Leibniz Legible

Machine transcription of the Leibniz Nachlass

Search the Nachlass

Leibniz-Handschriften zur Mathematik LH 35, 10, 7, fol. 23v

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: 0.83.

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. 24r); this page is its left half.

The machine reads it as

  1. a
  2. ex
  3. Compendio studeatur equationibus 1 et 2 neme q, co:p =co:b ut
  4. et b- nb= p+ p9 ducamus earum differentiales, ubi primum
  5. cripserimus b = p+ ap. Eexq fiet:
  6. 2
  7. + cob = cd p +n p 17, A seu ex + q p qpap+ qPa ( Co p EcipapA t p
  8. el ln
  9. ex 8q. lisenex
  10. P
  11. = eo p .
  12. ed prolixitatis evitandae causa utendum est aprtibus mei calculi differer
  13. sunt cniu nostra aequationes nihit aliud quam differertiales rectre se
  14. tialis. Nempe in og. 1. est co: p -co:b = n - q. seu est
  15. d c0: p = n - 9. jam d co: p (c d co v = d co. D-
  16. =- seu (- Co Co: p - co: p+ 2p (B) = co p + Co 2plp co p: p4
  17. sec
  18. seu dco: pr 2c(ap): p3 quod et alias ex nostro calculo differentiali
  19. (7)
  20. constabat etae et ex aeq. 1. ad inassignabiles) reformata fit 2C0 ap). p = n - g
  21. At 5g. 8. 2 e erat b -p patnb. seu dp = parnb, et
  22. fiet 2p = p9 + Pn + () sed (qun, quispe caeteris in comparabilis
  23. 10,
  24. ortasse negligi potest. jam tollamus q et n per aequationes 3 et 4, ex aequa=
  25. honibus 1, et 2 reformatis, seu ex op. 8 et 10. cum sit hee
  26. q v. seu per aeg 3. Glr dp et n- (dp)
  27. (11)
  28. ex aeg. 3 patet esse g = 1 - v. Est autem 2C18 seu = dp
  29. (14
  30. (14)
  31. itaque fiet q = dp - v. Rursus 3C2Q seu n = (d p) = se dp +ddp
  32. 2
  33. et fiet: itaque 4 + n = (dps2dpva v (+ dp + 2dp dap + ddp
  34. (4)
  35. quo valore ipsius 4 n substituto in aeq. 8. et deletis -dd p, tanquam
  36. incomparabiliter exiguii, fiet pivisisque amnibus per ap., tunc ex aequ.8.
  37. sequitur in
  38. fiet co. p N v+ dap Uende sequit
  39. casu arearum aequelaense uniformiter cresceptium v + ddx
  40. et vereor ne admisus erior, quod ap in aequ. 8. fut potius
  41. esse radiorum
  42. (ap) nempe et d et in 9. 8) pro (dp) ponendo dp + dap., fiet
  43. A Co ap4: p + fco dap: p = Z sy dp dap - Z ap V. ut autem
  44. 1b,
  45. secvetur lex homogeneorum pro eo scribatur aer, ut ( sit ipso ap
  46. homogenea, fiet; a qp: p - a e dap: p - ap dap = ap v. ubi
  47. videndum abjici oporteat a ui ddx: ps quippe caeleris incomparabile. Nam feri
  48. a
  49. inde po Nam aliquo casu contiagere posset, ut an ap: p dp V et
  50. ap dap haberent differentiam ipsis incomparabilem nempe asi dap: p3
  51. quo casu aaM et dax P: ae haberent differentam dd p; d ergo
  52. fieret sam seu tempus dapp: an = An in logaritEm p. Certe
  53. in his valde cauas esse nos oportet praesertim cumgenentles
  54. regulas constituimus quia fieri aliquando potest at in certis casibus ut
  55. eriustam sese destorautlomparabilia, quo casa supersunt
  56. ipsis incomparabilia
  57. q- dp- v
  58. n= dx + ddo
  59. na q- Eipaipo. 2 d
  60. Eo ap. P
  61. seu a piap: pd
  62. et dp adp

Cite

Leibniz-Handschriften zur Mathematik LH 35, 10, 7, fol. 23v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068160:0046?run=74