## Elementary Mathematics from an Advanced Standpoint: Geometry"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 |

209 | |

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