB: BN ex ratendum ditest
  32. -(4991 + 4 aaq
  33. +t+aa
  34. 19++ aaaque t D + a 44
  35. t
  36. +
  37. C
  38. 2t (++ +aa)
  39. arqaagtat
  40. H+aa
  41. gthaah
  42. 991F 4ggitaa
  43. X
  44. et fit x a 29tt + gaa = x =
  45. 9+t
  46. agqe
  47. aa + H
  48. =AB 29 - X = 2qua + 29+ t = 2gH =
  49. seu X = aa LH
  50. ad+H
  51. aat k, - 2aat
  52. ad
  53. WHtraa
  54. 29aa = B
  55. aa+H
  56. aa + H
  57. sa + H) 49+ d b- 4qVta a Fet 4aaqt d + (4, 9 (49t, dx
  58. et y = 29-X, F: q fiit yt
  59. dx =
  60. (2) aa+ tF
  61. 4aagt dt Et y ax = 8a gtt dF
  62. (et au + H
  63. 29a4 - 4=
  64. Blaa + tF
  65. hianculum sB CBP = Z yda CB. CB= HB -q = aatt
  66. seu dx.
  67. T2Iaa+FF
  68. 294a - qaa - +t,: aa + tt = qua q1eq aa- +C, : pa+ t1 quod
  69. dacendo in hyfit seu aati aatH fit aagt, aa- At = cBp. ejus
  70. aattt
  71. (a + H) aaqut 2tdt - naquet (ua 1) 2+ut
  72. + aa + tF, aaqatsaa - 11) - aa +H aaquet itat- aagt Caa 1F at2+at
  73. aa +FF
  74. elementum seu differentia
  75. se uaqu ( - 14) - 2 a a (aa +H) - 4 at gH. + (4nqt; Daat H
  76. 14) aa + t+
  77. = gagt (aa- tf) 2 (aa + FF) 2t dt,
  78. ser et, a g + aagt - 6a q tt,:, 13I aa + t = d. CBP cui adde ydx
  79. aq + aagH -Caegtt + 8aqtt,: (3 adt tF = elen. sest A3PA
  80. et fit qaa, a + + + 2 aa H,: B3l, aa +H seu elem sect
  81. aaque dt P9. seu BP. at
  82. fil dt,
  83. seu deniue Elementum secboris AspA: aat Huic addatur se
  84. es seu quana vocetur 9 fiat XLDdy. Est eulem
  85. ~B at. prorsus ut desiderabatur
  86. unt 2t, haadt,: (2)atEt) - ga - H, raaat;
  87. saa + tt
  88. s clega lim mus lanctae. Hia potend t haberi ser led dodio postoa est
  89. sen .
  90. elementum
  91. triansali
  92. +L gdys= (aa + t() anq. + Caa H) aag, at, (2) apet
  93. et recta CY, A
  94. parallela
  95. A I: BAH
  96. aq. CA: H B

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2b, fol. 89r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068198:0177?run=74