Book:Felix Klein/Elementary Mathematics from an Advanced Standpoint: Geometry
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Felix Klein: Elementary Mathematics from an Advanced Standpoint, Volume 2: Geometry
Published $\text {1939}$, Macmillan and Co., Limited (translated by E.R. Hedrick and C.A. Noble)
Translated from:
Subject Matter
Contents
- Preface to the First Edition (Göttingen, Christmas, $1908$: Felix Klein)
- Preface to the Third Edition (Göttingen, May, $1925$: Felix Klein)
- Translators; Preface (The Translators)
- Introduction
- Part One: The Simplest Geometric Manifolds
- I. Line-Segment, Area, Volume, as Relative Magnitudes
- II. The Grassman Determinant Principle for the Plane
- III. The Grassman Principle for Space
- IV. Classification of the Elementary Configurations of Space according to their Behavior under Transformation of Rectangular Coordinates
- V. Derivative Manifolds
- Part Two: Geometric Transformations
- I. Affine Transformations
- II. Projective Transformations
- III. Higher Point Transformations
- IV. Transformations with Change of Space Element
- V. Theory of the Imaginary
- Part Three: Systematic Discussion of Geometry and Its Foundations
- I. The Systematic Discussion
- II. Foundations of Geometry
- Index of Names
- Index of Contents