Sentence Examples

  • The determination of the true relation between the length of a pendulum and the time of its oscillation; the invention of the theory of evolutes; the discovery, hence ensuing, that the cycloid is its own evolute, and is strictly isochronous; the ingenious although practically inoperative idea of correcting the "circular error" of the pendulum by applying cycloidal cheeks to clocks - were all contained in this remarkable treatise.
  • If G was above M, the tangent drawn from G to the evolute of B, and normal to the curve of buoyancy, would give the vertical in a new position of equilibrium.
  • (12) Along the stream line xABPJ, 4) =o; and along the jet surface PJ, -1 >49> - oo; and putting 4 = -irs/c - I, the intrinsic quation is irs/c =cot 2 nO, (13) hich for n =I is the evolute of a catenary.
  • Apollonius' genius takes its highest flight in Book v., where he treats of normals as minimum and maximum straight lines drawn from given points to the curve (independently of tangent properties), discusses how many normals can be drawn from particular points, finds their feet by construction, and gives propositions determining the centre of curvature at any point and leading at once to the Cartesian equation of the evolute of any conic.
  • The envelope of this last equation is 27ay 2 =4(x-2a) 3, which shows that the evolute of a parabola is a semi-cubical parabola (see below Higher Orders).

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