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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:

SANBORN, CARTER, BAZIN & CO.,

25 & 29 CORNHILL.

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

In the Clerk's Office of the District Court of Massachusetts.

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PREFACE.

THE author of this treatise has endeavored to prepare a work which should sufficiently exercise the ability of most learners, 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 formulæ.

Most of the problems are original; others have been selected, which seemed the most appropriate.

Although this treatise is designed for students in the higher grade of seminaries, it is not beyond the reach of any, who have a good knowledge of arithmetic, and who are under the guidance of competent instructors. Should Articles 46, 58, 59, 153 and 154 be found too difficult for the beginner, on his first perusal of the book, they may be postponed for investigation in a review.

The writer is unwilling to close his remarks, without expressing his obligations to others, who have done so much to introduce into our country a natural and rational mode of studying mathematics. Among these none merits greater praise than Colburn; and his works have served as a guide in the composition of several others on the inductive plan. Day, Smyth, Davies and Peirce deserve also to be mentioned with great respect.

ENGLISH HIGH SCHOOL,
BOSTON, SEPT. 10, 1841.

THOMAS SHERWIN.

In this new edition of his work, the author would remark, that the few errors of the first edition have been carefully corrected; that a Key to the Algebra has been published; and that, in both the Algebra and Key, a marked distinction has been made between the full point when used as the sign of multiplication and when used as a decimal point; in the latter case, the type being inverted, and the sign consequently elevated.

APRIL 4, 1843.

T. S.

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