INTRODUCTION PART I. THE EARLIER HISTORY OF CONIC SECTIONS AMONG THE GREEKS CHAPTER I.THE DISCOVERY OF CONIC SEOTIONS: ME-NAECHMUS CHAPTER II.ARISTAEUS AND EUCLID CHAPTER III.ARCHIMEDES PART II. INTRODUCTION TO THE CONICS OF APOLLONIUS CHAPTER I.THE AUTHOR AND HIS OWN ACCOUNT OF THE CONIOS CHAPTER II.GENERAL CHARACTERISTICS §1.Adherence to Euclidean form, conceptions and language §2.Planimetric character of the treatise §3.Definite order and aim CHAPTER III.THE METHODS OF APOLLONIUS §1.Geometrical algebra (1)The theory of proportions (2)The application of areas (3)Graphic representation of areas by meansof auxiliary lines (4)Special use of auxiliary points in Book VII §2.The use of coordinates §3.Transformation of coordinates §4.Method of finding two mean proportionals §5.Method of constructing normals passing through a given point CHAPTER IV.THE CONSTRUCTION OF A CONIC BY MEANS OF TANGENTS CHAPTER V.THE THREE-LINE AND FOUR-LINE LOCUS CHAPTER VI.THE CONSTRUCTION OF A CONIC THROUGH FIVE POINTS APPENDIX. NOTES ON THE TERMINOLOGY OF GREEK GEO-METRY THE CONICS OF APOLLONIUS THE CONE THE DIAMETER AND ITS CONJUGATE TANGENTS PROPOSITIONS LEADING TO THE REFERENCE OF A CONIC TO ANY NEW DIAMETER AND THE TANGENT AT ITS EXTREMITY CONSTRUCTION OF CONIOS FROM CERTAIN DATA ASYMPTOTES TANGENTS, CONJUGATE DIAMETERS AND AXES EXTENSIONS OF PROPOSITIONS 17 RECTANGLES UNDER SEGMENTS OF INIERSECTING CHORDS HARMONIC PROPERTIES OF POLES AND POLARS INTERCEPTS MADE ON TWO TANGENTS BY A THIRD FOCAL PROPERTIES OF CENTRAL CONICS THE LOCUS WITH RESPECT TO THREE LINES ETC INTERSECTING CONICS NORMALS AS MAXIMA AND MINIMA PROPOSITIONS LEADING IMMEDIATELY TO THE DETER-MINATION OF THE EVOLUTE CONSTRUCTION OF NORMALS OTHER PROPOSITIONS RESPECTING MAXIMA AND MINIMA EQUAL AND SIMILAR CONICS PROBLEMS VALUES OF CERTAIN FUNCTIONS OF THE LENGTHS OF CONJUGATE DIAMFTERS
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