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Leibniz-Handschriften zur Mathematik LH 35, 13, 3, fol. 104v

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

One image of two folio pages side by side, registered by the library under both labels (also fol. 103r); this page is its left half.

The machine reads it as

  1. dax p d X seu ddx d X
  2. seu ax est media proportionalis
  3. inter x ddx et ordinariam quantitatem
  4. Generalibenta Habebit calculus.
  5. dx (1) O
  6. 3
  7. fiet dx D e iu C et ddx D + dx d D,, ddy c, dydo
  8. est esto autem dD dx +,dus et de ndx + pdue
  9. ergo fiet: ddx D C d,, d
  10. dyX p y+ ly. X+, dx D ddx -Bddy _ p - l d. X m axdy + n dy dx + p d’y
  11. est autem d du p dZf ds D e C d, Dar d0. + do. 0
  12. est autem Od Ddx Y Dddx + d D dx O, Ddx + Ld xt cu x
  13. ld X+mdxdys
  14. Ergo fier: ddus i) ta de ApDaxdus. 70D ddx fl d x Im Oax dy
  15. at supra H per 6. fiet. ad y si D ddx + 1d + maxdus = ndydx - pdy
  16. : Ergo hos duos valores aequando habebimus:
  17. = n D aex f pD dxdy = 0Dddx + 10 dx + mo dedque
  18. aluo
  19. d
  20. HOD ddx + lO d X + mO dxdys = nO du dus - p 0 dr y
  21. seu. An D L pro du substituatur valor D dx. et pro vater d 4 X
  22. +10
  23. fe
  24. - 10
  25. et sublatae erunt omnes differentiales ipsis y.
  26. nempe fiei.
  27. fn D d X f pD ~ x +10 d x = fm D dx
  28. +
  29. -
  30. I + OD ddx
  31. Unde patet aequationem esse identicam, s si fiat-
  32. nam et in equ. 3. et 10 latent amphiboliae. Ituque non
  33. potest to possunt tolli omnes difserentiales
  34. a
  35. satius ergo fi in aequ. b. tollamus solum diy ope dldys.
  36. fier enim: 5 d dx - C ddy p, + l d X - m d. X dy (+ p D dX
  37. eu landum an oste
  38. pdx +n dx dy 0.
  39. dy. ddg. dddus etc.
  40. simplicium nec ad potestates assurgentium tolli possint, omnes
  41. potentiae ab y. dus. ddgs. ex. Hoc enim Cfedd denique
  42. haberetur aequatio in qua qualibuscunque existentibus terminis
  43. ipsius f, fiat: dy ... + daus . . . + dddys .... erc. x
  44. ita enim posita y progressionis seometricae haberetur, y per quanti
  45. finitam
  46. per aquationem rationalem ex solis X. dx. ddx. daux et c. et
  47. norum potentiis. vel potius haberetur sacillime ex serie infihus
  48. ipsius Y. surgendo ly. dags. Cc. poncudoque dxsa. undle dax 0. absolu
  49. sed dubito an res sucedere possit. Res eo redit quomodo terminus
  50. seriei haberi possit ex numero terminorum antecedentium, et diferentis
  51. ne differentus differentiarum dc. si seriei ipsius.
  52. da D
  53. 4) 3

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 3, fol. 104v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068200:0210?run=74