Book:Felix Klein/Elementary Mathematics from an Advanced Standpoint: Geometry/Volume 2

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Felix Klein: Elementary Mathematics from an Advanced Standpoint: Geometry, Volume 2

Published $1939$, Macmillan and Co., Limited (translated by E.R. Hedrick).
Translated from:

Elementarmathematik vom höheren Standpunkte aus


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