If P lies on the surface we take the tangent plane of P as its polar.
To the line joining the centres of the two pencils as a line in one corresponds in the other the tangent plane at its centre.
Every plane which cuts a quadric surface in a line-pair is a tangent plane.
If it lies at the infinity, the plane at infinity is a tangent plane, and the surface is called a paraboloid.
An osculating plane of the curve (see 38 below) is a tangent plane of the torse all along a generating line.
This means of course that the spiral has been cut by a plane parallel to the tangent plane.
Considered as a curved surface, concentric with the earth, a tangent plane to such a surface is the plane of the horizon.