BY CHARLES DAVIES, LL.D.,
AJTEUR 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 AND CHICAGO.

1874.

DAVIES' MATHEMATICS. TH'D . West ::: :

And: Only :Thorough and Complete Mathematical Series.

QAS29
L42

POINT COURSETF62

Eneginecoing

Library

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.

11. ACADEMIC COURSE. Davies' University Arithmetic.*-Treating the subject exhaustively as

a science, in a logical series of connected propositions. Davies’ Blementary 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.

UI. 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 Institu-

tions 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' Dif. & Int. Calculus. siring to give full time to each branch. Davies' Descriptive Geometry.-With application to Spherical Trigonome

try, 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, III. LOGIC AND UTILITY OF MATHEMATICS,
II. OUTLINES 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.
L. GIFT OF I

UN.

Norge

PRE FACE.

Of the various Treatises on Elementary Geometry which lave appeared during the present century, that of M. LEGENDRE stands preëminent. Its peculiar merita 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 anthors, to denote a limited portion of space, seemas calculated to

foreign idea of matter