OF

ALGEBRA.

BY WILLIAM SMYTH, A. M.

PROFESSOR OF MATHEMATICS IN BOWDOIN COLLEGE.

Third Edition.

HALLOWELL:

GLAZIER, MASTERS & SMITH.

1836.

HARVARD COLLEGE

Left 271 1922

Duplicate money

Entered, according to act of Congress, in the year 1833, by WILLIAM SMYTh, A. M.

in the District Clerk's Office of the District of Maine.

ADVERTISEMENT TO THE THIRD EDITION.

THE design of the writer of the following treatise, is to provide a convenient text book for a College class, and the subjects are presented in such a manner, as from actual experiment in the recitation room has appeared adapted to this object. Care has been taken to proceed gradually from simple principles to those more difficult, and in general to furnish all needful helps to the learner without unnecessarily multiplying explanations, or in any case extending them so far, as to leave no room for the exercise of his own powers. Very considerable attention, it will be perceived, has been paid to the subject of generalization and to the discussion of problems and equations, topics which need to be clearly understood by the student, that he may fully appreciate the nature and powers of Algebra, and be enabled to proceed with ease to the various studies, in which it is employed as an instrument of investigation. A section has been devoted to Indeterminate Analysis, a subject not usually introduced into the elementary treatises published in this country, but one of great importance on account of the interesting problems, which it furnishes, and from its relation to the Application of Algebra to Geometry. A copious praxis is also added, designed particularly to exhibit the principal artifices, employed in the reduction of the more complicated equations.

In the present edition no material changes have been made. Some additional explanations, however, have been given, new examples have been added, where it was thought they would be useful, a few have been rejected as unnecessary, and oth