The maximum number of positive and negative real roots of a polynomial can be determined using this man's namesake rule of signs.
Before Soddy, this man discovered the formula for the radius of a fourth circle inscribed by or circumscribing a set of three mutually tangent circles. Before Euler, he discovered the formula relating the numbers of vertices, edges and faces of polyhedra. The maximum number of positive and negative real roots of a polynomial can be determined using this man's namesake rule of signs. He also gives his name to a system using the abscissa and ordinate as the axes of a rectangular coordinate system. For 10 points, name this French mathematician and philosopher who founded analytic geometry.
Before Soddy, this man discovered the formula for the radius of a fourth circle inscribed by or circumscribing a set of three mutually tangent circles.
René {Descartes}