Edve T 129.00. 170

HARVARD

COLLEGE

MAR 20 1931

LIBRARY

E. V. Hill

COPYRIGHT, 1900,
BY THE MORSE COMPANY.

PREFACE.

THE desirable results to be attained in the study of Algebra are the thought of letters as general symbols of number, familiarity with the laws of the algebraic notation, facility and accuracy in performing algebraic processes, skill in the use of the equation as a means of mathematical investigation, and the development of the reasoning powers. In the attainment of these results, the teacher is the important factor, but the character of the book used determines in a greater or less degree the character of the work done and the effects upon the student.

These considerations have been the motives for the preparation of this work, and it is confidently believed that the use of it will lead to broader views of numbers and their properties, and produce increasing mental power. It is designed for use in high schools and academies, and advanced classes in grammar schools. A distinguishing feature of the book is its arrangement. The definitions, demonstration of principles, derivation of rules, model solutions, and illustrations occupy the last half of the book, and the exercises and problems the first half. The reasons for this arrangement are evident, and it is believed that the separation of the text from the exercises and problems can be no inconvenience in the legitimate use of either. The text is complete in the clearness and conciseness of definitions, thorough demonstration of principles, careful derivation of rules, and the abundance of illustrations and model

solutions. Frequent notes to the teacher will be found in the first half of the book. The numbers in these notes refer to articles in the text, and the notes indicate that the following exercise contains new work, for which students must be prepared.

The other prominent features of the work are the fre quent exercises in algebraic expression, the unusual number and variety of examples and problems and the careful grading of the same, the early introduction of the equation and its use in the solution of problems, the thorough treatment of factoring, the completeness of the work on involution and evolution, the discussions and exercises on the signification of exponents, the character and amount of work in radicals, and the emphasis on the solution of complete quadratics by the method of factoring.

The author desires to acknowledge his indebtedness to A. B. Davis, A.M., Principal of High School, Mount Vernon, N.Y.; Lyman A. Best, A.M., Principal of School No. 13, Brooklyn, N.Y.; and J. Frank Shields, B.S., Professor of Mathematics, Adelphi College, Brooklyn, N.Y.; all of whom have critically read the MS. and made valuable suggestions concerning various features of the work.

The work is submitted to the profession with the hope that teachers and students may use it with the greatest pleasure and profit. This is the highest reward the author can desire.

GEORGE E. ATWOOD.