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SURVEYING

AND

NAVIGATION, NO

WITH A PRELIMINARY TREATISE ON

TRIGONOMETRY AND MENSURATION,

BY

A. ŞCHUYLER, M. A.,

Professor of Applied Mathematics and Logic in Baldwin University ; Author of

Higher Arithmetic, Principles of Logic, and Complete Algebra.

VAN ANTWERP, BRAGG & CO.,
137 WALNUT STREET,

28 BOND STREET,
CINCINNATI.

NEW YORK.

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A Thorough and Progressive Course in Arithmetic, Algebra,

the Higher Mathematics.

Primary Arithmetic.
Intellectal arithmetic.
Rudiments of Arithmetic.
Practical Arithmetic.

Higher Arithmetic.
Test Examples in Arithmetic.

New Elementary Algebra.
| New Higher Algebra.

Plane and Solid Geometry. By Eli T. TAPPAN, A.M., Pres't

Kenyon College. 12mo, cloth, 276 pp. Geometry and Trigonometry. By ELI T. TAPPAN, A.M.

Fres't Kenyon College. 8vo, sheep, 420 pp. Analytic Geometry. By Geo. H. HOWISON, A.M., Prof. in Mass.

Institute of Technology. Treatise on Analytic Geometry, especially as applied to the Properties of Conics : including the Modern

Methods of Abridged Notation. Elements of Astronomy. By S. H. PEABODY, A.M., Prof. of

Physics and Civil Engineering, Amherst College. Handsomely and profusely illustrated. 8vo, sheep, 336 pp.

KE Y S.

Ray's Arithmetical Key (To Intellectual and Practical);
Key to Ray's Higher Arithmetic;
Key to Ray's New Elementary and Higher Algebras.

GIFT OF

Dr. Horace Ivié The Publishers furnish Descriptive Circulars of the abovc Mathematical Text-Books, with Prices and other information concerning them.

EDUCATION DEPT Entered according to Act of Congress, in the year 1864, by SARGENT, Wilson & HINKLE, in the Clerk's Office of the District Court of the United

States for the Southern District of Ohio.

PREFACE.

Nearly twenty years ago the Publishers made the following announcement: “Surveying and Navigation ; containing Surveying and Leveling, Navigation, Barometric Heights, etc."

To redeem this promise, the present work now appears.

It is customary to preface works on Surveying by a meager sketch of Plane Trigonometry, but it has been thought best to include in this work a thorough treatment of Plane and Spherical Trigonometry and Mensuration. These subjects have been treated in view of the wants of our best High Schools and Colleges.

Certain modern writers have defined the Trigonometric functions as ratios; for example, in a right triangle, the sine of an angle is the ratio of the opposite side to the hypotenuse, etc.

The historical method of considering the sine, co-sine, tangent, etc., as linear functions of the arc, explains the origin of these terms — avoids the ambiguity of the word ratio; explains how the logarithm of the sine, for example, can reach the limit 10, which would be impossible if the limit of the sine itself is 1, and is much more readily apprehended by the student.

The advantages in analytic investigations resulting from defining these functions as ratios have been secured in the principles relating to the Right Triangle, Art. 64.

Each of the circular functions has, in the first place, been considered by itself, and its value traced, for all arcs, from 0° to 360°.

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