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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.