ELEMENTARY ALGEBRA

The

THE MACMILLAN COMPANY
NEW YORK • BOSTON • CHICAGO
DALLAS SAN FRANCISCO

MACMILLAN & CO., LIMITED
LONDON. BOMBAY . CALCUTTA
MELBOURNE

THE MACMILLAN CO. OF CANADA, LTD.

TORONTO

BY

JOHN W. HOPKINS

SUPERINTENDENT OF THE GALVESTON PUBLIC SCHOOLS

66

AND

P. H. UNDERWOOD

TEACHER OF MATHEMATICS, BALL HIGH SCHOOL, GALVESTON, TEXAS

AUTHORS OF MENTAL ARITHMETIC, PRIMARY ARITHMETIC,"
66 ELEMENTS OF ARITHMETIC IN THEORY AND PRACTICE "

99 66

New York

THE MACMILLAN COMPANY

1912

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AND

"As regards the method of teaching algebra, I would make it, in the earlier stages, as much a generalized arithmetic as possible. Results obtained by algebra would be verified by arithmetical instances; and the use of a formula would be indicated as including any number of instances. Elaborate (and to my mind wearisome) processes, useful for solving artificial combinations of difficulties, would be at least deferred. With a comparative beginner, progress towards new ideas or new stages of old ideas can, I think, best be made by the simplest instances, and it is on this account that I would build algebra entirely on arithmetical foundations so far as concerns the teaching of beginners."

-Professor Forsyth, M.A., D.Sc., F.R.S., Cambridge.

"It is assumed that pupils will be required throughout the course to solve numerous problems which involve putting questions into equations. Some of hese problems should be chosen from mensuration, from physics, and from commercial life. The use of graphical methods and illustrations, particularly in connection with the solution of equations, is also expected."

- Extract from the Report of the American Mathematical Society, 1903.