Algebraic theorems obtained by use of extended analytic geometry

Te understand the theorems presented here one must first understand the basic principles which have been developed by Dr. Ralph Underwood. The basic process is a method by which equations with three or more variables may be represented on the XY plane. While the process does not represent a true projection many of the basic features of the loci, in the case of three variables, are preserved. The two basic methods which have been used previously are called System A and System B, (9:527) however, an infinity of methods or plotting rules are available. In the first ten theorems presented here a more flexible method is employed. In graphing the locus of the equation a point on the locus is first found, and the equation of a tangent hyperplane is written by the method illustrated below« one then may use a graphing rule so that the locus of the tangent hyperplane is a straight line on the XY plane.