Leibniz Legible

Machine transcription of the Leibniz Nachlass

Search the Nachlass

Leibniz-Handschriften zur Mathematik LH 35, 13, 2c, fol. 4r

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: 0.75.

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

The machine reads it as

  1. sit aequato angentialis vedut dy: dx = yy+ xx, : aa
  2. fiat X: a = dZ: du et y: a = dv: d0, et fief
  3. ddv: dd Z = d2dZ dvdv + dZ dZ 3: deo dec et dco = S(a vav. +dq d Z : da vil1
  4. ponamus de esse constantem, et faciamus (post tot alia irrite tentata.
  5. da = dv (ddz dZ fiet dae di: (d v: d2) ddque + ddv. sddZ: dZ = 0 seu sddz idZ = - dx dd
  6. et deo =- ded v adZ: dZ d2 Unde (dv: dadZ) : iddx ddx
  7. et tandem dv. = dudvdZ dZ + d7
  8. 1 da
  9. avdv +d ZdZ3:, dar 2
  10. Td2
  11. quae aequatio est
  12. poteramus et facere. da= salZ, sed hac illud brevius
  13. poteramus et facere aliud quiddam, oeib. gr. ei =d b Sadzi d2 sed illud brevius
  14. tractabilis
  15. idem est ac isi fecissentus y: a = P: (dd7. 4Z et X. a = dZ: de sadzi Z
  16. et deiZ dae (ddZ: dZ constantem, ita fieret
  17. dy: cx = Z: d2 qu sddqe. d 7: ddZ: sda Z. Z = - dv : dqu (d z:. d c
  18. = dodv + dZdZ,: dudv (qu) sdtz. dt
  19. jam f
  20. jam fZ ddv sdaZ. dZ + (dv: dZ) adZ seu Sdd7: du = - du odque - dvaldus itqalla
  21. p
  22. quo vabore subsoituto fit dvidque = dedx + dqudqe,: + a v diZ. d2ddv. seu
  23. du d7d7 dedr + d7 = adv: ddzue ut ante.X
  24. seu
  25. ddv: sd Z = (d v dZ):, duav: d2 dqe + 1 du: dz = e: a et fiet:
  26. ui
  27. ddv: daZ = et: e aa ee + a Ergo ddz: 1Z = de, :, (C:, aa eet a) - e: a
  28. siu dez: dz = aa ee + a, de: et - ae - ac
  29. 17 = deo X: a, ddz = dco dX: a, et fiet dx 3X = Adzue. d2
  30. dued lco: dv = yeca 2= (ddZ: d7 daret y3a = )dX: X, quod non licet
  31. X lg: ax = XX+ y9,: aa
  32. 3 = y: a = Z. v rat
  33. gi a = vZ: aa et X: a = YB + ZZ: aa fut
  34. tiel dy : dx =
  35. vdque +Zdv vlx + 27dZ
  36. qoia
  37. XX = R +eX Y pIIX + 2, y,: g
  38. 30ca LSHXF3Xy
  39. X: a =
  40. yy 3 = 201 a + 21X + 221y
  41. u I 301a + 311X +321y
  42. a
  43. _ XN S0 x yta 3: a = 6 60 101 + 4 110X + 101y 0
  44. dy 3a. 8dC - Cd8
  45. dx
  46. 9d5- D a
  47. 110 dx + 10c dy
  48. 210 dX + 201 dy
  49. 101
  50. (d
  51. ∞
  52. X = 201 a + 210X + 201y = 2
  53. 2014 + 310x + 301y 4 1
  54. (d+ V
  55. X
  56. y = 0
  57. 3004 + 310 X +301
  58. X = D
  59. 2
  60. 8do . C7814 = 700+D + 9 DDdD- DECAY- D13
  61. tat 29fy d8 = 900d e d+8 = ( - tl)
  62. seu ag= C dD: Y sd msque 740 = 8 3γD = DOCdZ -V d
  63. 459 NdO DD+
  64. possumus facere aeqsation srle onduas y panere parte
  65. fit de
  66. si du soustans erit et nodx+ yydx couslans
  67. ponere constantem
  68. et fiat O = Xxadx + 2X dxdx A Z yyddx + 2ydydx
  69. dlyaa = xxdx +yydx
  70. Xa = y: g = x: 2
  71. X: a = dv: d2
  72. d dy sa vag 5 de- vaZue Z2
  73. de
  74. =aZaV d∞d13
  75. n
  76. d
  77. XXXyy, : aa = Z: a 2X dx + 2ydy,:, aa = dz: a
  78. l’av
  79. aadu - gydx = XXdx sit X = Z.7 fint d = yd Z- Z ly: 9y
  80. aaous p Ergo Hd G dus - y dzu X Zy dys = 2 7yd3- 7dy
  81. g: a = Zpr: t X a = +: F dy: dx = plae -vat, :, + 42- Zc+ -∞v + Z2,:t
  82. Lde+ Hva = tordz + +Z247 - Zrnat - y3d +
  83. X: a = 7+ v ia
  84. Ria = (X
  85. yia = Zv: aa dy: dx = Zdv + vdZ = Z2vr
  86. 312+ 31V + 30a
  87. a, 312+31V + 30a

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2c, fol. 4r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068199:0007?run=74