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Lectures De Potentia Restitutiva, Or Of Spring, fol. 20

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: 0.89.

Original at the GWLB · Page image · Annotations (IIIF) · Download text

The machine reads it as

  1. Etie porvers, that is, as the RoOE ot the porvers im.
  2. prested, and theporers imprest being asthe Praperi-
  3. um or he excels ot the Triangle or (quare OE the
  4. Wrhole space to be pastabore the lquare oF the space
  5. vetunpalled; it uxon the Center A, and (paCC AC
  6. (C beins che point trom wrhich the Springis suppoled
  7. let 90) a Cirole be describedas C OG F, and ordinates
  8. drarrn From any point ot C A thc space to DC Past,
  9. a5 From B, B, tothe said Circle, as BG, BC, chele Lines
  10. BC, B C, Will represent the Velocity ot the Spring re-
  11. turnins EromC tOB, B, ec. the Paid ordinates being
  12. alivars in the lame proportion ith thc Roots ot the
  13. LFAPCZILIS CDE B, CD EB FOr putinS AC =
  14. t0 a, and a B = b, B G rill alvays bc equal to
  15. L a2 =bb, the square oF che ordinate being alrays
  16. equal to the Rectansle oF theintercepted parts oF the
  17. Diameter.
  18. Hlarins thus Found theVelocities, tO Wit; BO, BO.
  19. AF, to lnd thetimes correspondins, on the Diame-
  20. ter A C dram a Parabola C HIF Whole Vertex is C, and
  21. irtrich passeth chrough the point P. The Oordinates
  22. oF ehis Parabola BII, BII, AP, arc in the lame prO-
  23. vorcion with thc ROOtSOFthe spaceS C B, C B, C A,
  24. then makino OB to HIB as IIB to IB, andchrouoh
  25. thc points C IIF draming thC CUrVC CTTTE, thC
  26. respectire ordinates oF this curre BaII represent the
  27. Proportionate time thac che Sprivs spends in re-
  28. curnins che spaceS C B, C B, C A.
  29. TE the porvers or Stiftnels oF the Spring be greater
  30. than wrhat I betore suppoled, and theretore must bc
  31. expressed by che Priangle C dc A. then che V elocities
  32. ils be cheOrdinates in an E Iliple aS C7 y N, oreater
  33. thon ehe Circle, a5 it will allo if the porver bc the
  34. Came, and the bulkmored by the Spring belels. Then
  35. villthe S. like Line oF times meet ith che Live A. F
  36. et a point as X within chepoint F. But if the porversot
  37. the Spring beeakerthan Isuppoled, thenwill C scc
  38. A seprelenE the POrerS, and C y yO the FIipHS OF
  39. relocus.

Cite

Lectures De Potentia Restitutiva, Or Of Spring, fol. 20. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/859264114:0026?run=74