MARSH'S CONSTRUCTIVE TEXT-BOOK

OF

PRACTICAL MATHEMATICS

FOR USE IN INDUSTRIAL, MANUAL TRAINING, TECH-
NICAL HIGH SCHOOLS AND COLLEGES, AND
APPRENTICE AND EVENING CLASSES

THE PRACTICAL ESSENTIALS OF ARITHMETIC, ALGebra, geom-
ETRY, TRIGONOMETRY, ANALYTICS, AND CALCULUS; IN-
CLUDING THE EXTENSIVE USE OF LOGARITHMS
AND THE SLIDE-RULE, WITH THOUSANDS

OF EXAMPLES AND APPLIED PROBLEMS

BASED ON INDUSTRIAL DATA

Each volume complete in itself. The entire course a unity. As constructive, developing, and creative as shop work. Educates through self-activity, affords self-realization through self-expression, and gives the knowledge and the use of the Mathematics of modern industries.

Head of Department of Mathematics, School of Science
and Technology, Pratt Institute

VOLUME II

TECHNICAL ALGEBRA

PART I

FIRST EDITION

NEW YORK

JOHN WILEY & SONS, INC.

LONDON: CHAPMAN & HALL, LIMITED

Copyright, 1913,

BY

HORACE WILMER MARSH

PRESS OF
BRAUNWORTH & CO.

BOOKBINDERS AND PRINTERS

BROOKLYN, N. Y.

PREFACE

PROFESSOR JOHN DEWEY long ago emphasized the idea that the school is truly educative only when it represents actual, social conditions. In the trade and technical school of secondary rank, such as the School of Science and Technology of Pratt Institute, we have been forced to recognize and prove the truth of Professor Dewey's assertion. The graduates of a school of this kind, although requiring an acquaintance with books, must be able to do and to direct others. Their mathematics must be of the sort which they can use and apply in their daily work after graduation. It must be presented in such form and manner during the entire course that its use and application shall be an acquired art the same as the use of any other tool.

This text in form and method is the result of an attempt to solve the problem of the teaching of mathematics, not from the point of view, therefore, of the mathematician but from the necessities of the student and the demands of the environment in which he is and into which he is to go. The mathematician sees mathematics only; the student sees the unknown and is estranged; the true teacher sees active boys and girls or young men and women whose study must be so directed that they shall become genuinely interested in mathematics and shall have a feeling of confidence and satisfaction in its use.

This direction is possible only when mathematics is regarded and taught, not primarily as a means to mental

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