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Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 290r

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. Va.
  2. e
  3. e e
  4. Co dy sd dus
  5. 0 ge
  6. re
  7. ad
  8. cd
  9. +B
  10. c
  11. sit
  12. Aequatio incrementalis
  13. eu CaxG. 2XXy = aaX: 3aa y - 2Xyy = dx: dy
  14. quid si faciamus dy5 = bco. seu y= acvidu
  15. Inde ex aeq. _1 per 3 fiet Ep aeq. 1. fit
  16. sublatis fractionibus 2XXydu -aaxdy = 3aa yd Exyyd
  17. Undo px aeg. 3. sit 2XX aC. du =aaxdus = haa dx qud 27a c. dx
  18. seu subtatis tructionibus fit.
  19. 2XX a co edyus
  20. aaxe dus
  21. e+ ponamus e+ 1= 0 fiet dy
  22. et
  23. +
  24. (6)
  25. 8.
  26. e
  27. ayre
  28. haa dxaco dy- 2Xa dxco.
  29. o et exegue scet
  30. et in aeq.6 supererit tantum seu du seu tidy
  31. a
  32. e
  33. 3 et proindi exaeq. 6 fiet fiet dy et 1) = 1 et
  34. A
  35. co
  36. a 2xxaco- et ex ag. 6 divisa per co fiet
  37. 2XXa
  38. a
  39. ed - aaX = 3a dx - 2Xaadx. q et
  40. ay
  41. sublatis fractionibus fat
  42. codu
  43. leV
  44. v
  45. 2XKa cody -aaXedco = 3a dx deo - 2X da dx dys
  46. seu dy = 3a dx aed + aa Xcoco
  47. ZXX a C + 2Xa4dX (11)
  48. Et quidem ex aequ. 3.
  49. ob aeg. 7. fit y = dy a: ed
  50. adeoque du ddus a: cd. vided autem aequationem
  51. nihil nobis prodesse. sed potius ex aeq. a descendendum
  52. esse ad differentio differentialem; di et deinde epe nova
  53. aequaddn lodendam X ut solum restet dx inde habebimus
  54. ade caeterum
  55. ia = dx: dy de dX: dus = Adx dy = dx deus; dus = dZ: a
  56. Ergo tdx idu - dx ddyidu
  57. (4
  58. dz: a
  59. si esset ydZ = constanti aco ter e =Z7 - 5c
  60. assumatur relatio talis inter exidus et dy: a aF
  61. denique daz: a (sea houm valores ut ea supposita
  62. aquatio reddaturtractabilis, et uuc absolute talis erit
  63. verte.
  64. conu

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 290r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0575?run=74