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A History of Mathematics   By:

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A HISTORY OF MATHEMATICS BY FLORIAN CAJORI, Ph.D. Formerly Professor of Applied Mathematics in the Tulane University of Louisiana; now Professor of Physics in Colorado College \I am sure that no subject loses more than mathematics by any attempt to dissociate it from its history."J. W. L. Glaisher New York THE MACMILLAN COMPANY LONDON: MACMILLAN & CO., Ltd. 1909 All rights reserved Copyright, 1893, By MACMILLAN AND CO. Set up and electrotyped January, 1894. Reprinted March, 1895; October, 1897; November, 1901; January, 1906; July, 1909. Norwood Pre&: J. S. Cushing & Co.Berwick & Smith. Norwood, Mass., U.S.A. PREFACE. An increased interest in the history of the exact sciences manifested in recent years by teachers everywhere, and the attention given to historical inquiry in the mathematical class rooms and seminaries of our leading universities, cause me to believe that a brief general History of Mathematics will be found acceptable to teachers and students. The pages treatingnecessarily in a very condensed form of the progress made during the present century, are put forth with great didence, although I have spent much time in the e ort to render them accurate and reasonably complete. Many valuable suggestions and criticisms on the chapter on \Recent Times" have been made by Dr. E. W. Davis, of the University of Nebraska. The proof sheets of this chapter have also been submitted to Dr. J. E. Davies and Professor C. A. Van Velzer, both of the University of Wisconsin; to Dr. G. B. Halsted, of the University ofTexas; Professor L. M. Hoskins, of the Leland Stanford Jr. University; and Professor G. D. Olds, of Amherst College,all of whom have a orded valuable assistance. I am specially indebted to Professor F. H. Loud, of Colorado College, who has read the proof sheets throughout. To all the gentlemen above named, as well as to Dr. Carlo Veneziani of Salt Lake City, who read the rst part ofmy work in manuscript, I desire to express my hearty thanks. But in acknowledging their kindness, I trust that I shall not seem to v lay upon them any share in the responsibility for errors which I may have introduced in subsequent revision of the text. FLORIAN CAJORI. Colorado College, December, 1893. TABLE OF CONTENTS Page INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . 1 ANTIQUITY . . . . . . . . . . . . . . . . . . . . . . . . . . 5 The Babylonians . . . . . . . . . . . . . . . . . . . . . 5 The Egyptians . . . . . . . . . . . . . . . . . . . . . . 10 The Greeks . . . . . . . . . . . . . . . . . . . . . . . . 17 Greek Geometry . . . . . . . . . . . . . . . . . . . . . 17 The Ionic School . . . . . . . . . . . . . . . . . . . 19 The School of Pythagoras . . . . . . . . . . . . . . 22 The Sophist School . . . . . . . . . . . . . . . . . . 26 The Platonic School . . . . . . . . . . . . . . . . . 33 The First Alexandrian School . . . . . . . . . . . . 39 The Second Alexandrian School . . . . . . . . . . . 62 Greek Arithmetic . . . . . . . . . . . . . . . . . . . . . 72 The Romans . . . . . . . . . . . . . . . . . . . . . . . . 89 MIDDLE AGES . . . . . . . . . . . . . . . . . . . . . . . . 97 The Hindoos . . . . . . . . . . . . . . . . . . . . . . . 97 The Arabs . . . . . . . . . . . . . . . . . . . . . . . . . 116 Europe During the Middle Ages . . . . . . . . . . . 135 Introduction of Roman Mathematics . . . . . . . . 136 Translation of Arabic Manuscripts . . . . . . . . . . 144 The First Awakening and its Sequel . . . . . . . . . 148 MODERN EUROPE . . . . . . . . . . . . . . . . . . . . . . 160 The Renaissance . . . . . . . . . . . . . . . . . . . . . 161 Vieta to Descartes . . . . . . . . . . . . . . . . . . . 181 Descartes to Newton . . . . . . . . . . . . . . . . . 213 Newton to Euler . . . . . . . . . . . . . . . . . . . . 231 vii TABLE OF CONTENTS. viii Page Euler, Lagrange, and Laplace . . . . . . . . . . . . 286 The Origin of Modern Geometry . . . . . . . . . . . 332 RECENT TIMES . . . . . . . . . . . . . . . . . . . . . ... Continue reading book >>



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