內容大鋼
阿基米德的著作,迄今發現的共有以下十一種:《論球和圓柱》《圓的度量》《論擬圓錐與旋轉橢體》《論螺線》《論平面圖形的平衡》《數沙者》《拋物線弓形求積》《論浮體》《引理彙編》《牛群問題》《方法》。
英國數學史家希思(Thomas Heath,1861—1940)在1897年翻譯出版了前10種,1912年翻譯出版了第11種,都是由劍橋大學出版社出版。今即將此二書合刊影印,而1897年版的書前有希思撰寫的長篇「導讀」,影印時不收。
目錄
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.Neuσeis referred to by Archimedes
§2.Mechanical constructions: the conchoid of Nico-medes
§3.Pappus' solution of the veuσis 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 vEuσEis
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