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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
THE WORKS OF ARCHIMEDES.
ON THE SPHERE AND CYLINDER, BOOK I 1
BOOK II. ... 56
MEASUREMENT OF A CIRCLE 91
ON CONOIDS AND SPHEROIDS 99
ON SPIRALS 151
ON THE EQUILIBRIUM OF PLANES, BOOK I. ... 189
BOOK II. ... 203
THE SAND-RECKONER 221
QUADRATURE OF THE PARABOLA 233
ON FLOATING BODIES, BOOK I 253
BOOK II 263
BOOK OF LEMMAS . 301
THE CATTLE-PROBLEM 319
The Works of Archimedes
Ancient Greece
Medieval Greece / Byzantine Empire
Modern Greece
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