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CINCINNATI:
SARGENT, WILSON & HINK LE.
CHICAGO: COBB, PRITCHARD & CO.

NEW YORK: CLARK & MAYNARD-

THE BEST AND CHEAPEST.

RA Y'S

MATHEMATICAL COURSE.

EACH BOOK COMPLETE IN ITSELF, AND SOLD SEPARATELY,

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PRIMARY ARITHMETIC, or First Book: Simple Mental Lessons

and Tables. For little learners. INTELLECTUAL ARITHMETIC, OR SECOND Book: the most interest

ing and valuable Intellectual Arithmetic extant. PRACTICAL ARITHMETIC, OR THIRD Book : a full and practical

treatise on the inductive and analytic methods of instruction. For

Schools and Academies.
HIGHER ARITHMETIC, or Fourth Book: the principles of Arith-

metic analyzed and practically applied. For advanced classes. TEST EXAMPLES : Three THOUSAND practical problems for the slate

or blackboard. For drill exercises and review. Two editions-one

without Answers; the other with Answers. ELEMENTARY ALGEBRA, or First Book: a simple, thorough, and

progressive elementary treatise. For Schools and Academies. HIGHER ALGEBRA, OR SECOND Bcok : a progressive, lucid, and com

prehensive work. For advanced Students, and for Colleges. KEYS TO ARITHMETICS AND ALGEBRAS : embracing full and

lucid solutions to all the more difficult problems in the Intellectual,

Practical, and Higher Arithmetics, and the Algebras.
ELEMENTS OF GEOMETRY: a comprehensive work on Plane and

Solid Geometry, with numerous practical exercises. For Colleges,

Schools, and private Students.
TRIGONOMETRY AND MENSURATION : Plane and Spherical Trigo-

nometry, with their applications ; Mensuration of planes and solids,

etc. (Preparing.) SURVEYING AND NAVIGATION : Surveying and Leveling, Navi

gation, Barometric Heights, etc. (Preparing.)

Entered according to act of Congress, in the year 1852, by W. B. SMITH, in the Clerk's Office of the District Court of the United States, for the District of Ohio.

Entered according to Act 1 - "ess, 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.

ELECTROTYPED AT THE FRANKLIN TYPE FOUNDRY, CINCINNATI,

HARVARD COLLEGE LITARY

GIFT OF
GEORCE ARTHUR PLIMPTON

JAWAY 25, 1924

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Algebra is justly regarded one of Ahe most interesting and useful branches of education, and an acquaintance with it is now sought by all who advance beyond the more common elements. To those who would know Mathematics, a knowledge not merely of its elementary principles, but also of its higher parts, is essential; while no one can lay claim to that discipline of mind which education confers, who is not familiar with the logic of Algebra.

It is both a demonstrative and a practical science-a system of truths and reasoping, from which is derived a collection of Rules that may be used in the solution of an endless variety of problems, not only interesting to the student, but many of which are of the highest possible utility in the arts of life.

The object of the present treatise is to present an outline of this science in a brief, clear, and practical form. The aim throughout has been to demonstrate every principle, and to furnish the student the means of understanding clearly the rationale of every process he is required to perform. No effort has been made to simplify subjects by omitting that which is difficult, but rather to present them in such a light as to render their acquisition within the reach of all who will take the pains to study.

To fix the principles in the mind of the student, and to show their bearing and utility, great attention has been paid to the preparation of practical exercises. These are intended rather to illustrate the principles of the science, than as difficult problems to torture the ingenuity of the learner, or amuse the already skillful Algebraist.

An effort has been made throughout the work to observe a natural and strictly logical connection between the different parts, so that the learner may not be required to rely on a prin

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