Leibniz Legible

Machine transcription of the Leibniz Nachlass

Search the Nachlass

LBr. 396 · Hermann, fol. 2r

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: 0.85.

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. 1v); this page is its right half.

The machine reads it as

  1. Modus expedite inveniendi Radium
  2. Osculi in qualibet Curvâ.
  3. In Schediasmate meo de Methodo inveniendi Radios Osculi in Curvis ex Fouis
  4. deccriptis Mens. Nov. Aet. Erudit. 1702. pag. 501 inserto oblitus sum ostendere candem,
  5. Methodum mutatis tantum mutandis omnibus indircriminat im curvii applicuri posse, ea
  6. enim mediante elegans se se, obtulit Cel. Dn. Jac. Bernoulli expresico Radii osculi in
  7. quibuovis algebraicis curvis, quam singulari suxer differentiali calculo observationi
  8. acceptam refert, et in Actes Erudit. 1700 pag. 509 publicavit. Ad talem vero formulam non
  9. fucile quis quam nisi vira prius Bernoulliana formula, trita via aut reapre pervenit, aut
  10. perventurus videtur. Et si Celeberr. Varignonus voti compos factus ert, veritati asser
  11. ti mei id nihil derogabit; nisi enim Calculi differentialis suiss et callentissimus, calcubum
  12. pro ea expressione radii orculi institutum eumque latio prolixum ad optatum finem nunquam
  13. perduxiss et, quod manifestum fiet, statim atque suam analytin publici juris fieri permillet.
  14. Mediocriter contra in Calculo versati, Dium hic pra monstrandam ineuntes facllime simul et
  15. brevissime intentum assequentur. Caeterum huc obiter monebo Bernoullianam methodum
  16. ad eandem expressionem ducentem a meu toto coelo divertam esse, quod Clarissimus Ille
  17. Vir Suoloco ostendet. Verum ad Rem.
  18. Radies Osculi generaliter vocetur literà R, demonstravit Clar. Pac. Bernoulli, exeo-
  19. rentibus Curva elementis do constantibus fore tum R = deds tum etiem R = + ayas
  20. (vid. Aet. Lipo. A. 1694 pag. 264.) fient ddx = + dis ds
  21. curvae
  22. day
  23. ddx
  24. A ady = xdi. Redacta itaque ae quatio
  25. ne ad secunda differentialia, substituendi sunt hi valores dx, ddy in ea aequatione, et
  26. loco elementorum absiessu, applicuta, et curou sive dx, dy et do, eorum proportionales
  27. applicata, subxormalis, et normalis curva surrogaa, aequatio inde energet quae debite re-
  28. duita valorem epsius in puris ordinarir dabit quantitatibus. 2. E. 1.
  29. 5- 1
  30. sit brevitatis eausa equatio RX y a = 0, Unde hrx y dx + RoXy oly =0
  31. 2
  32. 1 5-1
  33. s-2
  34. ad eoque Rrr - YX y dx +RrsX y dady + hss- 5 X y dy + RrZr- 1
  35. + hsX y ddy = 0, sive hrX y ddx + hs X y ddy = R, r - rr Ze
  36. 2
  37. 1
  38. 5-1
  39. R,5 - ss X y dy 2hrs X y
  40. dadis, Unde si substituatur pro ddx, + dyds, et
  41. 1
  42. pro ddlis, - dxds
  43. A Sice +rx ly dyds = hox y dxds
  44. r- 1 5-
  45. A
  46. 2hrsX y dxdy, et reduitâ hac aequatione erit,
  47. s
  48. hoXy de ds 4 hrx y dis ds
  49. h,r-er X y de + R, 5- 55X y dy -2hrs
  50. R
  51. a yd FhidX ay
  52. ubi si loco dx. dy, d2 Substituantur
  53. y, e et p (excitentibus e et p, subnormali et notmali) habelitur aequalio in finitis
  54. prneraitus
  55. RsX. 1 p +
  56. 2, a
  57. deds
  58. R=
  59. uod si

Cite

LBr. 396 · Hermann, fol. 2r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 305). https://leibnizlegible.com/page/DE-611-HS-973581:0003?run=305