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TRIGONOMETRY,

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APPLICATIONS EN MENSURATION

BY CHARLES DAVIES, LL. D.

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AOTIOR OF FIRST LESSONS IN ARITHMETIC, ELEMENTARY ALGEBRA,
FRACTICAL MATHEMATICS FOR PRACTICAL MEN, ELEMENTS OP
SURVEYING, ELEMENTS OF DESCRIPTIVE GEOMETRY,
SHADES, SHADOWS, AND PERSPECTIVE, ANA-
LYTICAL GEOMETRY, DIFFERENTIAL

AND INTEGRAL CALCULUS.

A. S. BARNES & COMPANY,

NEW YORK AND CHICAGO.

QA5. Dr. Horace Irie

1?SL DAVIES MATHEMATICS.

I dur, on

THE WEST POINT COURSE,

And Only Thorough and Complete Mathematical Series.

IN THREE PARTS.

1. COMMON SCHOOL COURSE Davies' Primary Arithmetic.—The fundamental principles displayed in

the Object Lessons. Davies' Intellectual Arithmetic.-Referring all operations to the unit 1 a.3

the only tangible basis for logical development. Davies' Elements of Written Arithmetic.--A practical introduction

to the whole subject. Theory subordinated to Practice. Davies' Practical Arithmetic.* - The most successful combination of

Theory and Practice, clear, exact, brief, and comprehensive.

II. ACADEMIC COURSE.

Davies' University 'Arith noetic.*_Treating the subject cxhaustively as

a stiexico, in a-logical series of connected propositions. Vavios. Fuenievitásy Atgçbra.* A connecting link, conducting the pupil

easily from arithmetical processes to abstract analysis. Davies' University Algebra.*-For institutions desiring a more complete

but not the fullest course in pure Algebra. Davies' Practical Mathematics.-The science practically applied to the

useful arts, as Drawing, Architecture, Surveying, Mechanics, etc. Davies' Elementary Geometry.-The important principles in simple form,

but with all the exactness of vigorous reasoning.
Davies' Elements of Surveying.-Re-written in 1870. The simplest and
most practical presentation for youths of 12 to 16.

III. COLLEGIATE COURSE.
Davies' Bourdon's Algebra.*_Embracing Sturm's Theorem, and a most

exhaustive and scholarly course.
Davies' University Algebra.*-A shorter course than Bourdon, for Insti-

tutions have less time to give the subject. Davies' Legendre's Geometry:-Acknowledged the only satisfactory trea

tise of its grade. 300,000 copies have been sold. Davies' Analytical Geometry and Calculus.-The shorter treatises,

comoined in one volume, are more available for American courses of study. Davies' Analytical Geometry. The original compendiums, for those deDavies' Diff. & Int. Calculus. siring to give full time to each branch. Davies' Descriptive Geometry.-With application to Spherical Trigonome

try, Spherical Projections, and Warped Surfaces. Davies' Shades, shadows, and Perspective.- A succinct exposition of

the mathematical principles involved.
Davies' Science of Mathematics.-For teachers, embracing,

I. GRAMMAR OF ARITHMETIC, III. LOGIC AND UTILITY OF MATHEMATICS,
II. OUTLINES OF MATHEMATICS, IV. MATHEMATICAL DICTIONARY.
* Keys may be obtained from the Publishers by Teachers only.

COPYRIGAT, 1858, BY CHARLES DAVIES.

COPYRIGHT RENEWED, 1986, BY MARY ANN DAVIES. EL. GEOM.

EDUCATION DEPT

PREFACE.

Those who are conversant with the properation of elementary text-books, have experienced the difficulty of adapting them to the various wants which they are intended to supply.

The institutions of education are of all grades, from the college to the district school, and although there is a wide difference between the extremes, the level, in passing from one grade to the other, is scarcely broken.

Each of these classes of seminaries requires text-books adapted to its own peculiar wants; and if each held its proper place in its own class, the task of supplying suitable works would not be difficult.

An indifferent college is generally inferior, in the system and scope of its instruction, to the academy or high school; while the district school is often found to be superior to its neighboring academy.

The Geometry of Legendre, embracing a complete course of Geometrical science, is all that is desired in the colleges and higher seminaries; while the Practical Mathematics for Practical Men, recently published, is designed to meet the wants of those schools which are strictly elementary and practical in their systems of instruction.

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But still a large class of seminaries remained unsup plied with a suitable text-book on Elementary Geometry and Trigonometry : viz., those where the pupils are car. ried beyond the acquisition of facts and mere practical knowledge, but have not time to go through with a full course of mathematical studies.

It is for such, that the following work is designed. It has been the aim of the author to present the striking and important truths of Geometry in a form more simple and concise than could be adopted in a complete treatise, and yet to preserve the exactness of rigorous reasoning.

In this system of Geometry nothing has been taken fo granted, and nothing passed over without being fully de monstrated.

The Trigonometry, including the applications to the measurements of heights and distances, has been written upon the same plan and for the same objects: it embraces all the important theorems and all the striking examples.

In order, however, to render the applications of Goometry to the mensuration of surfaces and solids complete in itself, a few rules have been given which are not demonstrated. This forms an exception to the general plan of the work, but being added in the form of an appendix, it does not materially break its unity.

'That the work may be useful in advancing the interests of education, is the hope and ardent wish of the author. FISIKILL LANDING,

May, 1861

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