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Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 378r

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: 0.84.

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The machine reads it as

  1. sit Trilineum orthogonium ABCA cujus certrum gravitatis. G augeatur nova
  2. B2BrC
  3. hona basi parallela B(B) ()C. Cuius centrum gravitatis, sit 19 jungatur G9
  4. et secetur 1G19 in 2G sic ut reciproce secundum a ut ABCA, et B B, (C) B, erit G
  5. centrum grabitatis totius A, B2CA. Eodem modo trilineum A2B+ A
  6. AP ALB2C A ad datudm B3B, C=CZgna 2B3B3C2C, cujus centrum 29,
  7. junctaque 292G rursus secando quaeratur centum commune 3G, patet curvae
  8. intero alla 1B2B, 203B sint infinite parva, esse gG rectas gG, tantes ex
  9. dio medio puncto ipsius BC e ductas, esse tangentes curvae centrorum GG
  10. Hinc si sit trilineum ABC A, et in eolinea centrorum pavitalis
  11. AG, transiens per omnia centra trilineorum praecedentium ad eandem curvam
  12. et Axem et ex M puncto medio basis ducatur recta ad MG
  13. ad centrum trilinei, ea recta curvam AG fanget,
  14. videamus an hoc generali calcuo m etiam calculo Einfinite simali
  15. perdraliter inveniri possit sit cueo AB, X et BC, y. fiet Area
  16. C du cendoad
  17. momentum ex axcerit Z Syydx. itaque ex
  18. axem normalem FG erit ea v 2 syyix: Sydx. Quaeramus et momentum ex
  19. ydx et
  20. normali per verticem, quod est Sxydx. Et fiet AF = sxydx: sydx =Z sit
  21. AF, Z et FG, v, fi
  22. ob 3
  23. 28 = sygdx: sydx et Q = sxydx: sydx. Et fiet
  24. 2a∞sydx + 9G 2B9 x = gyax. seu fiet
  25. yda
  26. pydda fit
  27. 2d7 = 2dQ sydx + y dx(syydx: sydx) = yydx. seu fiet dD-
  28. n. Z Z. v = sju ax. sxydx
  29. yyde = ydx (By, ex. sa ), . 1
  30. rursus fs Xsgax = (Xydx fint dx syax + By ax = xy dx seu de sydex + yda (Serexi be h) ey
  31. seu Ex = Xydx = ydx (sxydx: Sydx): sydx. Ergo fiet do: X
  32. re x (srgix sylX): ali x sstX) (sygax. fu (X) = BM - FG,: FB
  33. d
  34. FG = V = Esyydx. sy dx
  35. X = ( sXyax: Sydx. Ergo dv: dx = 4y -
  36. FB = AB - ex t AF = x -
  37. Syydx. Sydx
  38. 2x) ax -2) dx (Spy ex sy
  39. (Xydx: Sisdx, : , 2X
  40. ut ante. itaque idem theorema calculo obtinetur, quod ex inspectione
  41. y
  42. +
  43. BM =
  44. figurae duximus. sed hoc interest, quod ex calculo aliuo facile animad
  45. pertisset

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 378r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0751?run=74