vi CONTENTS Exercises 69 Chapter III. The Intersection of Two Circles 71 Exercises 74 Chapter IV. Property of the Inscribed Angle 75 Exercises 81 Chapter V. Constructions 83 Exercises 95 Chapter VI. On the Motion of Figures 99 Exercises 107 Problems for Book II 108 Book III On Similarity 111 Chapter I. Proportional Lines 113 Exercises 121 Chapter II. Similarity of Triangles 123 Exercises 126 Chapter III. Metric Relations in a Triangle 129 Exercises 136 Chapter IV. Proportional Segments in a Circle. Radical Axis 139 Exercises 144 Chapter V. Homothecy and Similarity 145 Exercises 154 Chapter VI. Constructions 157 Exercises 167 Chapter VII. Regular Polygons 169 Exercises 188 Problems for Book III 188 Complements to Book III 193 Chapter I. Directed Segments 195 Exercises 198 Chapter II. Transversal 201 Exercises 206 Chapter III. Cross Ratio. Harmonic Concurrent Lines 209 Exercises 212 Chapter IV. Poles and Polars with respect to a Circle 213 Exercises 219

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