IN TWO PARTS. PART FIRST, ADVANCED LESSONS IN MENTAL ARITHMETIC. PART SECOND, RULES AND EXAMPLES FOR PRACTICE IN FOR COMMON AND HIGH SCHOOLS. BY FREDERIC A. ADAMS, A. M. FORMER PRINCIPAL OF DUMMER ACADEMY. m Eleventh Thousand. LOWELL: PUBLISHED BY D. BIXBY & CO. BOSTON: B. B. Mussey & Co.; W. J. Reynolds & Co. NEW YORK: D. Appleton & & Allen. MOBILE: J. Dobler. NEW ORLEANS: J. B. Steele. ST. 1848. CARD CATALOGUED. Entered according to Act of Congress, in the year 1848, In the Clerk's Office of the District Court of the District of Massachusetts. RECOMMENDATIONS. From Mr. George B. Emerson, Boston. I have carefully examined the plan of Mr. Adams's work on Mental Arithmetic, and have given some attention to its execution; and I am confident that it will prove a very valuable addition to the means of instruction in Arithmetic. It is a successful extension of the admirable method of Colburn's First Lessons, with such modifications as seemed to be required in a higher work on the same general model. It occupies unappropriated ground; and it deserves, and I think it will take, a high place amongst the text-books. GEO. B. EMERSON. From Mr. Thomas Sherwin, Boston. I have carefully examined, in manuscript, the work of Mr. Adams on Mental Arithmetic, and am much pleased with it. His plan is good, and well executed. I would, therefore, heartily recommend his book to Teachers and School Committees, as one which will contribute very materially to the attainment of that very important, but much-neglected branch of study, Intellectual Arithmetic. T. SHERWIN, Principal of Boston English High School. From Professor Chase, of Dartmouth College. MR. F. A. ADAMS. HANOVER, OCT. 12, 1846. My Dear Sir:-I have examined, with some care, your treatise on Arithmetic, and am much pleased with it. The practice and habit of extending mental operations to large numbers is of great utility. I have occasion, very frequently, to see the inconvenience that young men suffer from the want of such a habit. Not less valuable than the habit of operating mentally upon large numbers, is the habit of performing the more advanced operations of arithmetic without the aid of the pencil. I like very much, also, the manner in which you have treated several of the principles which you have developed; as, for example, the subject of the common divisor, the least common multiple, the roots, ratio, and proportion. These are but few of the subjects, but I mention them as examples. I think the book will do much to promote the proper method of teaching arithmetic, by DEMONSTRATION and explanation. I am, Dear Sir, very truly yours, &c. S. CHASE. From Mr. John Tatlock, Professor of Mathematics, and Mr. A. Hopkins, Professor of Natural Philosophy. WILLIAMS COLLEGE, Nov. 20, 1846. I have examined a treatise on Arithmetic by F. A. Adams, and am much pleased with it. I think it well adapted to teach the science and art of numbers, and at the same time to teach the art of thinking. I am persuaded that a thorough training in this Arithmetic would prepare students for the farther study of mathematics better than nine tenths are now prepared. I should be glad if every student who enters college was master of this Arithmetic. JOHN TATLOCK. A. HOPKINS. IN SCHOOL COMMITTEE, ROXBURY, FEB. 17, 1847. The undersigned, members of the Committee on Text-Books, recommend that the Arithmetic prepared by Frederic A. Adams, be used in the grammar schools, by all the classes which now use Leonard's Arithmetic; and that hereafter no other Arithmetic be used in the public schools, than Adams's together with Colburn's First Lessons. SAM'L. H. WALLEY, Jr. DAN'L. LEACH, B. E. COTTING, THEO. PARKER. In School Committee, Feb. 17, 1847.-The above recommendation of the Committee on Text-Books, was this day adopted. JOSHUA SEAVER, Secr'y. STEREOTYPED AT THE BOSTON TYPE AND STEREOTYPE FOUNDRY. MD COL GEORGE ARTHUR JA PREFACE. THE study of Arithmetic in the schools of this country received its best impulse, unquestionably, in the publication of Colburn's First Lessons. The use of this book, and of others made on a similar plan, has done much towards placing this branch of study on its proper ground. In all our best schools, in the elementary stages of this study, the logical mode has taken the place of the merely formal; reason is the guide, instead of rule. The want of a higher work on Mental Arithmetic has long been felt by teachers; and by business men, who have been compelled, after having received all the training of the school-room, to adopt practical modes of calculation of their own, to meet the exigencies of their daily business. It is to meet these wants that the following work has been prepared. The design of it is,— To accustom the pupil to perform, with ease and readiness, mental calculations upon somewhat large numbers; To present these operations in their natural form, freed from the inverted and mechanical methods which belong of necessity to operations in Written Arithmetic; To train the student to such a power of apprehending the relations of numbers, as shall give him an insight into the grounds of the rules of Arithmetic; and, consequently, shall release him from dependence on those rules; To prepare the members of our schools, when they shall have left school, and engaged in the active pursuits of life, to solve mentally, and with ease and delight, a large share of those questions, of busi |