Entered, according to Act of Congress, in the year 1890, by

G. A. WENTWORTH,

in the Office of the Librarian of Congress, at Washington.

ALL RIGHTS RESERVED.

TYPOGRAPHY BY J. S. CUSHING & Co., BOSTON, U S.A.

PRESSWORK BY GINN & Co., BOSTON, U.S.A.

PREFACE.

THIS book, as the name implies, is written for High Schools and Academies, and is a thorough and practical treatment of the principles of Elementary Algebra. It covers sufficient ground for admission to any American college, and with the author's College Algebra makes as extended a course as the time allotted to this study in our best schools and colleges will allow. Great care has been taken to present the best methods, so that students in going from the lower book to the higher will have a good foundation, and have nothing to unlearn.

The problems are carefully graded. They are for the most part new; either original or selected from recent examination papers. They are sufficiently varied and interesting and are not so difficult as to discourage the beginner. The early chapters are quite full; for even if a student is perfectly familiar with the operations of Arithmetic, he must have, time, to learn the language and the fundamental processes of Algebra..

The introductory chapter should be read and discussed in the recitation room. This chapter brings before the student in brief review the knowledge he has already gained from the study of Arithmetic, states and proves the general laws of numbers, sets forth clearly the advantage of using letters to represent numbers in the statement of general laws, and leads him to see at the outset that Algebra, like Arithmetic, treats of numbers. In this chapter, also, the meaning of negative quantities is explained, and the laws which regulate the combinations of different arithmetical numbers are shown to apply to algebraic numbers. It is hoped