MATHEMATICAL TEXT-BOOKS By G. A. WENTWORTH, A.M. Mental Arithmetic. Elementary Arithmetic. Practical Arithmetic. Primary Arithmetic. Grammar School Arithmetic. High School Arithmetic. High School Arithmetic (Abridged). First Steps in Algebra. School Algebra. College Algebra. Elements of Algebra. Complete Algebra. Shorter Course in Algebra. Higher Algebra. New Plane Geometry. New Plane and Solid Geometry. Syllabus of Geometry. Geometrical Exercises. Plane and Solid Geometry and Plane Trigonometry. New Plane Trigonometry. New Plane Trigonometry, with Tables. New Plane and Spherical Trigonometry. New Plane and Spherical Trig., with Tables. New Plane and Spherical Trig., Surv., and Nav. New Plane Trig. and Surv., with Tables. New Plane and Spherical Trig., Surv., with Tables. Analytic Geometry. NEW SCHOOL ALGEBRA BY G. A. WENTWORTH AUTHOR OF A SERIES OF TEXT-BOOKS IN MATHEMATICS BOSTON, U.S.A. 1898 HARVARD COLLEGE LIBRARY GIFT OF MISS ELLEN L. WENTWORTH MAY 8 1939 COPYRIGHT, 1898, BY ALL RIGHTS RESERVED PREFACE. THE first chapter of this book prepares the way for quite a full treatment of simple integral equations with one unknown number. In the first two chapters only positive numbers are involved, and the beginner is led to see the practical advantages of Algebra before he encounters the difficulties of negative numbers. The definitions and explanations contained in these chapters should be carefully read at first; after the learner has become familiar with algebraic operations, special attention should be given to the principal definitions. The third chapter contains a simple explanation of negative numbers. The recognition of the fact that the real nature of subtraction is counting backwards, and that the real nature of multiplication is forming the product from the multiplicand precisely as the multiplier is formed from unity, makes an easy road to the laws of addition and subtraction of algebraic numbers, and to the law of signs in multiplication and division. All the principles and rules of this chapter are illustrated and enforced by numerous examples involving simple algebraic expressions only. The ordinary processes with compound expressions, including cases of resolution into factors, and the treatment of fractions, naturally follow the third chapter. The immediate succession of topics that require similar work is of the highest importance to the beginner, and it is hoped that the chapters on compound expressions will prove interesting, and give sufficient readiness in the use of symbols. |