Sentence Examples


  • With the values above of u, v, w, u', v', w', the equations become of the form p x + 4 7rpAx -Fax -{-hy-}-gz =o, - p - dy+ 4?pBy + hx+ay+fz =o, P d p + TpCZ +f y + yz = o, and integrating p p 1+27rp(Ax2+By2+CZ2) +z ('ax e +ay e + yz2 2 f yz + 2gzx + 2 hx y) = const., (14) so that the surfaces of equal pressure are similar quadric surfaces, which, symmetry and dynamical considerations show, must be coaxial surfaces; and f, g, h vanish, as follows also by algebraical reduction; and 4c2 (c 2 - a2) ?
  • The diameter of a quadric surface is a line at the extremities of which the tangent planes are parallel.
  • Acf aZpa, a ball or globe), in geometry, the solid or surface traced out by the revolution of a semicircle about its diameter; this is essentially Euclid's definition; 1 in the modern geometry of surfaces it is defined as the quadric surface passing through the circle at infinity.
  • The physical properties of a heterogeneous body (provided they vary continuously from point to point) are known to depend, in the neighbourhood of any one point of the body, on a quadric function of the co-ordinates with reference to that point.
  • Same is true of physical quantities such as potential, temperature, &c., throughout small regions in which their variations are continuous; and also, without restriction of dimensions, of moments of inertia, &c. Hence, in addition to its geometrical applications to surfaces of the second order, the theory of quadric functions of position is of fundamental importance in physics.

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