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