Definition. When two conics intersect each other at two points in such a manner that the tangents and normals of the one become the normals and tangents of the other, they may be said to cut each other orthogonally.

Theorem. 1st, A given conic can be cut at every point on it by two conics which are orthogonal to it; 2nd, every conic orthogonal to a given conic passes through two fixed points on the axis of the given conic.