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DEFINITIONS OF ALL THE TERMS EMPLOYED IN MATHEMATICS AN
ANALYSIS OF EACH BRANCH, AND OF THE WHOLE,

AS FORMING A SINGLE SCIENCE.

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ASSISTANT PROFESSOR OF MATHEMATICS, UNITED STATES MILITARY ACADEMY.

NEW YORK:
PUBLISHED BY A. S. BARNES & CO.,

No. 51 JOHN-STREET.

1857.

1863. aluch 10 R-X +850-4

$2.00 KF13081

DAVIES' COURSE OF MATHEMATICS.

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Primary Arithmetic and Table Book-An entire new book, designed to take the place of “ Davies' First Lessons.” It is composed of easy and progressive lessons, and adapted to the capacities of young children.

Intellectual Arithmetic, or AN ANALYSIS OF THE SCIENCE OF NUMBERS.—This is also a new book, and designed as a full and complete class-book for the advanced student of Mental Arithmetic in all our Public Schools and Academies. Great care has been taken in the arrangement and gradation of the lessons, in the character of the questions, and in the full, clear, and logical forms of the analysis.

New School Arithmetic, ANALYTICAL AND PRACTICAL, is a complete and thorough revision of the previous editions of his School Arithmetic. Much new matter has been introduced ; the arrangement is more natural and scientific; the methods introduced are those used by some of the best teachers in the country.

University Arithmetic.—The object of this work is to give a general view of the Science of Numbers, and to point out all the general methods of their application.

Practical Mathematics for Practical Men.-The design of this work is to afford to the Schools and Academics an Elementary work of a practical character.

Elementary Algebra.- This work is intended to form a connecting link between Arithmetic and Algebra, and to unite and blend, as far as possible, the reasoning in numbers with the more abstract method of analysis. It is intended to bring the subject of Algebra within the range of our common-schools, by giving to it a practical and tangible form.

Elementary Geometry and Trigonometry.—This work is designed for those whose education extends beyond the acquisition of facts and practical knowledge, but who have not time to go through a full course of mathematical studies. It is intended to present the striking and important truths of Geometry in a form more simple and concise than is adopted in Legendre, and yet preserve the exactness of rigorous reasoning.

Elements of Surveying.-In this work, it was the intention of the author to begin with the very elements of the subject, and to combine those elements in the simplest manner, so as to render the higher branches of Plane Surveying comparatively easy. All the instruments needed for plotting have been carefully described, and the uses of those required for the measurement of angles are fully explained.

Bourdon's Algebra-New and Enlarged Edition.—The Treatise on Algebra by M. Bourdon, is a work of singular excellence and merit. In France it is one of the leading textbooks. Shortly after its first publication it passed through several editions, and has formed the basis of every subsequent work on the subject of Algebra.

Legendre's Geometry and Trigonometry--REVISED Edition.—Legendre's Geometry has taken the place of Euclid, to a great extent, both in Europe and in this country.

Analytical Geometry.--This work embraces the investigation of the properties of geometrical figures by means of analysis.

Descriptive Geometry. -Descriptive Geometry is intimately connected with Architecture and Civil Engineering, and affords great facilities in all the operations of Construction.

Shades, Shadows, and Perspective. This work embraces the various applications of Descriptive Geometry to Drawing and Linear Perspective.

Differential and Integral Calculus.— This Treatise on the Differential and Integral Calculus, is intended to supply the higher seminaries of learning with a text-book on that branch of science.

Logic and Utility of Mathematics is an elaborate exposition of the principles which lie at ihe foundation of pure mathematics, and of the applications of those principles to the development of the essential idea of Arithmetic, Geometry, Algebra, Analytic Geometry, and the Differential and Integral Calculus.

Mathematical Dictionary and Cyclopedia of Mathematical Science - Embracing the definitions of all the terms of Matheinatical science, an analysis of each branch, and of the whole, as forming a single science-designed especially to illustrate the entire

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course.

Entered, according to act of Congress, in the year Eighteen Hundred and Fifty-five, by CHARLES DAVIES

& William G. Peck, in the Clerk's Office of the District Court of the United States, for the Southern

District of New York,
JONES & DENYSE, STEREOTYPXRS.

G. W. WOOD, PRINTER.

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PRE FACE.

• THE SCIENCE OF MATHEMATICS treats of the two abstract quantities, Number and Space. Primarily, it treats of the measurements and relations of these quantities, and of the operations and processes by means of which they are ascertained : and secondarily, of the applications of the principles thus developed to the practical affairs of life.

The quantities operated upon are denoted by figures or letters, and the operations to be performed are indicated by certain characters called Signs. The figures, letters and signs, are called symbols, and are elements of the mathematical language.

The language of mathematics is partly technical and partly popular, being made up of symbols which either represent quantity or denote operations, and of words adopted from our common vocabulary. Both branches of this language are undergoing changes corresponding to the progress and development of the science; and hence it is, that new terms become necessary, while the significations of the old ones are modified, either by enlargement or restriction.

It is of the first importance, in prosecuting mathematical inquiries, to acquiro an accurate knowledge of the office and power of every symbol, and a clear and distinct apprehension of the signification of every technical term. Most of the difficulty experienced in the study of mathematics, has arisen, we apprehend, from the use of terms in a vague or ambiguous sense ; and the discussions on “controverted points,” are mainly due to a misuse or misapprehension of the meaning of technical terms.

1. It is a leading object of this work, to define, with precision and accuracy, every term which is used in mathematical science; and to afford, as far as possible, a definite, perspicuous and uniform language.

2. A second object is, to present in a popular and condensed form, a separate and yet connected view of all the branches of Mathematical Science. Hence, the work has been called "A DICTIONARY AND CYCLOPEDIA OF MATHEMATICAL SCIENCE."

3. The work has also been prepared to meet the wants of the general reader, who will find in it all that he needs on the subject of mathematics. He can learn from it the signification and use of every technical term, and can trace such term, in all its connections, through the entire science. He will find each subject as fully treated as the limits of the work will permit, and the relations of all the parts to each other carefully pointed out.

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