AN INTRODUCTION TO A L G E B R A UPON THE INDUCTIVE METHOD OF INSTRUCTION. BY WARREN COLBURN, A. M. Boston: PUBLISHED BY HILLIARD, GRAY & CO. 1834. DISTRICT OF MASSACHUSETTS, to wit. District Clerk's Ofice. BE IT REMEMBERED, That on the twenty-fourth day of June, A. D. 1825, in the forly-ninth year of the Independence of the United States of America, WARREN COLBURN, of the said district, has deposited in this office the title of a book, the right whereof he claims as author, in the words following, to wit : “ An Introduction to Algebra, upon the Inductive Method of Instruction. By Warren Colburn, Author of First Lessons in Arithmetic, &c." In conformity to the act of the Congress of the United States, entitled " An act for the encouragement of learning, by securing the copies of maps, charts, and tooks, to the authors and proprietors of such copies, during the times therein mentioned ;” and also to an act, entitled '“ An act supplementary to an act, entitled An act for the encourage. ment of learning, by securing the copies of maps, charts, and books, to the authors and proprietors of such copies, during the times therein mentioned, and extending the bertefits thereof to the arts of designing, engraving, and etching historical and other prints." JNO. W. DAVIS, 5-8-45 ADE The first object of the author of the following treatise has been to make the transition from arithmetic to algebra as gradual as possible. The book, therefore, commences with practical questions in simple equations, such as the learner might readily solve without the aid of algebra. This requires the explanation of only the signs plus and minus, the mode of expressing multiplication and division, and the sign of equality ; together with the use of a letter to express the unknown quantity. These may be understood by any one who has a tolerable knowledge of arithmetic. All of them, except the use of the letter, have been explained in arithmetic. To reduce such an equation requires only the application of the ordinary rules of arithmetic; and these are applied so simply, that scarcely any one can mistake them, if left entirely to himself. One or two questions are solved first with little explanation in order to give the learner an idea of what is wanted, and he is then left to solve several by himself. The most simple combinations are given first, then those which are more difficult. The learner is expected to derive most of his knowledge by solving the examples himself ; therefore care has been taken to make the explanations as few and as brief as is consistent with giving an idea of what is required. In fact, explanations rather embarrass than aid the learner, because he is apt to trust too much to them, and neglect to employ his own powers ; and because the explanation is frequently not made in the way, that would naturally suggest itself to him, if he were left to examine the subject by himself. The best mode, therefore, seems to be, to give examples so simple as to require little or no explanation, and let the learner reason for himself, taking care to make them more difficult as he proceeds. This method, besides giving the learner confidence, by making him rely on his own powers, is much more interesting to him, because he seems to himself to be constantly making new discoveries. Indeed, an apt scholar will frequently make original explanations much more simple than would have been given by the author. |