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Leibniz-Handschriften zur Mathematik LH 35, 7, 1, fol. 29v

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: 0.80.

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. 30r); this page is its left half.

The machine reads it as

  1. Hinc quia
  2. 2
  3. Sy dx dx aego X sydx- syax per aequ. 2
  4. et xydx aequ. est 2 X) = 2 Sxxdy. per aequ. 1. hinc fiet
  5. Sydx dx aequ. X Sydx - L XX y + L sxx dus
  6. si detur reratio inter momentum Trilinei ABC ex AB, et ex
  7. vebitur linea in quam cadit necessario centrum gravitatis iiclinei
  8. e v.y.
  9. et inter
  10. s
  11. Eit cognita reratio inter sxy dx et inter syydx
  12. Cydxan.
  13. 1
  14. quae si esset constans foret:
  15. a Syydx aequossydxdx seu ayysdxogo b sy dx (dx et rursus
  16. fiet 24y dys aequoy dx. Ergo ay aego bx
  17. sci si haberetur Ssy axax itemque sy dx
  18. idem est si habeatur relatio inter Sxydo et inter yydu
  19. Multo magis hoc dicendum
  20. Quando habentur haec mor
  21. menta, ut in Hyperbola bubi xy aequaa RCb
  22. et faciendo
  23. Bxy dx aequ aax et syyax aequ)a dx seu
  24. AB sit a.
  25. ax
  26. a+X, y aequ ag seu ay +xy aequaa
  27. aa XX aego gy. fiet aX + bxX aquyy. pet
  28. syy dx aego = axx + 1 bx3. datur
  29. ergo momentum Hyperbolae ex
  30. axe AB. Pu X faciamus Z+ 9.
  31. tret aZ + aq +bZZ + 269Z + 99 aequ’yy
  32. aZ + 269Z aqu. 0. fiet: qaequa et habebinus.
  33. aa + aa
  34. 26 4bb
  35. s
  36. ib
  37. 2b
  38. crbarnus ee +bZZ aquyg. erit 8: 27dy cenu seedus +yydy
  39. seu momentum ipsius AEFCA ex EF est- P ecy +81
  40. 10
  41. eb
  42. 5b
  43. 13
  44. 2b b
  45. yy de erit aequ 9 L eedque + = b73d. Et Nomentom
  46. ipsius AB, exAB
  47. etZ + fb23C
  48. EC
  49. Momentum ipsius BF
  50. x AB est EF est: 173y a qua si an feratur Momentum ipsius AEFCA e
  51. e
  52. exEF habebitur 1779 - 2 eey + es. Phomentum ipsius ABC ex Ex
  53. L
  54. 20
  55. possumus ergo semper rectam ducere in quam cadat centrum oravitatis
  56. portionis Hyperbolices ABC. Nam sis id certiu esset L. foret EM adma ut B ad e

Cite

Leibniz-Handschriften zur Mathematik LH 35, 7, 1, fol. 29v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068073:0058?run=73