Elementary Mathematics from an Advanced Standpoint: Geometry

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Courier Dover Publications, 2004 - Mathematics - 214 pages
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"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.
  

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Contents

Introduction
1
The Grassmann Determinant Principle for the Plane
21
The Grassmann Principle for Space
29
Classification of the Elementary Configurations of Space according to their
39
Derivative Manifolds
54
Page
69
Higher Point Transformations
98
Theory of the Imaginary
117
Systematic Discussion of Geometry and Its Foundations
130
Application of Invariant Theory to Geometry
144
Foundations of Geometry
159
Index of Names
209
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1862-1953

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