"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 edition. 141 figures.

Contenuti

1. The Simplest Geometric Manifolds I. Line-Segment, Area, Volume, as Relative Magnitudes II. The Grassmann Determinant Principle for the Plane III. The Grassmann Principle for Space IV. Classification of the Elementary Configurations of Space According to their Behavior under Transformation of Rectangular Coordinates V. Derivative Manifolds 2. Geometric Transformations I. Affine Transformations II. Projective Transformations III. Higher Point Transformations IV. Transformations with Change of Space Element V. Theory of the Imaginary 3. Systematic Discussion of Geometry and Its Foundations I. The Systematic Discussion II. Foundations of Geometry Indexes

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