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. GREENLEAF'S NATIONAL ARITHMETIC, Forming a volume of upwards of 300 pages, handsomely printed on fine paper, and bound in leather. Fourteenth, Improved Stereotype Edition, Also, a COMPLETE KEY to this work, designed for T'eachers only. PUBLISHED BY ROBERT S. DAVIS, BOSTON, This work, having been adopted in many of the best Schools in various seco tions of the country, is highly commended by all intelligent Teachers who have used it, for its practical adaptation to make thorough scholars in this department of science. RECOMMENDATIONS. “ Haverhill, May 22, 1843. “B. GREENLEAF, Esq. - Dear Sir: We have examined your Arithmetics, the National and Introductory, and take pleasure in expressing to you our high satisfaction in them, as superior to any books in this branch of education with which we are acquainted. We are especially pleased with the accuracy and precision of the defini. tions, and with the clearness and fullness of illustration by the examples. The two together seem to be just what are needed, and we are inclined to say all that are needed on this subject in our Public Schools. In accordance with this view of your books, as members of the General School Committee, we have encouraged their use in the schools in this town. (Signed,) "EDWARD A. LAWRENCE, } Superintending, A. S. TRAIN, School Committee." " BENJAMIN GREENLEAF, Esq. - Dear Sir: I regard your National Arithmetic as one of the best I have ever seen. Perhaps the best proof of the estimation in which I hold its merits, is the fact that I use it in the school under my care. “I am, Sir, very respectfully yours, ROGER S. HOWARD, Principal of the Latin High School. “ Newburyport, May 5, 1843.” “Having used Greenleaf's Arithmetic, in the schools with which I have been connected for three years past, I am prepared to give it the preference over any other work of the kind with which I am acquainted. “ Very respectfully yours, A. FARWELL, Principal of Abbott Female Academy. “ Andover, June 6, 1843." From H. Morison, Esq., Professor of Mathematics and President of the University of Maryland, Baltimore. “This is one of the most complete books of its kind, both in the extent and ar. rangement of its matter, that has yet appeared... Combining, as it does, the Analytic and Synthetic methods, and abounding in familiar examples, it is admirably calcu. lated io interest the pupil, and lead him, by easy and progressive steps, through the difficulties of the science, to its complete mastery, and full comprehension. To make the work more perfect, than a treatise on Arithmetic merely could be, the author has added many geometrical, mechanical, philosophical, and astronomical problems, and a concise system of Book-keeping, so that, without the aid of any other book, it is calculated to make the perfect business man, in all his various departments. (Signed,) “H. MORISON.” Other testimonials to the merits of this work, will be found in the advertis ing sheet, at the end of the volume, to which the reader is referred. CAMBRIDGE: PRINTERS TO THE UNIVERSITY. 6-29.36 32490 PREFACE. 7-29-36. H6 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. THE AUTHOR. BRADFORD SEMINARY, Nov. 1st, 1842. 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 Newbury port, David P. Page, Esq., of the English High School, and Mr. Joseph Williams, of the Grammar School. BENJAMIN GREENLEAF. BRADFORD SEMINARY, July 1st, 1843. Sect. 1. Numeration 6. Application of the preceding Rules 7. Tables of Money, Weights, and Measures 10. Compound Subtraction 21. Addition of Vulgar Fractions 22. Subtraction of Vulgar Fractions 23. Multiplication of Vulgar Fractions 24. Division of Vulgar Fractions 25. Exercises in Vulgar Fractions 29. Multiplication of Decimals 48. Evolution, or the Extraction of Roots 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 add ed 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 7X6= 42, that is, 7 multi plied by 6 is equal to 42. • Sign of division ; as 42;6=7, that is, 42 divided by 6 is equal to 7. 7 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. 89 Implies, that 8 is to be multiplied into its square. 2 3 |