Elementary Mathmatics from an Advan (Dover Books on Mathematics)

This Dover edition, first published in 2004, is an unabridged republication of an earlier Dover reprint (1949) of the translation first published by The Macmillan Company, New York, in 1939. The translation follows volume 2 (Geometrie) of the three-volume third German edition of Elementarmathematik vom höheren Standpunkte aus, published by J. Springer, Berlin, in 1924–1928.”

"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.