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Leibniz-Handschriften zur Mathematik LH 35, 10, 7, fol. 24r

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. 23v); this page is its right half.

The machine reads it as

  1. superest igitur aequ. 10 ubi similiter explicari debent qet
  2. u est autem n = (dx) Ergo fiet p) ex ory. 10 si negligimus
  3. n ap seu ( apefiet (dx) fiet: p t p) = P4 seu fiet:
  4. pax = pl). Unde patet apn non poluisse negligi
  5. aequatio 10 exelicata ita stabit:
  6. 9p (ap ) = p dx = pV (F p (a p) seu B x (dp) - de = - v
  7. sinquidem (p) neglicimus, hoc est crescentibus. V = dap quando
  8. recrescentibus etiam crescunt ap secus mutato
  9. sign vel contiam secus mutato signo fiet V = dap sed
  10. lad tamen me male habent quod nondum certum adest indicium
  11. colligendi quod () (Ap) iie neglexerimus, renu restituamus
  12. et aequ. co explicata ila stabit.
  13. p) = (p ap) - p V + ap + 2dpdap + dap
  14. seu
  15. (paripad
  16. e seu pda seu pv = dp - p adp= Dupap andeferet
  17. Nam Verum jam video oquontro nec nec aliud
  18. quiddam in aequatione 2 deb
  19. 2
  20. v
  21. ret explicanda debuisse
  22. b = p + dp.
  23. negligi, nempe b - p = pg+ nb
  24. et g = dp- v et n = dp + dap. His substibulis fit:
  25. b =p (p) +(2 p dx A ax) = p) = (p ap p V f pd p + pdap (+ dp) t ap adp
  26. Et nenlecta quantitate in comparabili dp dap.
  27. X
  28. sit v= de p. Quod verum esse aliunde constabat.
  29. Et quap. jadu
  30. sunt ergo v differentiae differentiarum a radiis
  31. id vero aliunde etiam constabat ex natura impetus.
  32. pro iua aequatione
  33. co: v ecor: ( = (A p) + 2 dp dap (+ dax d p ) 2 dp V
  34. firi 4dpv = 4dpY
  35. d: pt
  36. d
  37. C p) corp dp + 16 dp fc0p
  38. seu pro co ponendo a n. fit -2a n p ap + a sp = 4 p V
  39. - + si dp = 2 p pV
  40. -: b = (pA 2pab + dp (= p): p( B +6P +B + 4pap
  41. n- 9 = (d + 2ap dap + dapF ap + 2+p adp dax)
  42. Ouneb
  43. semper pradit,
  44. YIn si dago seu Y proportionalis reciproce cubis ab a p. Quod tamen
  45. Ergo aN. 2 p + dp = p + 4 ap _ 4 ddjo p.
  46. el surdum t rem restripgit ad casum specialem Anergo non licet
  47. daas ejusdem diferentiales aquattones, in inassignabilibus
  48. quir nn alliaut uta hitat tamue ftertutenaturpe
  49. An soite non lieet
  50. hoc casu sumere
  51. u pro
  52. (B) se
  53. V
  54. ngdp dup

Cite

Leibniz-Handschriften zur Mathematik LH 35, 10, 7, fol. 24r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068160:0047?run=74