Sentence Examples


  • At infinity U = -me a cos (i = a m b oos (3, V= -me a sin 1 3 - C7,1 sin 0, (9) a and b denoting the semi-axes of the ellipse a; so that the liquid is streaming at infinity with velocity Q = m/(a+b) in the direction of the asymptote of the hyperbola (3.
  • A relation which is of historical interest connects the logarithmic function with the quadrature of the hyperbola, for, by considering the equation of the hyperbola in the form xy=const., it is evident that the area included between the arc of a hyperbola, its nearest asymptote, and two ordinates drawn parallel to the other asymptote from points on the first asymptote distant a and b from their point of intersection, is proportional to log bla.
  • The area of the loop, which equals the area between the curve and its asymptote, is 3a/2.
  • If A, B have opposite signs the form is au = sinh mO, (24) this has an asymptote parallel to 0=0, but the path near the origin has the same general form as in the case of (23).
  • This curve, bein~ an asymptote to its axis, is capable of being indefinitely proloi~ged towards X; but in designing pivots it should stop before the angle PTY becomes less than the angle of repose of the rubbing surfaces, otherwise the pivot will be liable to stick in its bearing.

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