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WILSON, HINKLE & CO.,
CINCINNATI:

NEW YORK:

137 WALNUT ST.

28 BOND ST.

tot

RAY'S SERIES,

EMBRACING

A Thorough and Progressive Course in Arithmetic, Alge

bra, and the Higher Mathematics.

Primary Arithmetic.
Intellectual Arithmetic.
Rudiments of Arithmetie.
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., Pres'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.

Descriptive Circulars and Price List upon Application

to the Publishers.

3

Entered according to Act of Congress, in the year 1866, by SARGENT, WILSON & HINKLE, in the Clerk's Office of the District Court of

the United States for the Southern District of Ohio,

CHARLE HERBERT THURBER

May 24,1988

PREFACE.

This work has been prepared with a view to meeting the wants of the primary and intermediate departments of large graded schools. The author has also sought to furnish a small, simple, and cheap class-book,, adapted to the requirements of pupils commencing the study of Practical Arithmetic in the common schools of the country, as well as in the graded schools of the larger towns and cities.

In entering upon the study of Practical Arithmetic, as presented in the more extended works in general use, the mind of the young learner is often confused and embarrassed by a multiplicity of methods, explanations, solutions, rules, exceptions, remarks, notes, etc. To avoid this evil, it has been the constant aim, in the preparation of this work, to present each subject in one form only, and that the most concise and simple consistent with clearness.

In treating each subject, a MODEL, designed to be thoroughly studied by the pupil, is given, embracing a full and lucid solution of an example, with accompanying operation, from which a general rule is deduced.

The definitions are plain and simple, and as brief as mathematical exactness will admit. Mental exercises precede the practical examples, which, without being unnecessarily multiplied, are sufficiently numerous, especially in the fundamental rules, to give the pupil a thorough drill, rendering him ready, quick, and accurate in the simpler arithmetical calculations.

It is not expected that the solutions and explanations given will, in all cases, preclude the necessity of additional illustra

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