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

Subject Matter

 * Geometry

Contents

 * Preface to the First Edition (Göttingen, Christmas, $1908$: )


 * Preface to the Third Edition (Göttingen, May, $1925$: )


 * 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