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INTRODUCTION CHAPTER I.ARCHIMEDES CHAPTER II.MANUSCRIPTS AND PRINCIPAL EDITIONS-ORDER OF COMPOSITION-DIALECT-LOST WORKS CHAPTER III.RELATION OF ARCHIMEDES TO HIS PREDECESSORS ¡ì1.Use of traditional geometrical methods . ¡ì2.Earlier discoveries affecting quadrature and cubature. ¡ì3.Conic Sections ¡ì4.Surfaces of the second degree ¡ì5.Two mean proportionals in continued propor-tion. CHAPTER IV.ARITHMETIC IN ARCHIMEDES ¡ì1.Greek numeral system ¡ì2.Addition and subtraction ¡ì3.Multiplication ¡ì4.Division ¡ì5.Extraction of the square root. ¡ì6.Early investigations of surds or incommensu-rables ¡ì7.Archimedes' approximations to 3. ¡ì8.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 ¡ì1.Neu¦Òeis referred to by Archimedes ¡ì2.Mechanical constructions: the conchoid of Nico-medes ¡ì3.Pappus' solution of the veu¦Òis referred to inProps. 8,9 On Spirals. ¡ì4.The problem of the two mean proportionals ¡ì5.The trisection of an angle ¡ì6.On certain pplane vEu¦ÒEis 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