Classification and properties of dual conical congruences ...

Excerpt from Classification and Properties of Dual Conical Congruences In the geometry of the plane, we have the two following methods of determining the various curved loci analytically; 1) that in which the coordinates of its elements satisfy an equation; and 2) that in which the coordinates of the elements are given as functions of a single parameter. From the above mentioned analogy, ' we are then led to ask concerning the nature of the configurations represented in the corresponding way in the new geometry. These are found to be Congruences of Rays to which we give the name Dual Congruences.