INTRODUCTION CHAPTER I.ARCHIMEDES CHAPTER II.MANUSCRIPTS AND PRINCIPAL EDITIONS-ORDER OF COMPOSITION-DIALECT-LOST WORKS CHAPTER III.RELATION OF ARCHIMEDES TO HIS PREDECESSORS ��1.Use of traditional geometrical methods . ��2.Earlier discoveries affecting quadrature and cubature. ��3.Conic Sections ��4.Surfaces of the second degree ��5.Two mean proportionals in continued propor-tion. CHAPTER IV.ARITHMETIC IN ARCHIMEDES ��1.Greek numeral system ��2.Addition and subtraction ��3.Multiplication ��4.Division ��5.Extraction of the square root. ��6.Early investigations of surds or incommensu-rables ��7.Archimedes' approximations to 3. ��8.Archimedes' approximations to the square rootsof large numbers which are not completesquares Note on alternative hypotheses with regard tothe approximations to /3 CHAPTER V.ON THE PROBLEMS KNOWN AS NEYSEIS ��1.Neu��eis referred to by Archimedes ��2.Mechanical constructions: the conchoid of Nico-medes ��3.Pappus' solution of the veu��is referred to inProps. 8,9 On Spirals. ��4.The problem of the two mean proportionals ��5.The trisection of an angle ��6.On certain pplane vEu��Eis CHAPTER VI. CUBIC EQUATIONS CHAPTER VII. ANTICIPATIONS BY ARCHIMEDES OF THE INTE-GRAL CALCULUS CHAPTER VIII. THE TERMINOLOGY OF ARCHIMEDES THE WORKS OF ARCHIMEDES ON THE SPHERE AND CYLINDER,BOOK I.. BOOK II. MEASUREMENT OF A CIRCLE ON CONOIDS AND SPHEROIDS ON SPIRALS ON THE EQUILIBRIUM OF PLANES,BOOK I. BOOK II. THE SAND-RECKONER QUADRATURE OF THE PARABOLA ON FLOATING BODIES,BOOK I. BOOK II. BOOK OF LEMMAS. THE CATTLE-PROBLEM