Leibniz Legible

Machine transcription of the Leibniz Nachlass

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LBr. 437 · Huygens, fol. 97v

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: 0.69.

Original at the GWLB · Page image · Annotations (IIIF) · Download text

The machine reads it as

  1. e
  2. Nolanonet
  3. captea.
  4. signom
  5. Tractoria
  6. sit filum AK, cui annexum ponduslk. sit AK affixum regulae
  7. AT. et applicanda ei manu, cum pars fili AT applicata erit ad
  8. regulam, reliqua TC erit tangens curvae cC applica tractionenter
  9. F= ydx: dys et
  10. applicandum descriptae, quaenitur curva cc
  11. X BC, y AH seu AT+ TC =a
  12. AT = X + ydx: du TC = _ sax +ay: du. ergo fiet =B.
  13. sit X - a = Z C et dx = de
  14. AB
  15. + ydx: dy + y saxtd: du = a
  16. 7 +ydz. dy +y dx +y . dy. fiet: ZZ + 2Zyz. dyf yy z: dyt
  17. gy +Z: dy) + yyale fiet ay. 4 = dz: dy = - , Z: + L y. Z
  18. 2
  19. V
  20. quy + (3 = = 1s
  21. es
  22. il
  23. jam
  24. l
  25. 2Zdy + 2ZY dZ = yydy seu L
  26. Si y=o occurret curva axi in BV. et firt y =0 ergo b = 0 itaque
  27. d
  28. 7yd = y s seu 32 = = 377 = 9y Ergu y = Z73 sed hoc est
  29. seu
  30. idetur enor oriri a signis. Nam quia crescentibus
  31. impossibele, ut linea CC sit recta
  32. ost 2dp
  33. uel x decrescunt y; videndum an non scribendum sit ideo non licet facere
  34. s
  35. yyu = 1y dus + 22yd7. sit enim ZZy Clee
  36. gyy + (
  37. (y) =
  38. nam
  39. 77+ 23dZ + 43, y - dy = L
  40. r21
  41. 7Z y) + 28y d7 - 22 dy (- ZZy)
  42. Hoc ergo exemplum
  43. A
  44. Alterum oportebat, vel initio pro
  45. l
  46. Ls
  47. qu
  48. du scribere- dy. vel si voluimus et considerare, ut quantitatem
  49. summe notandum.
  50. osolatam)oportuit ejus quantitatem considerare in differentiant
  51. Redesimus ad aeq. dZ: du = FBY - 2. sit y.qa ora setu
  52. b: y = v: a fiet dz: dy = a : 2V - b:3a Ergo dy: Y = duta
  53. e
  54. dv: a: afEx. - v: 2a = v: a (nam sit, Z: y = V sit Y du: y + Zdy: yy = d0
  55. Et
  56. seu dZ: dy) + v_: y = dv: dy seu _1: 2 = v: 2 Fv: y = av: dy.
  57. 1
  58. duidus Ergo dy: y = dv: 4: 20 +v.2a: a
  59. s du. y = seu dy: as = 2 + AV: aa + vo. itaque haec curva
  60. ergo
  61. paveniri ex suppossita hyperbolae quadratura
  62. P.
  63. AB, (X BC, y AE, a EC b san constans AFZ; EFV
  64. ZZ+ vV =aa
  65. BF seu CG = X- Z EG= x + 27 - 2XZ + v0 + yy - 20y = aa bb
  66. 13
  67. u seu IXX +gu = 2XZ - 2∞y + ad = bb, si a = b fiet XX+ yy = 2XZ- 2V9 =0
  68. a
  69. sit porro. dy: dx :: - V:X - Z fit dyx - dyZ = vdx = ydx fiet
  70. = Ed X = vdxidu +ydxidus = EN X. f y9. 2X. - vy: X. Ergo
  71. et
  72. it
  73. lat
  74. d
  75. y: 2 - yy. 2X +ydx. dus. dx: due - g. . Ergo At
  76. pqu Xdx: 2dy _ f. 2D (+ydx: 2 hyy3. 2∞-yfy.9
  77. dx : dy = H. X
  78. ne
  79. RXy seu Z = KX dx = gy dx - 2Xydy3 :, 2Xdy - Z y dy un
  80. 3 29
  81. dx ( yydX: X Ey
  82. v = XXdy -yydy +2Xydx 1: ,2∞ dx= 2ydy. Restat Z+ e= aa
  83. ita habetur li aea, sed panto protigur. Nempe
  84. Ammnuneue
  85. 31
  86. e
  87. +-
  88. 2
  89. e
  90. 1 2 X.
  91. e
  92. E
  93. +
  94. 1b
  95. 2
  96. et
  97. ee sit
  98. XH
  99. tu tit
  100. egayau
  101. rxerius

Cite

LBr. 437 · Huygens, fol. 97v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/DE-611-HS-3595205:0200?run=74