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Phoronomia, Sive De Viribus Et Motibus Corporum Solidorum Et Fluidorum Libri Duo, fol. 269

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: 0.90.

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  1. DE VIRTBOSETMOTTDVS CORPORDM. LIB. II. 269
  2. S CH OL ZO N.
  3. 467. Flaec propositio plurimum conducie reductioni elemento.
  4. rum sectorum tiyperbolicorum ad simpliciora elementa l0g. mica. Nam
  5. si AO =a; OD = m; OR = X; EB = Y; AF = Z, _E AF =11. AF.
  6. que his positis, exit
  7. T. y = V (∞∞ = aa), AF = aV (X∞ =aa: XX); adeoque Ff = a’ dX:
  8. vaer (xX = aa), e FFI. TTB = a dX: XaV (∞∞ = aa). Inde quia trianq.
  9. BOB: Friang. FOf =OFE: OA, reperietur duplum trianguli BOB =
  10. aadx: V (XX = aa). TIOC ideM BFCVIUS inVentum FIISTCE ODC RUM. IV.
  11. S. 466. uti ostendimus 2. BOb =OT. b0; nam b0 = ad∞: V (XX = aa)
  12. ec OT = aa: X, ergO OT. b0 = aadX: XV (∞X = aa) = aadX: V (X X -
  13. aa). Ta KHI = (aX = aV (XX = a4)): X, ec CFI vel OT = aa: X;
  14. atque triangula RHICBE KOD similia TUnE, erGOm =aa: X - V (∞X -
  15. aa) ec x = (aa L mm): 2m, qui ralor substitutus in praecedenti ex-
  16. prectione elementi BOB, producet 2BOb = aadm: m.
  17. TI. Ouia x = a + W _ dx = du, crit 2BOb = aadx: V (∞X = a1) =
  18. aadu: V (2aW = Wn), X W + a = (aa = mm): 2m, vel W = (M = a 2: 2M,
  19. qui ralor in Formula aadu: V (2au = un) suffectus, dabit iterum
  20. 2BOb = aadm: m.
  21. TTT. Propter triangula similia OAF _ OFB invenietur ay = XZ,
  22. hyperbola vero praebet y = Y (XX = aa); unde ∞ =V (aa - 2Z), CX
  23. criangulis vero similibus XTTCI _E KOD elicitur am -mZ = aV (aa
  24. =22) X Z =amm -- a: mm + aa, qui ralor ipsius 2 ejusque cle-
  25. menti ad2: aa = 22 = 2BOb substitutus, dabit etiamnum 2BOb =
  26. aadm: M.
  27. Similes regulas reducendorum sectorum hyperbolicorum ad lo-
  28. sarichmos ex lua methodo generali reducendi quadraturas curra-
  29. rum, quarum ordinatae Fractionibus rationalibus per abscillam rarie
  30. affectam ex datas, exhibitis exprimuntur, ad logarithmos, jam pri-
  31. dem elicuit Vir Celeb. Joh. Bernoulli in Comm. Acad. Res. Scient.
  32. Paril. 1702. d. T3 Decemb. e in Act. Lipl. 2703. P25. 30. _c3I. Cdetc-
  33. rum, et si praecedens theorema nostrum de lirperbolatantum requila-
  34. cera agit, paucis tamen mutatis ad quascunque hrperbolas Potest
  35. extendi.

Cite

Phoronomia, Sive De Viribus Et Motibus Corporum Solidorum Et Fluidorum Libri Duo, fol. 269. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/1066518432:0297?run=74