Elementary Mathematics from an Advanced Standpoint Geometry

"Nothing comparable to it."--Mathematics Teacher 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 ed. 141 figures.Klein, Félix is the author of 'Elementary Mathematics from an Advanced Standpoint Geometry', published 2004 under ISBN 9780486434810 and ISBN 0486434818.