HARVARD COLLEGE LIBRARY GIFT OF GINN AND COMPANY COPYRIGHT, 1902, BY LOUIS PARKER JOCELYN. 1 PREFACE THE demand for the latest and most improved books has led the author to prepare the present volume. It is the fruit of his years of experience as a teacher of algebra. The book will be found well adapted for use in high schools, academies, and other preparatory institutions. The latest methods and newest processes are fully presented throughout; at the same time, all those older features of the science which are of permanent value have been purposely retained. The plan of the book is such that it may be profitably used by students of different grades. The following is suggested as a good course for the more elementary classes: Fundamental Principles, - Notation, Addition, Subtraction, Multiplication, Division; Equations, the first six principles in Special Theorems and their application to Factoring, Highest Common Divisor, Lowest Common Multiple, Equations and Fractions; closing with Equations of two and three unknown quantities. The regular course for the more advanced high schools and academies should embrace the first seventeen chapters, while schools preparing students for universities having more advanced requirements will find in the additional chapters which the book contains all that may be needed. The plan of the book is the practical based upon the scientific. Students preparing for the professions of civil, mechanical, electrical, naval, and mining engineering will find the book specially well suited to their needs. It begins with the most elementary mathematical forms and grows simply, yet logically, at every step. From the simplest representation of numbers by letters, the student is, in the very beginning, unconsciously led up to the equation. The subject of the Equation, the chief instrument of all mathematical investigation, is not confined to one section, but is judiciously distributed throughout all the pages of the book. The equation is among the very first subjects to greet the student, and it remains with him to the last. The subject of Factoring, a special feature of the book, is first thoroughly treated by itself, and is then constantly used throughout the volume. It is based upon the chapter on Special Theorems and Symmetry, where the student is taught how expressions are built up, and is then made to see how they may again be separated into their parts. The principles of factoring are immediately applied to quadratic and higher equations, highest common divisor, lowest common multiple, and fractions. A ratio is treated as a fraction and a proportion as an equality of two or more fractions, hence their treatment immediately after the subject of Fractions. A section on Variation is added for the benefit of students of physical science. Involution, Evolution, Theory of Exponents, Radicals, and Imaginary and Complex Numbers, built up and dependent upon one another in the order named, are treated as constituting one great whole. The subject of Quadratics is thoroughly treated in a modern way. In simultaneous quadratics, as in factoring, the student is shown the way of discovering the sure and best way of working any example with all "cut and try" methods eliminated. The final chapters are mainly for schools requiring a more advanced course in algebra, and may serve the purpose of a graduate course. The synopses for review and the sample test questions will prove matters of prime importance. ANN ARBOR, MICHIGAN, August, 1902. LOUIS PARKER JOCELYN. |