SECONDARY ALGEBRA BY GEORGE EGBERT FISHER, M.A., Ph.D. AND ISAAC J. SCHWATT, PH.D. ASSISTANT PROFESSORS OF MATHEMATICS IN THE UNIVERSITY OF PENNSYLVANIA PHILADELPHIA FISHER AND SCHWATT 1900 PREFACE. In the preparation of this book, the aim of the authors has been to give the student a working knowledge of the elementary processes of algebra, with a conviction of the truth of principles through illustrations and particular examples. Each principle, or method, is therefore first clearly illustrated by numerous and simple exercises worked in the text. But the student is not left to assume that the principles are thereby proved. Even a beginner should not be encouraged, by textbook or teacher, to accept an illustrative example as a proof, or he will lose much of the educational value of the study. Particular attention has been paid to the grading of the exercises. The introductory chapter extends the familiar processes of arithmetic to the corresponding processes of algebra. The pupil is led by simple exercises, similar to those in arithmetic, to understand the use of letters to represent general and unknown numbers. Negative numbers are naturally introduced in connection with the extension of subtraction of arithmetical numbers. The meaning and use of positive and negative numbers, in the fundamental operations, are properly emphasized. Equations and problems are distributed throughout the book. The importance of equivalent equations is not overlooked, but is very briefly and simply considered in Chapter IV. Until that chapter is reached, the solutions of equations should be checked. |