ELEMENTS OF ALGEBRA BY G. A. WENTWORTH, A.M. AUTHOR OF A SERIES OF TEXT-BOOKS IN MATHEMATICS COMPLETE EDITION BOSTON, U.S.A. GINN & COMPANY, PUBLISHERS 1900 HARVARD 47*130 Entered, according to Act of Congress, in the year 1881, by G. A. WENTWORTH in the Office of the Librarian of Congress, at Washington. Com PREFACE. THE THE single aim in writing this volume has been to make an Algebra which the beginner would read with increasing interest, intelligence, and power. The fact has been kept constantly in mind that, to accomplish this object, the several parts must be presented so distinctly that the pupil will be led to feel that he is mastering the subject. Originality in a text-book of this kind is not to be expected or desired, and any claim to usefulness must be based upon the method of treatment and upon the number - and character of the examples About four thousand examples have been selected, arranged, and tested in the recitation-room, and any found too difficult have been excluded from the book. The idea has been to furnish a great number of examples for practice, but to exclude complicated problems that consume time and energy to little or no purpose. In expressing the definitions, particular regard has been paid to brevity and perspicuity. The rules have been deduced from processes immediately preceding, and have been written, not to be committed to memory, but to furnish aids to the student in framing for himself intelligent statements of his methods. Each principle has been fully illustrated, and a sufficient number of problems has been given to fix it firmly in the pupil's mind before he proceeds to another. Many examples have been worked out, in order to exhibit the best methods of dealing with different classes of problems and the best arrangement of the work; and such aid has been given in the statement of problems as experience has shown to be necessary for the attainment of the best results. General demonstrations have been avoided whenever a particular illustration would serve the purpose, and the application of the principle to similar cases was obvious. The reason for this course is, that the pupil must become familiar with the separate steps from particular examples, before he is able to follow them in a general demonstration, and to understand their logical connection. It is presumed that pupils will have a fair acquaintance with Arithmetic before beginning the study of Algebra; and that sufficient time will be afforded to learn the language of Algebra, and to settle the principles on which the ordinary processes of Algebra are conducted, before attacking the harder parts of the book. "Make haste slowly" should be the watchword for the early chapters. It has been found by actual trial that a class can accomplish the whole work of this Algebra in a school year, with one recitation a day; and that the student will not find it so difficult as to discourage him, nor yet so easy as to deprive him of the rewards of patient and successful labor. At least one-fourth of the year is required to reach the chapter on Fractions; but, if the first hundred pages are thoroughly mastered, rapid and satisfactory progress will be made in the rest of the book. Particular attention should be paid to the chapter on Factoring; for a thorough knowledge of this subject is requisite to success in common algebraic work. Attention is called to the method of presenting Choice and Chance. The accomplished mathematician may miss the elegance of the general method usually adopted in Algebras; but it is believed that this mode of treatment will furnish to the average student the only way by which he can arrive at an understanding of the principles underlying these difficult subjects. In the preparation of these chapters the author has had the assistance and coöperation of G. A. Hill, A. M., of Cambridge, Mass., to whom he gratefully acknowledges his obligation. The chapter on the General Theory of Equations has been contributed by Professor H. A. Howe of Denver University, Colorado. The materials for this Algebra have been obtained from English, German, and French sources. To avoid trespassing upon the works of recent American authors, no American text-book has been consulted. The author returns his sincere thanks for assistance to Rev. Dr. Thomas Hill; to Professors Samuel Hart of Hartford, Ct.; C. H. Judson of Greenville, S.C.; O. S. Westcott of Racine, Wis.; G. B. Halsted of Princeton, N.J.; M. W. Humphreys of Nashville, Tenn.; W. LeConte Stevens of New York, N.Y.; G. W. Bailey of New York, N.Y.; Robert A. Benton of Concord, N.H.; and to Dr. D. F. Wells of Exeter. There will be two editions of the Algebra: one of 350 pages, designed for high schools and academies, will contain an ample amount to meet the requirements for admission to any college; the other will consist of the Elementary part and about 150 pages more, and will include the subjects usually taught in colleges. Answers to the problems are bound separately in paper covers, and will be furnished free to pupils when teachers apply to the publishers for them. Any corrections or suggestions relating to the work will be thankfully received. EXETER, N.H., G. A. WENTWORTH. |