MARSH'S CONSTRUCTIVE TEXT-BOOK OF PRACTICAL MATHEMATICS FOR USE IN INDUSTRIAL, MANUAL TRAINING, TECHNICAL HIGH SCHOOLS AND COLLEGES, AND APPRENTICE AND EVENING CLASSES THE PRACTICAL ESSENTIALS OF ARITHMETIC, ALGEBRA, GEOMETRY, TRIGONOMETRY, ANALYTICS, AND CALCULUS; INCLUDING THE EXTENSIVE USE OF LOGARITHMS AND THE SLIDE-RULE, WITH THOUSANDS OF EXAMPLES AND APPLIED PROBLEMS BASED ON INDUSTRIAL DATA As Each volume complete in itself. The entire course a unity. 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 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 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 333153 |