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ELEMENTS OF ALGEBRA:

ON

THE BASIS OF M. BOURDON:

EMBRACING

STURM'S AND HORNER’S THEOREMS,

PRACTICAL EXAMPLES.

BY CHARLES DAVIES, LL.D.

AUTHOR OF ARITIMETIC, ELEMENTARY ALGEBRA, ELEMENTARY GEOMETRY, PRAMO
GEOMETRY, ELEMENTS OF SURVEYING, ELEMENTS OF DESCRIPTIVE AND

ANALYTICAL GEOMETRY, ELEMENTS OF DIFFERENTIAL
AND INTEGRAL CALCULUS, AND A TREATISE
ON SHADES, SHADOWS AND PER-

SPECTIVE.

NEW YORK:
A. S. BARNES & BURR, 51 & 53 JOHN STREET

BOLD BY BOOKSELLERS, GENERALLY, THROUGHOUT THE UNITED STATES.

1860.

EDUCATION DEPT.

Dabies'

QA153
D 32
Educ.
Dept.

Course of Mathematics.

Davies' Primary Arithmetic AND Table-Book-Designed for Beginners ;

containing the elementary tables of Addition, Subtraction, Multiplication, Division, and Denominate Numbers ; with a large number of easy and prac

tical questions, both mental and written. Davies' First Lessons in Arithmetic-Combining the Oral Method with the

Method of Teaching the Combinations of Figures by Sight. Davies: Entellectual Arithmetic-An Analysis of the Science of Numbers, with

especial reference to Mental Training and Development. Davies' New School Aritymetic-Analytical and Practical. Bey to Davies' New School Arithmetic. Davics' Grammar of Arithmetic—An Analysis of the Language of Numbers

and the Science of Figures. Davies: New University Arithmetic--Embracing the Science of Numbers, and

their Applications according to the most Improved Methods of Analysis and

Cancellation. Key to Babies' New University Arithmetic. : Davies' Elementary Algeux&– Embficing the First Principles of the Science. Bey to Davies' Elementary. Algebra.. Davies Elementaży. GidístijAND :Triaprometyr-With Applications in

Mensuration. Davies' Practical Mathematics--With Drawing and Mensuration applied to

the Mechanic Arts. Davies' University Algebra-Embracing a Logical Development of the

Science, with graded examples. Davies' Bourdon's Algebra-Including Sturm's and Horner's Theorems,

and practical examples. Davies' Legendre's Geometry and Trigonometry-Revised and adapted to

the course of Mathematical Instruction in the United States. Davies' Elenrents of Surveying and Navigation-Containing descriptions

of the Instruments and necessary Tables. Davies' Analytical Geometrn-Embracing the Equations of the Point, the

Straight Line, the Conic Sections, and Surfaces of the first ind second order. Davies' Differential and Entegral Calculus. Davies' Descriptive Geometry-With its application to Spherical Trigonomo

try, Spherical Projections, and Warped Surfaces. Davies' Shades, Shadows, AND Perspective. Davies' Logic and Titility of Mathematics--With the best methods of In

struction Explained and Illustrated. Davies' and Peck's Mathematical Dictionary and Cyclopedia of Mathes

matical Science-Comprising Definitions of all the terms employed n Mathematics-an Analysis of each Branch, and of the whole, as forming a single Science.

ENTERED according to Act of Congress, in the year one thousand eight hundred and Afty.

three, by CHARLES DAVIES, in the Clerk's Office or the Distri Court of the United States for the Southern District of New York.

WILLIAN DENYSE, STEREOTYPER AND ELECTROTYPER, 183 William Street, New York.

C.

7,

1

PREFACE

THE Treatise on Algebra, by M. Bourdon, is a work of singular excellence and merit. In France, it has long been one of the standard Text books. Shortly after its first publication, it passed through several editions, and has formed the basis of every subsequent work on the subject of Algebra, both in Europe and in this country.

The original work is, however, a full and complete treatise on the subject of Algebra, the later editions containing about eight hundred pages octavo. The time which is given to the study of Algebra, in this country, even in those seminaries where the course of mathematics is the fullest, is too short to accomplish so voluminous a work, and hence it has been found necessary either to modify it essentially, or to abandon it altogether.

In the following work, the original Treatise of Bourdon has been regarded only as a model. The order of arrangement, in many parts, has been changed; new rules and new methods have been introduced: the modifications indicated by its use, for twenty years, as a text book

M251902

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