## Elementary geometry from an advanced standpoint |

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### Contents

THE ALGEBRA OF THE REAL NUMBERS | 1 |

INCIDENCE GEOMETRY IN PLANES AND SPACE | 36 |

SEPARATION IN PLANES AND SPACE | 61 |

Copyright | |

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AABC ADEF algebraic altitude angles are congruent Archimedean postulate base belongs bisector called Cavalieri's principle Chapter circular sector congruent contains convex convex polygonal convex set coordinate system defined definition denoted dihedral angle elements end points equation Euclid Euclidean geometry exactly exterior angle exterior angle theorem FIGURE following theorem formula area graph half planes holds hyperbolic geometry inequalities interior of Z.BAC intersects isometry L-line Lemma length mathematical means merely one-to-one correspondence opposite sides ordered field 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 surd plane synthetic tangent triangular regions upper bound vertices Z.ABC