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COURSE OF MATHEMATICS

Davies' First Lessons in Arithmetic-For Beginners.
Bavies' 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. Davies' Bourdon's Algebra—Including STURM'S THEOREM–Being an abridg

ment of the Work of M. OURO 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 LOGARITIMS and LOGARITHMIC SINES. 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 Conic SECTIONS—of the LINE AND PLANE IN SPACE ; also, the discussion of the GENERAL EQUATION of the second degree, and of Sub

FACES of the second order.
Davies' 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 the United States for the Southern District of New York.

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PRE FACE.

The Elements of Surveying, first published in 1830, was designed as a text-book for the pupils of the Military Academy, and in its preparation little regard was had to the supposed wants of other institutions.

The work, however, was received by the public with more favor than was anticipated, and soon became a leading text-book in the Colleges, the Academies, and the higher grade of Schools.

For the purpose of adapting it, more fully, to the supposed wants of these institutions many changes have been made, since its first publication, and the present edition will be found to differ, in many respects, from those which have preceded.

It has been the intention to begin with the very ele ments 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.

The conventional signs adopted by the Topographical Bureau, which are now used by the United States Engineers in all their Charts and Maps, are given in plates 5 and 6.

Should these signs be generally adopted in the country, it would give entire uniformity to all maps and delineations of the ground, and would establish a kind of lan. guage by which all the peculiarities of soil and surface could be accurately represented.

A section has also been added on Geodesy. This branch of Surveying is extensively applied in the Coast Survey, and now forms an important element of a practical or scientific education.

A full account is also given of the manner of survey. ing the public lands; and, although the method is simple, it has, nevertheless, been productive of great results, by defining, with mathematical precision, the boundaries of lands in the new States, and thus settling their titles on an indisputable basis.

This method was originated by Col. Jared Mansfield, whose great acquirements in science introduced him to the notice of President Jefferson, by whom he was appointed surveyor.general of the North-Western Territory.

May it be permitted to one of his pupils, and a graduate of the Military Academy, further to add, that at the organization of the institution in 1812, he was appointed Professor of Natural and Experimental Philosophy. This situation he filled for sixteen years, when he withdrew from the Academy to spend the evening of his life in retirement and study. His pupils, who had listened to his instructions with delight, who honored his learning and wisdom, and had been brought near to him by his kind and simple manners, have placed his portrait in the public library, that the institution might possess an enduring memorial of one of its brightest ornaments and distin. guished benefactors.

At the solicitation of several distinguished teachers, there is added, in the present edition, an article on Plane Sailing, most of which has been taken, by permission of the author, from an excellent work on Trigonometry and its applications, by Professor Charles W. Hackley. FISHKILL LANDING

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