Leibniz Legible

Machine transcription of the Leibniz Nachlass

Search the Nachlass

Leibniz-Handschriften zur Mathematik LH 35, 8, 9, fol. 4v

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: 0.82.

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

The machine reads it as

  1. sit dy ydx +Xdx fict Y- fy dx
  2. caeterum nombire est alium adhuc calculum potuisse institui
  3. locoquan
  4. in ag. 4 non substatusen sem substituissemus valorem ipsius y ex aegl.
  5. ad valorem ipsius u ex ipsa aeq. 4, ut in ag. 3. subptis semsubstiferimus
  6. 1)
  7. exsagu
  8. valorem ex ipsa aeq. 3.
  9. Nempe faet lobaequaro
  10. y x x+ LXX+ X+ X+
  11. 113
  12. et rurjus in aeq. 18 emisubstituendo aeq. 18. fiet
  13. 1.28 S.
  14. k. dx
  15. 2IX + LXX + F+ 1 X + X + X eu. et ita hocmdo
  16. 1.23 b2.38 1. 2. 3, 45 1. 2.3.4.5.
  17. 12.
  18. prodit eadem prorsus aequatio quae per viam priorem
  19. umamus aliam aequationem
  20. dus = ydx + XdX. seu v= =X + Sydx. Et semisubstituendo in aeque 2 exaya
  21. fit y = LXX + L X + Sydx dx. Et rursus semisubestiluendo in aeq. 3 ex g. 2. fit
  22. 4)
  23. ZXx + L9X+ X +Sydx dxde et ita porio.
  24. 1
  25. Ergo habemus problema solutum. Nam quia posita BY X= sdZ
  26. e
  27. quae est aeq. 2
  28. est fera raculi scedentis
  29. ita
  30. (
  31. est per rq. 2 et 9 calculi praecedentis et q hujus vagx C-E+y.
  32. fiet utique y = 7 - x, posulo Eberi bore R ad , ut num
  33. posito 1+Z habere se ad X, ut numerus ad suum logurithmum ob aeg. 5.
  34. Hinc si sit du = Ydx + dx + xax + X dx erc. semper solvitur problema
  35. dy:dx = y4 N. semper solvitur
  36. per loganthuos. Sed si sit generaliter talis aequalio per Hyperboles quatraterom posito
  37. du a+bxicuFaxCf ec = dx L= mx tnyEppEgru e (esse rtiona
  38. cribere poterimus sic du fnium se dy- D+x.
  39. per x
  40. sBn
  41. si sic dy = dX + (X dx + X dx erc + yax + m y ex + ny ax ere satasse similitur
  42. serviel methodus Y = ax + bX + L Cx etc + L ax+ bx + L ex + en sed 1es pauto implicatia
  43. sed sorte aliud onmodm remedium, quaerantur deq et adius, ec. Done ponento
  44. d
  45. ddx =0 perdd sit aeq. dy = ydx + my dx sirt ddus = dus ax +2 mydydx
  46. Ergo log dus = X + 2 in sy ex ab fyax = y - sy ax. Ergo log. su = X + 2mys = s ax
  47. sed hoc parum potius inaegor. An sic det de- adus: N. dus+ Emyay
  48. la
  49. differentio. Differentialis =0
  50. Hnc arte semper effici pt ut ea litera, cujus
  51. habeatur sola ab una parte sit
  52. ere
  53. iter express

Cite

Leibniz-Handschriften zur Mathematik LH 35, 8, 9, fol. 4v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068104:0008?run=73