# Quadric Sentence Examples

The diameter of a

**quadric**surface is a line at the extremities of which the tangent planes are parallel.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.When referred to its principal axes, the equation of the

**quadric**takes the form Axi+By2+Czi=M.Since they are essentially positive the

**quadric**is an ellipsoid; it is called the momental ellipsoid at 0.A curve of the second order is a conic, and is also called a

**quadric**curve; and conversely every conic is a curve of the second order or**quadric**curve.AdvertisementIt is to be remarked that an equation may break up; thus a

**quadric**equation may be (ax+by+c) (a'x.+b'y+c') = o, breaking up into the two equations ax+by+c = o, a'x+b'y+c' = o, viz.But it is an improper

**quadric**curve; and in speaking of curves of the second or any other given order, we frequently imply that the curve is a.It is a leading point in the theory that a curve in space cannot in general be represented by means of two equations U= o, V = o; the two equations represent surfaces, intersecting in a curve; but there are curves which are not the complete intersection of any two surfaces; thus we have the cubic in space, or skew cubic, which is the residual intersection of two

**quadric**surfaces which have a line in common; the equations U= o, V= o of the two**quadric**surfaces represent the cubic curve, not by itself, but together with the line.He next gives by aid of these projective rows and pencils a new generation of conics and ruled

**quadric**surfaces, "which leads quicker and more directly than former methods into the inner nature of conics and reveals to us the organic connexion of their innumerable properties and mysteries."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)?AdvertisementSimilar results hold for the three-dimensional case, with a

**quadric**surface.