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BY CHARLES DAVIES, LL.D.,
AJTHOR OF ARITHMETIC, ALGEBRA, PRACTICAL MATHEMATICS FOR PRACTICAL MEN,
ELEMENTS OF DESCRIPTIVE AND OF ANALYTICAL GEOMETRY, ELEMENTS
OF DIFFZRENTIAL AND INTEGRAL CALCULUS, AND SHADES,

SHADOWS, AND PERSPECTIVE.

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NEW YORK :
BARNES & BURR, PUBLISHERS, 51 & 53 JOHN ST.

CHICAGO: GEORGE SHERWOOD, 118 LAKE ST.
CINCINNATI: RICKEY AND CARROLL.
ST. LOUIS: KEITH AND WOODS.

1864.

ASTOR, LENOX AND
ILLAN FOUNDATIONS.

1902

Contit of Mathematics.

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

containing the elementary tables of Addition, Subtraction, Vultiplication, Division, and Denominate Numbers ; with a large number oi 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.
Bavies' Entellectual Arithmetic-An Analysis of the Science of Numbers, with

especial reference to Mental Training and Development.
Davies' New School Arithmetic-Analytical and Practical.
Bey to Davies' New School Arithmetic.
Davies' 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.
Bey to Davies' New University Arithmetic.
Davies' Elementary Algebra-Embracing the First Principles of the Soience.
Bey to Davies' Elementary Algebra.
Davies' Elementary Geometry AND Trigonometry— With Applications in

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

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

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' Elements 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 and second order.
Dadies' 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 Utility of Mathematics— With the best methods of In-

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

matical Scienie-Comprising Definitions of all the terms employed in 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 eigbt hundred and

sixty-two, by CHARLES DAVIES, in the Clerk's Office of the District Court of the United States for the Southern District of New York.

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

PRE FACE.

Of the various Treatises on Elementary Geometry which have appeared during the present century, that of M. LEGENDRE stands preëminent. Its peculiar merits have won for it not only a European reputation, but have also caused it to be selected as the basis of many of the best works on the subject that have been published in this country.

In the original Treatise of LEGENDRE, the propositions are not enunciated in general terms, but by means of the diagrams employed in their demonstration. This departure from the method of EuclID is much to be regretted. The propositions of Geometry are general truths, and ought to be stated in general terms, without reference to particular diagrams. In the following work, each proposition is first enunciated in general terms, and afterwards, with reference to a particular figure, that figure being taken to represent any one of the class to which it belongs. By this arrangement, the difficulty experienced by beginners in comprehending abstract truths, is lessened, without in any manner impairing the generality of the truths evolved.

20 MAY 02

The term solid, used not only by LEGENDRE, but by many other authors, to denote a limited portion of space, seems calculated to introduce the foreign idea of matter