Instead of a circle or sphere we may take any conic or quadric.
Every plane section of a quadric surface is a conic or a line-pair.
These are called chief-tangent curves; on a quadric surface they are the above straight lines.
Now from a quadric equation we derive, in like manner, the notion of a complex or imaginary number such as is spoken of above.
This plane is called the polar plane of the point P, with regard to the quadric surface.
Each ray cuts its corresponding plane in a point, the locus of these points is a quadric surface.
Evidently the method gives for L a quadric equation, which is the “resolvent” equation in this particular case.
The surface itself is therefore called a quadric surface, or a surface of the second order.
These planes intersect in p2, so that p2 is a line on the quadric cone generated by the axial pencils l1 and l2.
Every line which has three points in common with a quadric surface lies on the surface.