The book < Geometry and the Imagination > (written by David Hilbert) introduces a property of a Quadric Surface without a proof.
Property : The cone consisting of all the tangents from a fixed point to a quadric cuts every plane in a conic, and the points of contact of this cone with the surface form a conic.
Moreover, the quadrics are the only surfaces having any of these properties.
It was easy to prove the property itself, but i found it difficult to prove that it is a sufficient condition for a surface to be a quadric. (the statement starting with "Moreover, ...") I would like to know the proof of this statement.
