BY GEORGE W. EVANS Instructor in Mathematics in the English High School NEW YORK HENRY HOLT AND COMPANY 1899 Edue T 128.99.375 HARVARD COLLEGE LO GIFT OF GEORGE ARTHUR PLIMPTON Copyright, 1899, BY HENRY HOLT & CO. ROBERT DRUMMOND, PRINTER, NEW YORK PREFACE. IN the arrangement of topics in this book an effort has been made to preserve the pupil from the besetting sin of conceiving algebraic operations as a species of legerdemain. This end could best be secured, it seemed to me, by making practical problems the point of departure, initially and at each new turn of the subject. With a concrete case in mind, the pupil can hardly fail to perceive not only the need for the process that he is set to study, but also its rational basis and its economy. In this larger appeal to the practical sense it will be found that there is no slighting of mental dexterity, no injurious deviation from accepted methods, and certainly no sacrifice of mathematical rigor. If the arrangement of chapters here adopted is not acceptable, it is entirely feasible to take the topics in the traditional order. The index will facilitate this rearrangement. Whether or not teachers agree with me in respect to the ordering of topics or the method of attack which I have found fruitful in class, they are sure to appreciate the very large collection of examples-some thirty-five hundred all told-which are not reprinted from other text-books. In the following features also I think the book possesses advantages: 1. The careful classification of problems, so that due emphasis may be given to the several types of equations arising from them. 2. The insistence upon a scheduled explanation of steps in the reduction of equations; and the clearness and brevity of reference and explanation obtained by denoting an equation by its serial number enclosed in a circle. 3. The introduction of supplementary sets of constants for some important problems, as on pages 28 and 39 and in Chapter V. 4. The thorough study of literal equations and generalized problems; and especially of literal quadratics. 5. The prominence given to the solution of equations by factoring as a fundamental method; and the treatment of "completing the square" as a method of factoring. 6. The treatment of Rules and Formulæ in Chapter II, and of Theorems and Identities in Chapter IV. 7. The separation of Elimination into two parts suitable for linear systems and for linear-quadratic pairs respectively; the discussion of simultaneous, independent, and consistent equations; the "Equations of the New Set," page 160. 8. The treatment of H. C. F. by elimination of highest and lowest terms. Much of the book has been used, in manuscript and in proof, for class-work, but I can hardly hope that all mistakes have been corrected: notice of remaining errors will be gratefully received. For friendly aid and suggestion I am indebted to several of my colleagues; and especially to Mr. P. F. Gartland, who scrutinized for me every letter of the proofs. ENGLISH HIGH SCHOOL, BOSTON, February 3, 1899. G. W. E. |