Entered according to Act of Congress, in the year 1842, BY BENJAMIN GREENLEAF, 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 respectfully 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, Richmond, Charleston, Savannah, Mobile, New Orleans, and other cities. PARKER'S PROGRESSIVE EXERCISES In English Composition Forty-fifth improved stereotype edition. Price 25 cents. THE CLASSICAL READER, 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 Education; with numerous Illustrations, a full Glossary, or explanation of Technical Terms, and practical Questions at the bottom of the page. Designed for Schools and Families. Ninth stereotype edition, revised and enlarged. A GRAMMAR OF THE GREEK LANGUAGE. By Benjamin Franklin Fisk. Twenty-sixth improved stereotype edition. Fisk's Greek Grammtar is used in Harvard University, and in many other distinguished Collegiate and Academic Institutions, in various parts of the United States. 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 inaxime 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. Caii 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. THE following treatise is intended for that class of pupils, who may not have sufficient time to read the larger work on this science, published by the author a few years. since, and which has had extensive circulation. It is believed, that this book contains all, that is necessary to prepare the young for the common avocations of life. If the student wishes to obtain an extensive and full knowledge of this science, he can consult the National Arithmetic. It has been a great object with the author to render the work practical; how far he has succeeded, the public must judge. The questions are original, although there may be a similarity between some of these and others, which are before the public, and which could not be well avoided. Although the author has carefully examined every question, yet, it is possible, some few mistakes may be found in this work. These, however, will be corrected in a future edition. With these few prefatory remarks, the author commends this small volume to the candor of an enlightened Public. BRADFORD SEMINARY, Nov. 1st, 1842. THE AUTHOR. NOTICE. A KEY to this work, in which the method of solving the questions is fully exhibited, has just been published, for the convenience of teachers only. October 25th, 1844. ADVERTISEMENT TO THE SECOND (STEREOTYPE) EDITION. THE first edition of this work having been favorably received by the public, the author is now induced carefully to revise it, and make a few additions. It is believed, that, in the present edition, all the answers to the questions will be found correct. Great pains have been taken to make the rules and demonstrations intelligible. In revising his work, the author has availed himself of the aid and suggestions of many practical teachers; among whom he would particularly acknowledge his obligations to two distinguished teachers in Newburyport, David P. Page, Esq., of the English High School, and Mr. Joseph Williams, of the Grammar School. BRADFORD SEMINARY, BENJAMIN GREENLEAF. ADVERTISEMENT TO THE NINTH STEREOTYPE EDITION, IMPROVED. THIS edition has been very carefully revised, and the author has added a Method of Cancelling, which is well adapted to the capacities of young students. He has also annexed a Supplement, containing many practical questions in the elementary principles, and in Interest, adapted to the rates per cent. which are legal in the Middle and Southern States, where this work is extensively used. The author believes these additions will increase the value and usefulness of the work, and give it a still wider circulation. BRADFORD SEMINARY, BENJAMIN GREENLEAF. 21. Addition of Vulgar Fractions 22. Subtraction of Vulgar Fractions 23. Multiplication of Vulgar Fractions 24. Division of Vulgar Fractions CHARACTERS USED IN THIS WORK. $ Contraction, for U. S., United States' currency, and is prefixed to dollars and cents. Sign of equality; as 12 inches = 1 foot, signifies, that 12 inches are equal to one foot. Sign of addition; as 8+6=14, signifies, that 8 added to 6 is equal to 14. Sign of subtraction; 8-6=2, that is, 8 less 6 is equal to 2. X Sign of multiplication; as 7×6=42, that is, 7 multiplied by 6 is equal to 42. Sign of division; as 42÷6=7, that is, 42 divided by 6 is equal to 7. 2 Numbers placed in this manner imply, that the upper line is to be divided by the lower line. :::: Signs of proportion; thus, 2: 4 :: 6: 12, that is, 2 has the same ratio to 4, that 6 has to 12; and such numbers are called proportionals. 15-5+3=13. Numbers placed in this manner show, that 5 is to be taken from 15, and 3 added to the remainder. The line at the top is called a vinculum, and connects all the numbers, over which it is drawn. 9 Implies, that 9 is to be raised to the second power; that is, multiplied by itself. 8 Implies, that 8 is to be multiplied into its square. |