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:

Elementarmathematik vom höheren Standpunkte aus

Subject Matter


Preface to the First Edition (Göttingen, Christmas, $1908$: Felix Klein)
Preface to the Third Edition (Göttingen, May, $1925$: Felix Klein)
Translators; Preface (The Translators)

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