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HISTORY &P MAM EM AT VOLUME I I GENERAL SURVEY OF THE HISTORY OF ELEMENTARY MATHEMATICS BY DAVID EUGENE SMITH DOVER PUBLICATIONS, INC. NEW YORK NEW YORK CS COPYRIGHT, 1951, BY EVA MAY LUSE SMITH COPYRIGHT, 1923, BY DAVID EUGENE SMITH ALL RIGHTS RESERVED This new Dover edition, first published 1958, is an unaltered and unabridged publication of the last edition. through special arrangement in re- It is published with GINN AND COMPANY. PRINTED IN THE UNITED STATES OF AMERICA 357.3 PREFACE iis work has been written for the purpose of supplying teachers ana students with a usable textbook on the history of elementary the first steps in the is, of mathematics through subject has come to be recognized as an important one in the preparation of teachers of mathematics and in the liberal mathematics, that calculus. The education of students in colleges and high schools. Although several upon the history of mathematics are already available, the ^p||$ ainiior feel? a book written from somewhat different stand- that be found helpful to those who are beginning the study of in our universities, colleges, and normal schools, and subject ^he because of this belief the present work has been prepared. A history of mathematics may be constructed on several general points will which may be justified by the purpose in mind. For may be arranged solely with a view to the chronological plans, each of example, it of events, or as a series of biographies, or according to the branches of mathematics, or as a source book of material ucK, or with respect to national or racial achievements, or in sequel itf us jther ways, each of which may have certain advantages. The general plan adopted in the preparation of this work is that presenting the subject from two distinct standpoints, the first, as Volume leading to a survey of the growth of mathematics by Chronological periods, with due consideration to racial achievements ; the second, as in Volume II, leading to a discussion of the evolujbid ion of certain important topics. To attempt to fuse these two feaf |n refc I, ind thus to carry them along together has often been attempted. Sjjjj^iracterizes, for example, the monumental treatise of Montucla For the teacher, however, this the not and excellent work of Tropfke is an satisfactory, plan of to the break from the mere chronological example tendency away and, to a large extent, that of Cantor. is recital of facts. Long experience in teaching the subject in colleges has convinced the author that a general historical presentation iii is PREFACE iv desirable for the purpose of relating the development of mathematics to the development of the race, of revealing the science as a great stream rather than a static mass, and of emphasizing the human element, but that this ought to lead to a topical presentation by which the student may understand something of the life history of the special subject which he be studying, whether it be the the methods of calculation, the may elementary theory of numbers, solution of equations, the functions of trigonometry, the common symbolism in use, the various types of elementary geometry, the early steps in the calculus, or one of the various other important topics of elementary mathematics. The general plan can best be understood by a glance at the table of contents in each volume.