Improved Stereotype Edition. THE NATIONAL ARITHMETIC, ON THE INDUCTIVE SYSTEM; COMBINING THE ANALYTIC AND SYNTHETIC METHODS, IN WHICH THE PRINCIPLES OF ARITHMETIC ARE EXPLAINED IN A PERSPICUOUS PRACTICAL SYSTEMS OF MENSURATION, GUAGING, GEOMETRY, AND BOOK-KEEPING; WITH AN APPENDIX, COMPRISING THE CANCELLING METHOD: FORMING A COMPLETE MERCANTILE ARITHMETIC. DESIGNED FOR COMMON SCHOOLS AND ACADEMIES. BY BENJAMIN GREENLEAF, A. M., PRINCIPAL OF BRADFORD TEACHERS' SEMINARY. BOSTON: ROBERT S. DAVIS, AND GOULD, KENDALL, & LINCOLN. And sold by the trade generally. In the Clerk's Office of the District Court of the District of Massachusetts. STANDARD BOSTON SCHOOL BOOKS. GREENLEAF'S SERIES OF ARITHMETICS. 1. MENTAL ARITHMETIC, upon the Inductive Plan, designed for beginners. By Benjamin Greenleaf, A. M., Principal of Bradford (Mass.) Teachers' Seminary. 2. INTRODUCTION TO THE NATIONAL ARITHMETIC, designed for Common Schools. Twelfth improved stereotype edition. 196 pages, half bound. 3. THE NATIONAL ARITHMETIC, for advanced Scholars in Common Schools and Academies. Eighteenth improved stereotype edition. 324 pages, full bound. COMPLETE KEYS TO THE INTRODUCTION AND NATIONAL ARITHMETICS, containing Solutions and Explanations, for Teachers only. (In separate volumes.) **The attention of Teachers and Superintendents of Schools generally is respect fully invited to this popular system of Arithmetic, which is well adapted to all classes of students. The National Arithmetic' has been extensively introduced in various sections of the United States, and is highly recommended by many distinguished teachers who have used it, for its adaptedness to give students a thorough practical knowledge of the science. It is the text-book in the Normal Schools in Massachusetts, and New York city, and the best schools in Boston, New York, Philadelphia, Rich mond, Charleston, Savannah, Mobile, New Orleans, and other cities. PARKER'S PROGRESSIVE EXERCISES In English Composition. Forty-fifth improved stereotype edition. Price 25 cents. A Selection of Lessons in Prose and Verse, from the most esteemed English and American writers. Intended for the use of the higher classes in public and private seminaries. By Rev. F. W. P. Greenwood, D. D. and G. B. Emerson, A. M. of Boston. Tenth edition, stereotyped. With an engraved Frontispiece. SMITH'S CLASS BOOK OF ANATOMY, Explanatory of the first principles of Human Organization as the basis of Physical A GRAMMAR OF THE GREEK LANGUAGE. FISK'S GREEK EXERCISES (New Edition.) Greek Exercises; containing the substance of the Greek Syntax, illustrated by passages from the best Greek authors, to be written out from the words given in their simplest form, by Benjamin Franklin Fisk. Consuetudo et exercitatio facilitatem maxime parit.'-Quintil. Adapted to the Author's Greek Grammar.' Sixteenth stereotype edition. Fisk's Greek Exercises are well adapted to illustrate the rules of the Grammar, and constitute a very useful-accompaniment thereto. LEVERETT'S CÆSAR'S COMMENTARIES. Call Julii Cæsaris Commentarii de Bello Gallico ad Codices Parisinos recensiti, a N. L. Achaintre et N. E. Lemaire. Accesserunt Notulæ Anglicæ, atque Index Historicus et Geographicus. Curavit F. P. Leverett, A. M. FOLSOM'S CICERO'S ORATIONS. M. T. Ciceronis Orationes Quædam Selectæ, Notis Illustratæ. [By Charles Folsom, A. M.] In Usum Academiæ Exoniensis. Editio stereotypa, Tabulis Analyticis instructa. I have examined with some attention Cæsar's Commentaries, edited by Leverett, and Cicero's Orations, edited by Folsom, and am happy to recommend them to classical teachers, as being, in my estimation, far superior to any other editions of those works to which students in this country have general access. 'JOHN J. OWEN, Editor of 'Xenophon's Anabasis,' and Principal of Cornelius Institute, N. Y. City. ALGER'S MURRAY'S GRAMMAR, AND EXERCISES. ALGER'S MURRAY'S READER AND INTRODUCTION. Published by ROBERT S. DAVIS, School-Book Publisher, BOSTON, and sold by all the principal Booksellers throughout the United States. Also constantly for sale, (in addition to his own publications,) a complete assortment of School Books and Stationery, which are offered to Booksellers, School Committees, and Teachers, on very liberal terms. PREFACE. THE author of the following work is far from flattering himself, that he is about to present to the public any considerable number of new principles in the science of arithmetic. But from thirty years' experience in the business of teaching, he has been led to suppose, that some improvement might be made in the arrangement and simplification of the rules of the science. How far he has succeeded in his attempt at making this improvement, the public must judge An opinion has prevailed among some teachers, that the pupil should have no rule to perform his questions by, but should form all his rules himself, by mere induction. This plan might do very well, could it be carried into effect. But, if the experience of the author has been of any service to him, one thing, it has taught him, is, that, in a given time, a student will acquire more knowledge of arithmetic by having some plain rules given him, with examples, than he will without them; especially, if he be required to give an analysis of a suitable number of questions under each rule. A few of the rules, which some arithmeticians of the present day have laid aside as useless, the author has thought best to retain; as Practice, Progression, Position, Permutation, etc. For though some of these rules are not of much practical utility, yet, as they are well adapted to improve the reasoning powers, they ought not, in the author's judgment, to be laid aside by any, who wish to become thorough arithmeticians. The author does not think it expedient, that the pupil should spend a long time on mental arithmetic without the use of the slate. He has introduced, as much mental arithmetic, as he thinks necessary for students generally; unless they are very young, and for such he would recommend the "Introduction to the National Arithmetic," recently published. |