PREFACE THE aim of this book is to introduce the young student to the study of algebra, in particular to those portions of algebra that are indispensable to the study of geometry, mensuration, physics, and chemistry as pursued in secondary schools. The book is an outgrowth of classroom experience, lays stress on fundamental principles, and illustrates these principles so that the beginner may not 66 regard algebra as a very arbitrary affair, involving the application of a number of fanciful rules to the letters of the alphabet." As far as the authors know, this is the first beginners' book that graphically illustrates the fundamental rules, fundamental laws and facts, and incidentally brings out in bold relief the essential connections of arithmetic, algebra, and concrete geometry. Whoever wishes to obtain a clear and sound knowledge of the fundamental operations of algebra must have recourse to arithmetic and to geometric illustrations, since learning is, at bottom, largely a process of visualizing. Every point that we have found to give trouble to the young learner is dealt with in a way that will bring into play the perceptive powers of the student. Professor Minchin well says: "Effective teaching requires a great deal more than a bare recitation of facts, even if these are duly set forth in logical order. The probable difficulties. which the intelligent student will naturally and necessarily encounter in some statement of fact or theory, these things our authors seldom or never notice, and yet a recognition and anticipation of them by the author would often be of priceless value to the student." Few of our pupils in secondary schools have a clear conception of why having like signs in the multiplication of two numbers produces a plus result. This is one place where a textbook should come to the assistance of the student. The first ten chapters furnish an easy introduction to the study of algebra. There are a great many simple problems, the typical solutions are natural, and there is no obvious striving to arrive at hasty generalizations. The last ten chapters demand more maturity on the part of the learner. It is a good practice to fix principles in the mind by means of easy examples, and then to move forward to difficult ones. The examples here are of medium grade, neither too easy nor too hard, and have been used in teaching classes in the Ball High School. Occasionally an example is inserted that will provoke serious thought. This book leaves out the Euclidean method of finding the Highest Common Factor because it is not a practical topic. It also omits certain theorems in the Theory of Exponents, Surds, and Imaginary Numbers and the Theory of Limits because they are too difficult for the pupils of secondary schools. A large number of the examples are new; the others are mainly from examination papers. GALVESTON, TEXAS. April 7, 1912. THE AUTHORS. CONTENTS The Equation. Problems XVI. Surds. Fractional Exponents. Radical Equations |