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The Project Gutenberg EBook of First Course in the Theory of Equations, by
Leonard Eugene Dickson
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Title: First Course in the Theory ofEquations
Author: Leonard Eugene Dickson
Release Date: August 25, 2009 [EBook #29785]
Language: English
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FIRST COURSE
IN THE

THEORY OF EQUATIONS
BY

LEONARD EUGENE DICKSON, Ph.D.
CORRESPONDANT DE L’INSTITUT DE FRANCE
PROFESSOR OF MATHEMATICS IN THE UNIVERSITY OF CHICAGO

NEW YORK

JOHN

WILEY

&

SONS,

Inc.

London: CHAPMAN & HALL, LimitedCopyright, 1922,
by
LEONARD EUGENE DICKSON

All Rights Reserved
This book or any part thereof must not
be reproduced in any form without
the written permission of the publisher.

Printed in U. S. A.
PRESS OF
BRAUNWORTH & CO., INC.
BOOK MANUFACTURERS
BROOKLYN, NEW YORK

PREFACE

The theory of equations is not only a necessity in the subsequent mathematical courses and theirapplications, but furnishes an illuminating sequel to
geometry, algebra and analytic geometry. Moreover, it develops anew and in
greater detail various fundamental ideas of calculus for the simple, but important, case of polynomials. The theory of equations therefore affords a useful
supplement to differential calculus whether taken subsequently or simultaneously.
It was to meet the numerous needs ofthe student in regard to his earlier and
future mathematical courses that the present book was planned with great care
and after wide consultation. It differs essentially from the author’s Elementary
Theory of Equations, both in regard to omissions and additions, and since it
is addressed to younger students and may be used parallel with a course in
differential calculus. Simpler and moredetailed proofs are now employed.
The exercises are simpler, more numerous, of greater variety, and involve more
practical applications.
This book throws important light on various elementary topics. For example, an alert student of geometry who has learned how to bisect any angle
is apt to ask if every angle can be trisected with ruler and compasses and if
not, why not. After learning how toconstruct regular polygons of 3, 4, 5, 6,
8 and 10 sides, he will be inquisitive about the missing ones of 7 and 9 sides.
The teacher will be in a comfortable position if he knows the facts and what
is involved in the simplest discussion to date of these questions, as given in
Chapter III. Other chapters throw needed light on various topics of algebra. In
particular, the theory of graphs ispresented in Chapter V in a more scientific
and practical manner than was possible in algebra and analytic geometry.
There is developed a method of computing a real root of an equation with
minimum labor and with certainty as to the accuracy of all the decimals obtained. We first find by Horner’s method successive transformed equations
whose number is half of the desired number of significant figures...