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D abies'

Course of Mathematics.

Davies! Primary Arithmetic AND Table-Book-Designed for Beginners ;

containing the elementary tables of Addition, Subtraction, Multiplication, Division, and Denominate Numbers; with a large number of easy and prac

tical questions, both mental and written.
Davies' First Lessons in Arithmetic-Combining the Oral Method with the

Method of Teaching the Combinations of Figures by Sight.
Davies' Intellectual Arithmetic-An Analysis of the Science of Numbers, with

especial reference to Mental Training and Development.
Dabies' New School Arithmetic-Analytical and Practical.
Bey to Dabies' New School Arithmetic.
Davies' Grammar of Arithmetic--An Analysis of the Language of Nuubers

and the Science of Figures.
Davies: New University Arithmetic-Embracing the Science of Numbers, and

their Applications according to the most Improved Methods of Analysis and

Bey to Davies' New University Arithmetic.
Davies' Elementary Algebra-Embracing the First Principles of the Science.
Rey to Davies' Elementary Algebra.
Bavies' Elementary Geometry AND Trigonometry— With Applications in

Davies' Practical Mathematics--With Drawing and Mensuration applied to

the Mechanic Arts.
Davies' University Algebra-Embracing a Logical Development of the

Science, with graded examples.
Davles' Bourdon's Algebra-Including Sturm's and Horner's Theorems,

and practical examples.
Davies' Legendre's Geometry and Trigonometry--Revised and adapted to

the course of Mathematical Instruction in the United States.
Babies' Elenrents of Surveying and Navigation—Containing descriptions

of the Instruments and necessary Tables.
Davies' Analytical Geometry-Embracing the Equations of the Point, the

Straight Line, the Conic Sections, and Surfaces of the first and second order.
Davies' Differential and Entegral Calculus.
Davies' Descriptive Geometry-With its application to Spherical Trigonome-

try, Spherical Projections, and Warped Surfaces.
Davies' Shades, Shadows, AND Perspective.
Davies' Logic and Utility of Mathematics-With the best methods of In-

struction Explained and Illustrated. Davies' and Peck's Mathematical Dictionary and Cyclopedia of Mathe

matical Science—Comprising 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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ENTERED according to Act of Congress, in the year one thousand eight hundred and fifty

one, by CHARLES Davies, in the Clerk's Ofice of the District Court of the United States for the Southern District of New York.



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 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 bave 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 delinea. tions of the ground, and would establish a kind of language by which all the peculiarities of soil and surface 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 gradu. ate 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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