# 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. - 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. - And therefore varies as the square of the perpendicular drawn from 0 to a tangent plane of a certain
**quadric**surface, the tangent plane in question being parallel to (22). - If the co-ordinate axes coincide with the principal axes of this
**quadric**, we shall have ~(myz) =0, ~(mzx) =0, Z(mxy) = 0~ (24) and if we write ~(mx) = Ma, ~(my1) = Mb, ~(mz) =Mc2, (25) where M=~(m), the quadratic moment becomes M(aiX2+bI,s2+ cv), or Mp, where p is the distance of the origin from that tangent plane of the ellipsoid ~-,+~1+~,=I, (26) - (30) Hence the planes of constant quadratic moment Mk2 will envelop the
**quadric**a2+b2+c2~~ (31) - If we construct the
**quadric**Axi+By2+Czi 2Fyz2Gzx 2HXy = M~4, (3c~) where e is an arbitrary linear magnitude, the intercept r which it makes on a radius drawn in the direction X, u, v is found by putting x, y, z=Ar, ur, Pr. - The moment of inertia about any radius of the
**quadric**(39) therefore varies inversely as the square of the length of this radius. - 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 is of the first order, second order, third order, &c., according as it is represented by an equation of the first order, ax+by+c = o, or say (1 x, y, 1) = o; or by an equation of the second order, ax 2 +2hxy+by e +2fy+2gx+c=o, say (*I x, y, 1) 2 =o; or by an equation of the third order, &c.; or what is the same thing, according as the equation is linear,
**quadric**, cubic, &c. - 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. - It 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. - The pair of lines is considered as a
**quadric**curve. - 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."