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GEOMETRY AND TRIGONOMETRY,

TROX TEL WORKS OF

Adrien Marie

A. M. LEGENDRE.

REVISED AND ADAPTED TO THE COURSE OF MATHEMATICAL INSTRUCTION IN

THE UNITED STATES,

BY CHARLES DAVIES, LL. D.,

AUTHOR OF ARITHMETIC, ALGEBRA, PRACTICAJ. MATHEMATICS FOR PRACTICAL MEN,
ELEMENTS OF DESCRIPTIVE AND OF ANALYTICAL GEOMETRY, ELEMENTS
OF DIFFERENTIAL AND INTEGRAL CALCULUS, AND SHADES,

SHADOWS, AND PERSPECTIVE,

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

No. 51 JOHN-STREET.
OINCINNATI: H. W. DERBY & U0.

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6 DA VIES'. Math 50863.

50 COURSE OF MATHEMATICS

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

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

ing a connecting link between ARITHMETIO 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. Davies' Practical Mathematics for practical Men-Embracing the Princi

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

to the Mechanic Arts. Dabies' Bourdon's Algebra_Including SturM'S THEOREM-Being an abridg

ment of the Work of M. BOURDON, with the addition of practical examples. Davies' Legendre'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 Sixes.
Davies' Surveying—With a description and plates of the THEODOLITE, COM

PASS, PLANE-TABLE, and LEVEL; also, Maps of the TOPOGRAPHICAL SIGNs adopted by the Engineer Department-an explanation of the method of surveying the Public Lands, Geodesic and Maritime Surveying, and an Elementary Treatise on NAVIGATION. Davies' Descriptive Geometry— With its application to SPHERICAL PROJEO

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

STRAIGHT LINE—of the Cono SECTIONS—of the LINE AND PLANE IN SPACE ;
also, the discussion of the GENERAL EQUATION of the second degree, and of SUR-

FACES of the second order.
Babies' Differential and Entegral Calculus.
Davies' Logic and Utility of Mathematics.

ENTERED according to Act of Congress, in the year one thousand eight hundred and

fifty-one, by Charles Davies, in the Clerk's Office of the District Court of tb United States for the Soutliern District of New York.

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PRE FACE.

In the preparation of the present edition of the Geom. etry of A. M. LEGENDRE, the original has been consulted as a model and guide, but not implicitly followed as a standard. The language employed, and the arrangement of the arguments in many of the demonstrations, will be found to differ essentially from the original, and also from the English translation by DR. BREWSTER.

In the original work, as well as in the translation, the propositions are not enunciated in general terms, but with reference to, and by the aid of, the particular diagrams: used for the demonstrations. It is believed that this departure from the method of Euclid has been generally regretted. The propositions of Geometry are general truths, and as such, should be stated in general terms, and without reference to particular figures. The method of enunciating them by the aid of particular diagrams seems to have been adopted to avoid the difficulty which beginners experience in comprehending abstract proposi. tions. But in avoiding this difficulty, and thus lessening, at first, the intellectual labor, the faculty of abstraction, which it is one of the primary objects of the study of Geometry to strengthen, remains, to a certain extent, un improved.

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