COPYRIGHT, 1923, BY DAVID EUGENE SMITH ALL RIGHTS RESERVED PRINTED IN THE UNITED STATES OF AMERICA 328.10 The Athenæum Press PREFACE This work has been written for the purpose of supplying teachers and students with a usable textbook on the history of elementary mathematics, that is, of mathematics through the first steps in the calculus. The subject has come to be recognized as an important one in the preparation of teachers of mathematics and in the liberal education of students in colleges and high schools. Although several works upon the history of mathematics are already available, the author feels that a book written from somewhat different standpoints will be found helpful to those who are beginning the study of the subject in our universities, colleges, and normal schools, and because of this belief the present work has been prepared. A history of mathematics may be constructed on several general plans, each of which may be justified by the purpose in mind. For example, it may be arranged solely with a view to the chronological sequence of events, or as a series of biographies, or according to the leading branches of mathematics, or as a source book of material for study, or with respect to national or racial achievements, or in various other ways, each of which may have certain advantages. The general plan adopted in the preparation of this work is that of presenting the subject from two distinct standpoints, the first, as in Volume I, leading to a survey of the growth of mathematics by chronological periods, with due consideration to racial achievements; and the second, as in Volume II, leading to a discussion of the evolution of certain important topics. To attempt to fuse these two features and thus to carry them along together has often been attempted. It characterizes, for example, the monumental treatise of Montucla and, to a large extent, that of Cantor. For the teacher, however, this plan is not satisfactory, and the excellent work of Tropfke is an example of the tendency to break away from the mere chronological recital of facts. Long experience in teaching the subject in colleges has convinced the author that a general historical presentation is |