DISTRICT OF MASSACHUSETTS, TO WIT: BE IT REMEMBERED, that on the twenty-fifth day of May, A. D. 1826, and in the fiftieth 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: "Arithmetic upon the Inductive Method of Instruction: being a Sequel to Intellectual Arithmetic. By Warren Colburn, A. M." 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 books, to the authors and proprietors of such copies, during the times therein mentioned ;" and also an act, entitled, "An act supplementary to an act, entitled, An act for the encouragement 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 benefits thereof to the arts of designing, engraving, and etching, historical and other prints.” JNO. W. DAVIS, Clerk of the District of Massachusetts. Lyman RECOMMENDATIONS. 6-27-36 32490 From B. A. GOULD, Principal of the Public Latin School, Boston DEAR SIR, I have been highly gratified by the examination of the second part of your Arithmetic. The principles of the science are unfolded, and its practical uses explained with great perspicuity and simplicity. I think your reasonings and illustrations are peculiarly happy and original. This, together with your "First Lessons," forms the most lucid and intelligible, as well as the most scientific system of Arithmetic I have ever seen.-Its own merits place it beyond the need of commendation. With much esteem, Sir, your obedient servant, B. A. GOULD. Mr. WARREN COLBURN. From G. B. EMERSON, Principal of the English Classical School, Boston. Boston, 22d Oct., 1822. DEAR SIR, I have carefully examined a large portion of your manuscript, and do not hesitate to recommend it very highly to every person who wishes to teach arithmetic intelligibly. The arrangement is very much better, the explanations more convincing, and the rules, from the mode in which they are introduced, are clearer and simpler, than can be found in any book on the subject with which I am acquainted I am, with great respect, Yours, &c. Mr WARREN COLBURN. G. B. EMERSON. PREFACE Ir will be extremely useful, though not absolutely necessary, for pupils of every age to study the "First Lessons," previous to commencing this treatise. There is an intimate connexion between the two, though this is not dependent on the other. It is hoped that this will be found less difficult than other treatises on the subject, for those who have not studied the "First Lessons." Pupils may commence the "First Lessons" to advantage, as soon as they can read the examples; and even before they can read, it will be found very useful to ask them questions from it. This may be done by other pupils who have already studied it. Those who commence early, may generally obtain sufficient knowledge of it by the time they are eight or nine years old. They may then commence this. This Sequel consists of two parts. The first contains a course of examples for the illustration and application of the principles. The second part contains a developement of the principles. The articles are numbered in the two, so as to correspond with each other. The two parts are to be studied together, when the pupil is old enough to comprehend the second part by reading it himself. When he has performed all the examples in an article in the first part, he should be required to recite the corresponding article in the second part, not verbatim, but to give a good account of the reasoning. When the principle is well understood, the rules which are printed in Italics should be committed to memory. At each recitation, the first thing should be to require the pupil to give a practical example, involving the principle to be explained, and then an explanation of the principle itself. When the pupil is to learn the use of figures for the first time, it is best to explain to him the nature of them as in Art. I., to about three or four places; and then require him to write some numbers. Then give him some of the first examples in Art. II., without telling him what to do. He will discover what is to be done, and invent a way to do it. Let him perform several in his own way, and then suggest some method a little different from his, and nearer the common |