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OF

SURVEYING,

AND

NAVIGATION,

WITH DESCRIPTIONS OF THE INSTRUMENTS AND THE

NECESSARY TABLES.

BY CHARLES DAVIES, LL. D.,
AUITIOR OF ARITHMETIC, ALGEBRA, PRACTICAL MATHEMATICS FOR PRACTICAL MEN
ELEMENTS OF DESCRIPTIVE 'GEOMETRY, SHADES, SHADOWS, AND PEL-
SPECTIVE, ANALYTICAL GEOMETRY, DIFFERENTIAL AND

INTEGRAL CALCULUS.

REVISED EDITION.

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

No. 51 JOHN-STREET.
CINCINNATI: H. W. DERBY & CO.,

1857.

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 theu

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

ing a connecting link between ARITHMETIC 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. 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 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 PROJEC

TIONS.

Davies' Shades, Shadows, And Linear Perspective.
Dabies' 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 Suz:

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

UNTERED 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 Conrt of tb

629864 /

47 SQB D28 2

PREFACE.

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 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 Engi. neers 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 language by which all the peculiarities of soil and surface could be accurately represented.

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