## Elementary Geometry from an Advanced Standpoint |

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### Contents

THE ALGEBRA OF THE REAL NUMBERS | 1 |

prepared class may go rapidly through Chapters 17 and devote most of its time | 14 |

and 20 and still not get to Chapter | 25 |

Copyright | |

30 other sections not shown

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### Common terms and phrases

AABC ABAC ADEF algebraic altitude angles are congruent base belongs bisector called Cavalieri's principle Chapter circular sector congruent contains convex convex polygonal convex set coordinate system defined definition denoted dihedral angle distance elements end points equation Euclid Euclidean geometry exactly example exterior angle exterior angle theorem FIGURE following theorem formula area graph half planes holds hyperbolic geometry inequality intersects isometry L-line Lemma length mathematics means measure merely one-to-one correspondence opposite sides order relation ordered field pair parallel postulate perpendicular point Q polygonal region polynomial positive integers positive number PROBLEM SET Proof Pythagorean theorem radius rational numbers real number system rectangle RESTATEMENT right angle right triangle root ruler and compass ruler postulate Saccheri quadrilateral satisfies Section segment sequence side of AC Suppose surd synthetic tangent triangular regions true upper bound vertices Z.ABC