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Leibniz-Handschriften zur Mathematik LH 35, 13, 2c, fol. 12v

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: 0.77.

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. 13r); this page is its left half.

The machine reads it as

  1. ay: dx = xx Fgy: aa seu gy: aa = dus : dx + xx: aa et y = Ysaa dydx + Xx da dx)
  2. Si ly=
  3. a dxdx
  4. ...) +
  5. aa dyadx + _xa LX ddue + 2X dx + 2 xx dx lx
  6. 2adx YC,...)
  7. Aax dax (uas X FXptnlx)) (Taa yrelutl -. aa dxddus lx - 2X X dlx ( 2. X . t dx llx)
  8. alte
  9. qu aa Aysd dex t aa (lx dx ldys + 2x d P + 2 X Xdatx) ddx
  10. aadysdx xxdxdx
  11. a dy dxd ddydax.
  12. 4qu (aatdy ddx + aa dxdx ditus + 2 dx + 2XX dx dx dd x)
  13. 4, aadydx + Xx dxdx
  14. aady = Xx dx + yydx fiot aatus aa dxdius - a adyddx exdxtxrax
  15. dxdx
  16. 2Xdx F2ydy
  17. aa d X ddys = aa dy ddx = 2x dx - y = aa dy xX du lx)
  18. 2 dxdx dys
  19. a xx dlus dibus 2 2 a dxdys dux dius - + aa x dud ddus + a du dydliexdd - 4 ca X X du Llx + 4 XX d e
  20. Paequ. Aaa dxdus = 4Xx dxd dydus 1. Compendio
  21. L12r dy3
  22. 100. + 11I dy + 2 doly +dP dy.ly F, 12 cldy + 122d dy ddy = 0
  23. ubi 100 = 4 XX d x6 et 11I = = +aa xd ddx et 121 = at ddx lax + 4 XXdX et 131 - - q aace
  24. et 100 + 110 du + 120 dydy + 130dy + 10) ddy + , 11 dy adys + 102 dy ddy = 0
  25. fiet 100 = a xx dx et 110 = ( 4aa X dx dd X et 120 = (a dox dx, 4 XX dx ut 130 = - +aadX
  26. et 101 = = 4 aa X dx et 111 = - 2a d X ddx = 0 et 102 = a d xd X ubi ponanus dix =0
  27. fiat ly = 4Z. Z et ddy = Z dazue - d7d z , : Z2 ddy ddy = 22 dd zal aze = 27 447 laZ + 424,: 24
  28. = - d7, Z -1 et dy ddy = Z 4Zd 1Z - 423: 23: 1. Et fiat jam
  29. et
  30. Z d (dZ. Z) sunuuri.
  31. peest
  32. 2
  33. =Csvix dz = Bdx ( sax 1 daque - duax b +rlxd x
  34. ind potius fit quod eodem redit pial initio tati-
  35. du vdx du = vdx, et habetur aequatio d
  36. unu 3 differentialis uno gradu altior posita ax est aute. si abest
  37. hest
  38. ba
  39. in aeq. differentio differentiali sunt quantitates dy: dx et als. adx
  40. X ddx: dxdx , et X: a fiat X. a = ZV et dy: dx = AV: Z
  41. et X: a = Sdz: Z et _ et tZ d x = asdZ: Z et dx = adz: Z et ddx = a d (2)
  42. et Xddx: dxdx = A(Z: Z) d (az. Z): (d7 dq: 22) et ddus = afi ad 2 d (X) + a 1 d2) ~
  43. e ddus: daZ = (dZ. 2) d v. Z) + d dZ. Z) v: Z 3 :, d (dZ. 2)
  44. ita tollitur a
  45. 22
  46. porro non habetur ddv. Ergo ponendo ddZ = 0, habetur 59. E differentialis ubi
  47. est x Z: V, de: d et (dZ. g
  48. idem est initro in differenticali ot dinania fiat X: a = fdz: Z, et y: a = v: Z
  49. habesitur aequatio in qua erunt v:Z, SaZ. Z et de: 4Z
  50. 2 et. = b et v - cobt fit ftz.Z) = t
  51. su vi co: t sit Z- ad dZ = 4 d Z dco: a
  52. et dys dy = L
  53. aute
  54. seu dydys
  55. scop
  56. dgrx dy: dx
  57. ded
  58. dlsa h 2do2t R
  59. d2
  60. daqu neque
  61. 1
  62. M. 2
  63. -adx

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2c, fol. 12v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068199:0024?run=74