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ELEMENTS OF ALGEBRA:

ON

Louis Perre Marie
THE BASIS OF M. BOURDON:

EMBRACING

STURM'S AND HORNER'S THEOREMS,

AND

PRACTICAL EXAMPLES.

BY CHARLES DAVIES, LL.D.

AUTFIOR OF ARITHMETIC, ELEMENTARY ALGEBRA, ELEMENTARY GEOMETRY, PRACTICAL
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:

PUBLISHED BY A. S. BARNES & CO.,

No. 51 JOHN STREET.

1857.

1957 Auto of Rafn Broun the drept try of Sinsigheid

bloss of 1843 Math 2058.57

Atatti 2008.LA VIES'
COURSE OHMATHEMATICS

UNIVERSITY
LIBRARY

Babies' Arithmetical Table-Book.
Davies' First Lessons in Arithmetic-For Beginners.
Davies' Arithmetic Designed for the use of Academies and Schools
Bey to Davies' Arithmetic.
Babies' University Arithmetic-Embracing the Science of Numbers and their

numerous Applications.
Bey to Davies' University Arithmetic
Davies' Elementary Algebra—Bemg an introduction to the Science, and form-

ing a counecting link between ARITHMETIC and ALGEBRA.
Bey to Davies Elementary Algebra.
Davies' Elements of Geometry and Trigonometry, with APPLICATIONS IN

MENSURATION. -This work embraces the elementary principles of Geometry and
Trigonometry. The reasoning is plain and concise, but at the same time strictly

rigorous.
Bavies' Practical Mathematics for Practical Men-Embracing the Princi-

ples of Drawing, Architecture, Mensuration, and Logarithms, with Applications

to the Mechanic Arts. Bavies' Bourdon's Algebra— Including Sturm's THEOREM-Being an abridg.

ment of the Work of M. BOURDON, with the addition of practical examples. Davies' Zegendre's Geometry and Trigonometry-From the works of A. M.

Legendre, with the addition of a Treatise on MENSURATION OF PLANES AND

Solids, and a Table of LOGARITHMS and LogARITHMIC SINES.
Dabics' Surveying-With a description and plates of the THEODOLITE, CON-

PA-S, PLANE-TABLE, and LEVEL; also, Maps of the TOPOGRAPHICAL Signs adopted
by the Engineer Department—an explanation of the method of surveying the
Pubiic Lands, Geodesic and Maritime Surveying, and an Elementary Treatise

on NAVIGATION. Davies' Descriptive Genmetry— With its application to SPHERICAL PROJEC

TIONS.

Davies' Shades, Shadows, AND Linear Perspective.
Davies' Analytical Geometry—Embracing the EQUATIONS OF THE POINT AND

Straight Line-of the Conic Sections—of the LINE AND PLANE IN SPACE;
also, the discussion of the GENERAL EQUATION of the second degree, and of Sub-

FACES of the second order.
Dabies' Differential and Integral Calculus.
Dabies' Logic and Utility of Mathematics.

1521

54-135 8

나 4

ENTERED according to Act of Congress, in the year one thousand eight hundred and fifty-three by CHARLES Davies, in the Clerk's Office of the District Court of the United States for the Southern District of New York.

J P. JONES & CO., STBE BOTYPERS.

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 alto gether.

In the following work, the original Treatise of Bourdon has been regarded only as a mode). The order of arrangenient, 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

in the Military Academy have been freely inade, for the purpose of giving to the work a more practical character, and bringing it into closer harmony with the trains of thought and improved systems of instruction which prevail in that institution.

But the work, in its present form, is greatly indebted to the labors of William G. Peck, A. M., U. S. Topographical Engineers, and Assistant Professor of Mathematics in the Military Academy.

Many of the new definitions, new rules and improved methods of illustration, are his. His experience as teacher of mathematics has enabled him to bestow upon the work much valuable labor which will be found to bear the marks of profound study and the freshness of daily instruction. FISHKILL LANDING, May, 1863.

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