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Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 317r

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. N A. Hicprserenon quae ssue iose meligsatia invertis A int regrecendis
  2. Quaenitur dx: dys =yy- XX;, 2yX = = bx + EC fingamus:
  3. dZ Z + deo co + du 6. 20 et faciama esse
  4. 5D
  5. Z G. X et co = y. X et v = y. X
  6. quibus valoribus
  7. Substitutis in aeg. 2. ibt ex aeg. 3. 4. 5. peibt debet prodine
  8. aeg. 1. ita Tangentes inversae erunt reductae ad quadraturas.
  9. sit egoRem melius exprimamus:
  10. dx: dy = X. 9: X. ) 5q. data
  11. d2ZF
  12. C, (2
  13. quaeritur dx b: v + dZ Z: Z + deo Cd: co oita ut ponendo
  14. = (3
  15. (4)
  16. Xy
  17. et v= Xy: F y et Z = X J: X
  18. et c0 = X. y: F. y et has valores substa atque ita collendo ∞, g, co
  19. ex ag. 2. prodeat aeq. 1. porro eb +.3 est du x y dx, 1, 4 du
  20. ab ag. 4 est dz XB dx +, F XG dus ∞ ob aeg. 5 est deo d X. y dxtax. y dy
  21. et ex rofiet A pri 5.g. X 3: kg: X.
  22. F. FG. Xy
  23. do = X. 1 ∞. y ax + X. y = X y dy - X y d F. ax = X. y = X. y dy: 1 xy
  24. 1Z2 1X. + X dx + X , _ Xty dy =xiy d X. dx = x = F. 8 dy. LC X y
  25. similiter aco. Sed fortasse re im licebrt traclare bieoius, hoc modo
  26. dx: dy = a: b. de v: P + du Z: 3d + dco Co: =0
  27. sit v = m: n ∞ = p: 4 co =r: t du- a centm dx tn d ay
  28. du nam dx + n d Mdu -m dn dx - m An dy,: un 2 exaegue
  29. dy 2) 4 d dx + 4 ap dy - p d q dx - p dg dus, : 99 3. 4.5
  30. U
  31. de + dr dx + + drdy = Y d + dx -y at dus,:
  32. Ex aequo 3, 4, 5, 6,7, 8, substituantur valores in aeg. 2. fiet
  33. m: m an: nn, m:n: m: n, .. C- dm. n tumdn:un, min: m. n
  34. + d p. g- p dg: 44 p. q: p. qu (per = ap: q + p d9: 99, p. 4: p. q
  35. + dr: t - rdt: H, rot: r: F ,)
  36. l - dr. t + Ydr: H, F: F: Eat
  37. ) ay: dx) b: a ubi explicaudo m n pg
  38. ubi explicando m n p, qrt perfstmutas rationalese sounatas X, y
  39. ignificare etiam formatione cocle intequ
  40. et ponendo c et e esse signi et s et g, et et
  41. colegiam, potent fieri as explicatio generalis. Sed brevitalis causu eligamus casum specialem
  42. simplictorem, cum n= a = + = 1 unitati, tunque enim ex aequlo fiet:
  43. am m: m + ap Pd: pd + dr F: F: Bm m: m +XpE: p + = rY:
  44. dy: dx) =b: a et redudis omnibus ad coem denominatorem, fiet.
  45. e1
  46. compendii distinctionis causa, pro C, C, f, 9, n, scrib. 3, 4, 5, 6,78
  47. am m dp + d ita ut soperioribus respondeant un pares, inferioribus pares
  48. fiet: am pe apmr am npr +ap mr+ r
  49. id est tomtis assumtis formulis in p, r, (ete) ex Xety
  50. -dg: dx) = - b: a; ratimd ser interre sopiis, t rursus formuli, x
  51. item ex p, itam ex Y formatis, significalis per n
  52. quicqud in formulae in difereutia multiplicatur per dx, et in quicquod inea mullipercatur pera

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 317r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0629?run=74