The Works of Archimedes, T. L. Heath

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CONTENTS

INTRODUCTION.

CHAPTER I. ARCHIMEDES xv

CHAPTER II. MANUSCRIPTS AND PRINCIPAL EDITIONS ORDER OF COMPOSITION DIALECT LOST WORKS . xxiii

CHAPTER III. RELATION OF ARCHIMEDES TO HIS PREDECESSORS xxxix

1. Use of traditional geometrical methods . . xl

2. Earlier discoveries affecting quadrature and cubature xlvii

3. Conic Sections lii

4. Surfaces of the second degree .... liv

5. Two mean proportionals in continued proportion lxvii

CHAPTER IV. ARITHMETIC IN ARCHIMEDES .... lxviii

1. Greek numeral system lxix

2. Addition and subtraction lxxi

3. Multiplication lxxii

4. Division ........ lxxiii

5. Extraction of the square root .... lxxiv

6. Early investigations of surds or incommensurables lxxvii

7. Archimedes' approximations to square root of 3 . . . lxxx

8. Archimedes' approximations to the square roots of large numbers which are not complete squares lxxxiv

Note on alternative hypotheses with regard to the approximations to square root of 3 . . . . xc



CHAPTER V. ON THE PROBLEMS KNOWN AS NEUSEIS . .

1. Neuseis referred to by Archimedes ... c

2. Mechanical constructions : the conchoid of Nicomedes cv

3. Pappus' solution of the neuseis referred to in Props. 8, 9 On Spirals cvii

4. The problem of the two mean proportionals . cx

5. The trisection of an angle .... cxi

6. On certain plane neuseis cxiii

CHAPTER VI. CUBIC EQUATIONS cxxiii

CHAPTER VII. ANTICIPATIONS BY ARCHIMEDES OF THE INTEGRAL CALCULUS cxlii

CHAPTER VIII. THE TERMINOLOGY OF ARCHIMEDES ... civ

BOOK II. ... 203

The Works of Archimedes