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The surface itself is therefore called a quadric surface, or a surface of the second order.

ELLIPSOID, a quadric surface whose sections are ellipses.

The diameter of a quadric surface is a line at the extremities of which the tangent planes are parallel.

The tangent plane to a quadric surface either cuts the surface in two lines, or it has only a single line, or else only a single point in common with the surface.

The following propositions follow:— A quadric surface has at every point a tangent plane.