ADAPTED TO THE COURSE OF MATHEMATICAL INSTRUCTION IN
THE UNITED STATES,

BY CHARLES DAVIES, LL.D.,

AUTHOR OF ARITHMETIC, ALGEBRA, PRACTICAL MATHEMATICS FOR PRACTICAL MEN.
ELEMENTS OF DESCRIPTIVE AND OF ANALYTICAL GEOMETRY, ELEMENTS

OF DIFFERENTIAL AND INTEGRAL CALCULUS, AND SHADES,

SHADOWS, AND PERSPECTIVE.

A. S. BARNES & COMPANY,

NEW YORK, CHICAGO AND NEW ORLEANS.

[1875,0

Math 5086.3.53

HARVARD COLLEGE

Mali 5108.62.3 MAY 24 1897
DAVIES MATHEMATICS.

L

IBRARY

THE WEST POINT COURSE,
W. M. Woodworth.
And Only Thorough and Complete Mathematical Series.

IN THREE PARTS.

I. COMMON SCHOOL COURSE

Davies' Primary Arithmetic.-The fundamental principles displayed in
Object Lessons.

Davies' Intellectual Arithmetic.-Referring all operations to the unit 1 as
the only tangible basis for logical development.

Davies' Elements of Written Arithmetic.-A practical introduction to the whole subject. Theory subordinated to Practice.

Davies' Practical Arithmetic.*-The most successful combination of Theory and Practice, clear, exact, brief, and comprehensive.

II. ACADEMIC COURSE.

Davies' University Arithmetic.*-Treating the subject exhaustively as a science, in a logical series of connected propositions.

Davies' Elementary Algebra.*-A connecting link, conducting the pupil easily from arithmetical processes to abstract analysis.

Davies' University Algebra.*-For institutions desiring a more complete but not the fullest course in pure Algebra.

Davies' Practical Mathematics.-The science practically applied to the useful arts, as Drawing, Architecture, Surveying, Mechanics, etc.

Davies' Elementary Geometry. The important principles in simple form, but with all the exactness of vigorous reasoning.

Davies' Elements of Surveying.-Re-written in 1870. The simplest and most practical presentation for youths of 12 to 16.

III. COLLEGIATE COURSE.

Davies' Bourdon's Algebra.*-Embracing Sturm's Theorem, and a most exhaustive and scholarly course.

Davies' University Algebra.*-A shorter course than Bourdon, for Institutions have less time to give the subject.

Davies' Legendre's Geometry.-Acknowledged the only satisfactory treatise of its grade. 300,000 copies have been sold.

Davies' Analytical Geometry and Calculus.-The shorter treatises, combined in one volume, are more available for American courses of study. Davies' Analytical Geometry. The original compendiums, for those deDavies' Diff. & Int. Calculus. siring to give full time to each branch. Davies' Descriptive Geometry. With application to Spherical Trigonometry, Spherical Projections, and Warped Surfaces.

Davies' Shades, Shadows, and Perspective. A succinct exposition of the mathematical principles involved.

Davies' Science of Mathematics.-For teachers, embracing

I. GRAMMAR OF ARITHMETIC,

II. OUTLINES OF MATHEMATICS,

III. LOGIC AND UTILITY OF MATHEMATICS

IV. MATHEMATICAL DICTIONARY.

*Keys may be obtained from the Publishers by Teachers only.

Entered, according to Act of Congress, in the year 1862, by
CHARLES DAVIES,

In the Clerk's Office of the District Court of the United States for the Southern District of

New York.

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L.

PREFACE.

F the various Treatises on Elementary Geometry which

LEGENDRE stands preeminent. 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.

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 into a science, which deals only with the abstract properties and relations of figured space. The term volume, has been introduced in its place, under the belief that it corresponds more exactly to the idea intended. Many other departures have been made from the original text, the value and utility of which have been