NEW ELEMENTARY ALGEBRA EMBRACING THE FIRST PRINCIPLES OF THE SCIENCE BY CHARLES DAVIES, LL.D. AUTHOR OF A FULL COURSE OF MATHEMATICS EDITED BY J. H. VAN AMRINGE, Ph.D., PROFESSOR OF MATHEMATICS, COLUMBIA COLLEGE NEW YORK ::: CINCINNATI ::- CHICAGO PREFACE. In the admirable series of mathematical text-books, still unequaled in many essential particulars, which the late Professor Charles Davies issued, the “ Elementary Algebra” has an important place. The intent and scope of the work is set forth in the preface to the latest edition that the accomplished author prepared : " Algebra naturally follows arithmetic in a course of scientific studies. The language of figures, and the elementary combinations of numbers, are acquired at an early age. When the pupil passes to a new system, conducted by letters and signs, the change seems abrupt; and he often experiences much difficulty before perceiving that algebra is but arithmetic written in a different language. “It is the design of this work to supply a connecting link between arithmetic and algebra ; to indicate the unity of the methods; and to conduct the pupil from the arithmetical processes to the more abstract methods of analysis, by easy and simple gradations. The work is also introductory to the University Algebra,' and to the ‘Algebra' of M. Bourdon, which latter is justly considered, both in this country and in Europe, as the best text-book on the subject which has yet appeared. “In the 'Introduction,' or ‘Mental Exercises,' the language of figures and letters are both employed. Each lesson is so arranged as to introduce a single principle not known before ; and the whole is so combined as to prepare the pupil, by a thorough system of mental training, for those processes of reasoning which are peculiar to the algebraic analysis." The definitions are precise ; the fundamental principles and operations are lucidly explained ; and the whole subject within the range of the treatise is simply and logically developed, and well illustrated by appropriate examples. The present edition is the result of a careful reëxamination of the work, and in it are incorporated such emendations as the progress of educational science and practical experience in teaching have suggested. JULY, 1891. CONTENTS. I. DEFINITIONS. . . . . . . . . · · · · · · · · Exercises in writing Algebraic Expressions ..... Exercises in Interpretation of Algebraic Language. II. FUNDAMENTAL OPERATIONS ........... · Multiplication ............... III. FACTORING, GREATEST COMMON DIVISOR, AND LEAST Com- Useful Formulas . . . . . . . . . . . . . . Least Common Multiple. ........ IV. FRACTIONS ...... ........... Transformation of Fractions .......... Addition of Fractions .......... Subtraction of Fractions ; . . . . . . Multiplication of Fractions. .......... Division of Fractions . . . . . . . . . . . . 5 |