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Phoronomia, Sive De Viribus Et Motibus Corporum Solidorum Et Fluidorum Libri Duo, fol. 382

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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The machine reads it as

  1. 82
  2. A P P F N D
  3. I X.
  4. tio y = ax =aa, in qua abscisae a lumantur à centro, lemilatere
  5. transverlo existente =a, sintque tenacitates aut Airmitates currae
  6. proportionales distantiis punctorum currae a centro, hoc eAt, t=
  7. V (X L yy). FF S. 26T. praebebit r = 1: aa, et B (=ardt: td5) = 2 ∞y
  8. nec non k =Ht: a; hinc aequatio prima de =hdg: R praebebit dg =
  9. trdt: 2∞7 = 2t∞d∞: 2∞) = td∞: Y; aEqui FdN =7d5, ersodq (= t dx: y
  10. =7d5: γ = ds, Tdcirco potentix BFI, Ceu dq. Cunt ut elementa currX
  11. Bb, carum que directiones in centro hyverbolae coeunt, quoniam tan-
  12. Sens anguli DBFI inventa eAt = 2∞7: a, et haec exprestio etiam tan-
  13. sentem ansuli, quem normalis trperbolae BD cum recta ex puncto B
  14. ad centrum hyperbolae ducta continet. Propterea est hyperbola
  15. quilatera catenaria. s srarium directiones in centro hyperbolae con-
  16. currere supponuntur, uc lupra circa tinem 3. 205. Sine demonstra-
  17. tione diccum est. Pariter si poluissem dg = ds et h =2∞y: a in hy-
  18. perbola cadem, invenissemus t =V Xx L yy.
  19. Generalius, si directiones grarium conrersunt in punctum, abscis-
  20. Exeque lumantur in axe ab hoc centro grarium, crit h = axdx L aydy:
  21. xdy -yda, ec hujus ac alterius di =hdg: k opC, in suppositione dq=
  22. ds inrenissemus t =V ax L yy e 7y = ∞∞ = aa.
  23. Si directiones grarium axi AC parallelae sunt, erit h = ad x: dy,
  24. ac substituendo loco da, et dy carum proportionales n de m, fiet
  25. h (=adX: dy) = an: m. Item in requatione quarta, Currosando m de
  26. dn pror et ds, quibus proportionales TunE, AeT an: m =amat: tdn,
  27. et at: t=nan: mm (aUE, Quia Mm + nn = aa, eC
  28. nan = -mam) = - mdm: nm = - dm: M, CFGO
  29. It =I (aa: M), id CA, t = aa: m = ads: dy, ut ha-
  30. bet aequatio nona. Substicuendo isitur ralorem
  31. inrentum ipsius t in aequatione secunda invenie.
  32. tur xquatio septima, et ex hac ope analosix dp:
  33. dg = a: R, = aV: ds, elicietur aequatio octava.
  34. 5. B = adio: a
  35. 6. k = ads: dy
  36. 7. dp = ads: rdy
  37. 8. aq = ad5: rdy
  38. 9. t = ad5: dy
  39. Tlinc, ex hisce tribus ap, dq e t una data in indeterminatis curvX
  40. ee constantibus utlibet inricem permixtis. Facile inrenientur reli-
  41. quae dux, si non algebraice, laltem transcendenter.
  42. Si directiones Potentiarum BFI (unt currae normales, crit B =0,
  43. et k = a, et Pola aequatio secunda sufticie; hunc casum particula-
  44. rem Celeb. Joh. Bernoullius solutum dedit jam pridem in Commen-
  45. tariis Academiae Res. Paris. Scientiarum 1706, et nuper adhuc in
  46. Li

Cite

Phoronomia, Sive De Viribus Et Motibus Corporum Solidorum Et Fluidorum Libri Duo, fol. 382. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/1066518432:0410?run=74