CONTENTS vii Chapter V. Inverse Figures 221 Exercises 227 Chapter VI. The Problem of Tangent Circles 231 Exercises 235 Chapter VII. Properties of Cyclic Quadilaterals. Peaucellier’s Inverter 237 Exercises 244 Problems for the Complements to Book III 244 Book IV On Areas 247 Chapter I. The Measure of Areas 249 Exercises 255 Chapter II. Comparison of Areas 259 Exercises 260 Alternative Proofs of the Theorem on the Square of the Hypotenuse 262 Chapter III. Area of the Circle 263 Exercises 265 Chapter IV. Constructions 267 Exercises 268 Problems Proposed for Book IV 269 Note A: On the Methods of Geometry 271 (a) Theorems to Prove 271 (b) Geometric Loci Construction Problems 278 (c) The Method of Transformations 281 Note B: On Euclid’s Postulate 289 I 289 II 292 Note C: On the Problem of Tangent Circles 297 Note D: On the Notion of Area 303 Miscellaneous Problems . 309 Appendix: Malfatti’s Problem 325
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