The Quarterly Journal of Pure and Applied Mathematics, Volume 13J.W. Parker, 1875 - Mathematics |
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Common terms and phrases
action angle asymptotes axes B₁ b²)² biangular biangular coordinates body brachystochronous c²)² catenary central axis circle coefficients cone conic constant coordinates corresponding cos² cose cosy curvature curve cylinder denote diameter direction distance dt dt ellipse ellipsoid envelope equation evanescent expression foci force function given Hence hyperbola infinity integral intersection locus motion nodes normal obtained orbit P₁ parabola paraboloid parallel particle perpendicular point of contact polar poles quadric quartic surface radius radius of curvature ray-surface rays refraction refractor represents ruled surface sin² singular solution SP.HP spherical substituting tangent plane theorem triangle Trilinear Coordinates vanishing vector velocity vertex vis viva аф
Popular passages
Page 192 - Denoting, as in the corresponding problem for the free motion of a material particle under the action of a central force, by u and 9 the reciprocal of the radius vector and the polar angle respectively, by p.
Page 40 - C and 0 contains a set of points of the body which are momentarily at rest, the most general motion of a rigid body of which one point is fixed consists in the rolling of a cone fixed in the body upon a cone fixed in space — the vertices of both being at the fixed point.
Page 108 - The discussion, when и is negative, is left to the student. EXAMPLE . Express the area of a segment of a parabola cut off by any focal chord in terms of I, the length of the chord, and p, the parameter of the parabola.
Page 59 - Cycloid. The cycloid is a curve generated by a point on the circumference of a circle which rolls on a straight line tangent to the circle.
Page 221 - A uniform flexible cord, in free equilibrium under the action of a central repulsive force varying inversely as the square of the distance...
Page 225 - ... according to the law of the inverse fifth power of the distance.
Page 87 - Find the locus of a point, the square of whose distance from a given point is proportional to its distance from a given line.