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Elementary Mathematics from an Advanced Standpoint: Geometry by Felix Klein ISBN: 0486434818 Dover Publications Price: $12.95 click here to see this book This text begins with the simplest geometric manifolds, the Grassmann determinant principle for the plane and the Grassmann principle for space; and more. Also explores affine and projective transformations; higher point transformations; transformations with change of space element; and the theory of the imaginary. Concludes with a systematic discussion of geometry and its foundations. 1939 edition. 141 figures. Unabridged republication of the Dover reprint of the 1925 3rd edition. Table of Contents for Elementary Mathematics from an Advanced Standpoint: Geometry 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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