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Leibniz-Handschriften zur Mathematik LH 35, 13, 2c, fol. 134r

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.

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The machine reads it as

  1. 101 + 11 X X = 12 Xdy
  2. iy
  3. 3dus ydx
  4. sit WXX = 20 +2) X + 22Xy + 23XX et diffecentiando 214X + 2Exdus f 13Xdx
  5. 1
  6. jy
  7. fiat 10= 21 = 10 et 22 =11, et 23 = 4, 12
  8. 9 = 20 F21 X + 22Xy + 23XX + 24XXy + 25 X + 26XX yy +27 X3y +28X, + en
  9. differennti
  10. audo fit
  11. y3
  12. sit aequatio.
  13. Xgy
  14. yd ydy yydx
  15. diffecea tialisdata 1 des + 12 X ly YT3 x dx + 14 XX dy + 15 X
  16. 12
  17. Xy
  18. iy ydx gdus. qydx
  19. dy
  20. gydy gyxex
  21. sit aequatio differentialis Homoepplota data
  22. yax
  23. Sstay
  24. 100 dx + 110 Xdx + 101 X dy F 1IIXy dx 4 120XXdx + 102XXdy + 121 XXy dx + 112 XXydy + 139X dx + 103 Xdy + ey
  25. dy
  26. dy
  27. yydy
  28. y dy
  29. ydx
  30. yda
  31. yydus Xyydx ydus yax
  32. sit aequatio ordinaria assumta
  33. 200 + 210X + 21I Xy fl 220 Xx + 221 XXy + 230X + 222 XXyy + 231X27 + 240X, + et
  34. Xyy
  35. quam aequationem differentiando fiet
  36. - 20 dx +A 22oXdu 2II XaG +, 221 pydx + eX
  37. ily
  38. 2) dx + 22xdy 1 23Xdx + e4Xxdu +2. 24 X ydy + 25 XCdx +26. 2. XXydy L27. X du + G,. 3XXydx + 28 4 X dx , et
  39. dy
  40. dy
  41. ydus ydx
  42. dy
  43. 4y3
  44. 221 Xdy + 3. 231 XXydy F 2. U2 X KyL, + 25)OXd. F 31X dus
  45. 3. 230pp dx
  46. gydu
  47. gydx Kyydx
  48. Xyyax yay Vx
  49. O = 100 220=110 211=10) 221 =111:2 =102 230 = 120:3 231 =121:3 =103 222=112.2 240 =130:4
  50. sit aequalio dydoi dz = ZZ + vv,: aa Fial Z = xty et v = xyi fiet dZ = dxtdy et do = xdytyax.
  51. et habebimus xdus +ydx,: adxt du =9a (X X + 2Xy F gu) + xxyy: a, seu fiet
  52. - axdus lgax aaxX ax FaaXy dx + aagydx F XXyydx.
  53. odx
  54. da yy dy
  55. dy
  56. du aa xxdy
  57. 210 = 220 =190 = 0 211 = 101 = - a 221 =111: 2= 2aa = aa quod est absurdum
  58. coincidentia aequationi
  59. Ergo ope aeqque. C et D tollatur au, fiet aequalio sine dus, ex, data =
  60. Hoc in gentrali etiam reapse tentandum
  61. Za= X R D: a = (dx:y Z. a = fag:u dv.: dque = dx: du = qu. six: B = qu sdy: y
  62. vel salten ejus multiplae
  63. v: a = y: X
  64. XX
  65. Z. a = (dy: y fiel X dy - yax: dy = yy + qu sdy, et fiet
  66. X
  67. dy) 2Z d(+): dys - 22 d3 = qu say unde pono
  68. du
  69. du ddZ = a() d-
  70. dydus: yy
  71. CX
  72. y X
  73. 2u299 dZ - 22dd Z = 2 sdy dy
  74. an
  75. Et tollendo ay s
  76. differenio differentiatem: qua abest a. Ponamus ab eadem
  77. etam abesse simul assumi relatiorem inter X, y, dx, du,ddx, dt ys
  78. vaerendus et modus problencam a curvae ex proprietate
  79. Vangentium reduo cendi ad lineas positione datas quaesitam tangentes
  80. l
  81. 0
  82. Sax Snus
  83. yay

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2c, fol. 134r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068199:0267?run=74