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AN

ELEMENTARY TREATISE

ON

ALGEBRA,

FOR THE USE OF STUDENTS

IN

HIGH SCHOOLS AND COLLEGES.

BY THOMAS SHERWIN, A. M.,
Principal of the English High School, Boston.

SEVENTH EDITION.

BOSTON:

HALL AND WHITING,

32 BROMFIELD STREET.

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ARVAR
UNIVERSITY
LIBRARY

047*172

Entered according to act of Congress, in the year 1841,
BY THOMAS SHERWIN,

In the Clerk's Office of the D'strict Court of Massachusetts.

PREFACE.

THE author of this treatise has endeavored to prepare a work which should sufficiently exercise the ability of most earners, without becoming, at the same time, repulsive to them by being excessively abstract. Some writers err in expecting too much, and others err, in an equal degree, by requiring too little of the student. What success has attended an attempt to attain a proper medium it is left for competent teachers to decide.

This work commences in the inductive manner, because that mode is most attractive to beginners. As the learner advances, and acquires strength to grapple with it, he meets with the more rigorous kind of demonstration. This course seems the most natural and effective. Induction is excellent in its place; but when an attempt is made to carry it into all the departments of an exact science, the result often shows, that the main object of study was misapprehended. The young frequently fail to deduce clearly the general principle from the particular instances which have engaged their attention.

Several parts of algebra, which are either omitted or not explained with sufficient distinctness in other works, have received particular attention in this. These parts treat of principles and operations, with which students. rarely become familiar, but which are essential to a clear comprehension of the subject. Among these operations may be mentioned the separation of quantities into factors, finding the divisors of quantities, and the substitution of numbers in algebraic fo mulæ.

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