Elementary Mathematics from an Advanced Standpoint: Geometry

Nothing comparable to it. -- <i>Mathematics Teacher. </i>This comprehensive three-part treatment begins with a consideration of the simplest geometric manifolds: line-segment area and volume as relative magnitudes; the Grassmann determinant principle for the plane and the Grassmann principle for space; classification of the elementary configurations of space according to their behavior under transformation of rectangular coordinates; and derivative manifolds. The second section on geometric transformations examines affine and projective transformations; higher point transformations; transformations with change of space element; and the theory of the imaginary. The text concludes with a systematic discussion of geometry and its foundations. 1939 edition. 141 figures.