WENTWORTH'S SERIES OF MATHEMATICS. First Steps in Number. Mental Arithmetic. Primary Arithmetic. Elementary Arithmetic. Grammar School Arithmetic. High School Arithmetic. Exercises in Arithmetic. School Algebra. College Algebra. Higher Algebra. Elements of Algebra. New Plane Geometry. New Plane and Solid Geometry. Analytic Geometry. Exercises in Geometry. New Pl. and Sol. Geometry and Pl. Trigonometry. Plane Trigonometry and Tables. Plane and Spherical Trigonometry. Surveying. Pl. and Sph. Trigonometry, Surveying, and Tables. Trigonometry, Surveying, and Navigation. Logarithmic and Trigonometric Tables (Seven). Log. and Trig. Tables (Complete Edition). NEW SCHOOL ALGEBRA BY G. A. WENTWORTH AUTHOR OF A SERIES OF TEXT-BOOKS IN MATHEMATICS BOSTON, U.S.A. 1898 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. The chapter on Factors has been made as complete as possible for an elementary text-book, with a view to shorten subsequent work. The easy method of resolving quadratic trinomials into factors, whether the coefficient of the square of the letter involved is unity or greater than unity, and the Factor Theorem, explained on page 102, will be found of very great service in abridging algebraic processes. Examples of short methods for finding the highest common factor of compound expressions are given on page 118; and examples of short methods for solving quadratic equations by resolving them into factors are given on pages 272 and 273. A five-place table of logarithms is placed at the end of the book instead of a four-place table. Five-place logarithms are in common use for practical calculations, and are required by most colleges and science schools for the solution of problems set in entrance examination papers. The exercises throughout the book are carefully graded. They are sufficiently varied and interesting, and are not so difficult as to discourage the learner, or so easy as to deprive him of the satisfaction of well-earned success. The author has spared no pains to make this a model text-book in subject-matter and mechanical execution. The remarkable favor with which his other Algebras have been received is shown by the fact that nearly a million copies have already been sold, and the sale continues to increase from year to year. The author trusts that this new candidate for favor will have the same generous reception, and be found to meet fully the requirements of the recent advance in the science and method of teaching Elementary Algebra. The author is under obligations to many teachers for valuable suggestions, and he will be thankful for corrections or criticisms. EXETER, N. H., June, 1898. G. A. WENTWORTH. |