sometimes translated into a more convenient and familiar language. The greater part of my account is a compilation from existing histories or memoirs, as indeed must be necessarily the case where the works discussed are so numerous and cover so much ground. When authorities disagree I have generally stated only that view which seems to me to be the most probable; but if the question be one of importance, I believe that I have always indicated that there is a difference of opinion about it. I think that it is undesirable to overload a popular account with a mass of detailed references or the authority for every particular fact mentioned. For the history previous to 1758, I need only refer, once for all, to the closely printed pages of M. Cantor's monumental Vorlesungen über die Geschichte der Mathematik (hereafter alluded to as Cantor), which may be regarded as the standard treatise on the subject, but usually have have given given references to the other leading I authorities on which I have relied or with which I am acquainted. My account for the period subsequent to 1758 is generally based on the memoirs or monographs referred to in the footnotes, but the main facts to 1799 have been also enumerated in a supplementary volume issued by Prof. Cantor last year. I hope that my footnotes will supply the means of studying in detail the history of mathematics at any specified period should the reader desire to do so. My thanks are due to various friends and corre spondents who have called my attention to points in the previous editions. I shall be grateful for notices of additions or corrections which may occur to any of my readers. TRINITY COLLEGE, CAMBRIDGE, May 1908. W. W. ROUSE BALL. TABLE OF CONTENTS. PREFACE TABLE OF CONTENTS CHAPTER I. EGYPTIAN AND PHOENICIAN MATHEMATICS. The history of mathematics begins with that of the Ionian Greeks Knowledge of the science of numbers possessed by the Phoenicians PAGE V ix 12235 First Period. Mathematics under Greek Influence. This period begins with the teaching of Thales, circ. 600 B.C., and ends CHAPTER II. THE IONIAN AND PYTHAGOREAN SCHOOLS. The Pythagorean School . PYTHAGORAS, 569-500 B.C. The Pythagorean teaching The Pythagorean geometry The Pythagorean theory of numbers Epicharmus. Hippasus. Philolaus. Archippus. Lysis His solution of the duplication of a cube Theodorus. Timaeus. Bryso Other Greek Mathematical Schools in the Fifth Century B.C. Oenopides of Chios Zeno of Elea. Democritus of Abdera CHAPTER III. THE SCHOOLS OF ATHENS AND CYZICUS. CIRC. 420-300 B.C. PAGE 19 19 20 22 24 28 28 29 30 .30 30 31 Authorities 33 Mathematical teachers at Athens prior to 420 B.C.. Anaxagoras. The Sophists. Hippias (The quadratrix) Three problems in which these schools were specially interested Letters used to describe geometrical diagrams The problem of the duplication of the cube Plato, 429-348 B.C. Introduction in geometry of the method of analysis. 34 34 36 37 37 38 39 39 41 42 43 44 Ꮩ CHAPTER IV. THE FIRST ALEXANDRIAN SCHOOL. CIRC. 300-30 B.C. Authorities Foundation of Alexandria The Third Century before Christ EUCLID, circ. 330-275 B.C. Euclid's Elements The Elements as a text-book of geometry. The Elements as a text-book of the theory of numbers Aristarchus, circ. 310-250 B.C. Method of determining the distance of the sun Conon. Dositheus. Zeuxippus. Nicoteles . His works on plane geometry ARCHIMEDES, 287-212 B.C. His works on geometry of three dimensions His two papers on arithmetic, and the "cattle problem The principles of geometry assumed by Archimedes . APOLLONIUS, circ. 260-200 B.C. His conic sections His other works His solution of the duplication of the cube Contrast between his geometry and that of Archimedes Eratosthenes, 275-194 B.C. The Sieve of Eratosthenes The Second Century before Christ Hypsicles (Euclid, book XIV). Nicomedes. Diocles Perseus. Zenodorus HIPPARCHUS, circ. 130 B.C. Foundation of scientific astronomy Foundation of trigonometry HERO of Alexandria, circ. 125 B.C.. Foundation of scientific engineering and of land-surveying PAGE 50 51 52 52 53 54 57 60 62 62 64 64 67 70 71 73 76 76 77 77 80 81 82 83 83 84 85 86 86 87 88 88 88 89 91 |