PRACTICAL ARITHMETIC, IN WHICH THE RULES ARE RENDERED SIMPLE IN THE OPERATION, AND USEFUL QUESTIONS, CALCULATED TO GIVE THE PUPIL A FULL KNOWLEDGE OF FIGURES, IN THEIR APPLICATION TO TRADE AND BUSINESS; ADAPTED PRINCIPALLY TO FEDERAL CURRENCY; DESIGNED AS AN ASSISTANT TO THE PRECEPTOR IN COMMUNI- SCIENCE OF ARITHMETIC; TO WHICH IS ADDED, A NEW AND CONCISE SYSTEM OF BOOK-KEEPING, BOTH BY SINGLE AND DOUBLE ENTRY; THE FORMER CALCULATED FOR THE USE OF TRADERS IN RETAIL BUSINESS, AND THE LATTER FOR WHOLESALE DOMESTIC AND FOREIGN TRADE, AS CON- UNITED STATES. The whole designed for the use of Schools and Academies. BY DANIEL STANIFORD, A. M. Tantum scimus, quantum memoria tenemus. BOSTON: PRINTED BY J. H. A. FROST, FOR WEST, RICHARDSON & LORD, No. 75, Cornhill. B DISTRICT OF MASSACHUSETTS—TO WIT : E it remembered, that on the seventeenth day of November, in the year of our Lord one thousand eight hundred and eighteen, and in the forty-second year of the Independence of the United States of America, DANIEL STANIFORD, 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: "Staniford's Practical Arithmetic, in "which the rules are rendered simple in the operation, and illustrat"ed by a variety of useful questions, calculated to give the pupil a "full knowledge of figures, in their application to trade and business; "adapted principally to Federal Currency; designed as an Assistant "to the Preceptor in communicating, and to the pupil in acquiring "the science of Arithmetic; to which is added, a new and concise "system of Book-Keeping, both by single and double entry; the "former calculated for the use of Traders in retail business, Farm"ers and Mechanics; and the latter for wholesale, domestic and "foreign trade, as conducted in the United States. The whole designed for the use of Schools and Academies, By DANIEL STANI66 FORD, A. M. Author of the Art of Reading, and Elements of Eng"lish Grammar." "Tantum scimus quantum memoria tenemus." In conformity to an 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 to 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." J. W. DAVIS, Clerk of the District of Massachusetts. A true copy-Attest, 11-20-40 dive. Hist. I Serince 11-19-40 42026 PREFACE. FACE TO the question commonly asked, on the appearang of a new book, "Is there any thing new in it?" the author replies, that although the subject of arithmetic can admit but little novelty, yet in this treatise there is something new, which may be easily discovered by an examination of its contents. The general rules in most of the Arithmetics used in our schools are too synthetical for the young Arithmetician. They contain too many principles blended together, unaccompanied with sufficient elucidations. The scholar therefore is in danger of passing over many essential parts, without fully comprehending them. design therefore of this treatise is to give an Analysis of these general rules, resolving them into their simple constituent parts, illustrating them by easy practical questions. One As the work, also, is principally designed to furnish a system of practical Arithmetic, adapted to the currency of the United States, all mathematical demonstrations are purposely omitted, to give place to clear illustrations of the rules by easy examples, and such as tend to prepare the scholar for business; referring those, who wish to acquire a knowledge of the higher branches of the Mathematics in those elaborate, though useful parts of the science, to authors particularly designed for the purpose. This omission will leave for the instructor enough for the exercise of his skill in explaining the nature of each rule to the pupil, as he advances in his pursuit, and becomes capable of comprehending those abstruse parts of the science. The instructor is left, also, to supply at his discretion various additional questions for exercise in the application of the several rules. This will prevent the fatal practice, too much indulged among scholars, of copying from each other's manuscripts. The same question should never be proposed by the instructor a second time. Although the currency of the United States is generally adopted through the work, yet, as the accounts and invoices of goods of American and English merchants trading together are kept in Sterling money, so much only of that money is applied as was thought necessary to give the scholar a competent knowledge to transact that part of commercial business. The whole arrangement of the work is founded on the natural dependence of the several parts on each other for their respective operations. A few remarks are offered in support of the present arrangement. 1. REDUCTION. As by this rule compound addition, multiplication and division are performed, its place naturally precedes them. In reducing time 365 days is commonly called a year, omitting the fractional parts. 2. VULGAR FRACTIONS. These, having their origin from simple division, seem to require a place immediately subsequent to that rule yet as their operation depends on other rules, a place is assigned them, following those on which they are dependent, and preceding others which depend on them for an accurate solution. Vulgar Fractions being indispensably necessary for the solution of many important questions in common arithmetic as well as in the higher branches of Mathematics, they have received particular attention in this treatise. 3. DECIMAL FRACTIONS. These being similar in their operation with whole numbers, seem to claim a place in close connexion with them; yet as the changing of them from one form into another is performed by other rules, their order should succeed them. 4. CIRCULATING DECIMALS. These are subjoined for the benefit of those who would wish to have a comprehensive view of the whole nature and doctrine of Decimals; particularly for those who wish to extend their mathematical enquiries. The finite decimals are contained in the first cases, and are all that is necessary for common business; the circulates may, therefore, be omitted as circumstances may justify. 5. FEDERAL MONEY. Some, perhaps, may have thought it more proper to arrange this currency immediately following the simple rules of Arithmetic, because of their simplicity; yet as Federal Money is founded in the nature and principles of Decimals, and performed by the same rules in its operation, its natural order is certainly subsequent to decimals. Particular attention has been given to it in connexion with decimals, as the foundation and only guide for the American Accountant. 6. The operations of Practice, Tare and Tret, with Duodecimals, being dependent on Compound Multiplication and Division, are placed after them. 7. RULE OF THREE. The importance and extensive utility of this rule in the ordinary concerns of life, has given it the distinguishing title of "The golden Rule." As most of the subsequent rules in Arithmetic are performed by the Rule of Three, great care has been taken to render it intelligible by a minute investigation of its nature, with an analysis of the general rule in simplifying it in all its varieties. 8. Position, Allegation and Permutation are inserted at the close of the Practical Arithmetic, more for the purpose of gratifying curiosity, than for their utility in business. In executing the work nothing superfluous has been added, and nothing omitted that would contribute to perfect its design, and render it serviceable to youth. Those, however, who are in the habit of teaching superficially, with a view of flattering the pupil and the parent with the mistaken idea of extraordinary progress, may probably raise objections against the work, as containing too many things to be committed to memory. They will burden, fatigue and confuse the mind of the scholar. Such persons have yet to learn both the susceptibility and capacity of the young mind, and that although a single complex idea in its undigested form, crowded into the mind of a child, may confuse and embarrass it; yet, in direct proportion to the number of simple ones, impressed, will it become more invigorated, more enlightened, more improved. Similar objections would as readily be started against an abridgement of the smallest sise, by those only who have neither the ability nor inclination to lay the whole nature of the subject open to the understanding, and lead the pupil, gradually, into that train of logical reasoning, peculiar to the mathematics. 9. BOOK-KEEPING. This useful branch of learning has been almost totally neglected in our schools and academies. The neglect of a study so essential to the best literary interest of youth proves a material defect in the present system of education. It may, perhaps, be attributable, in a great degree, to the want of a concise treatise on the subject, divested of those numerous difficulties which envelope in mystery even the best system extant. So intricate and tedious are they, for the most part, that even instructors themselves have been deterred from giving instruction by them. The short system in this publication has been used by the author with considerable success. It is now offered as an attempt to simplify the Art of Book-keeping, and to adapt it to the capacity of youth. It furnishes such rules and explanatory remarks in discriminating the titles of Dr. and Cr. in journalizing and posting the several mercantile transactions, as were thought best calculated to render easy and clear a subject of so much importance. Of such immense benefit is this part of science to a young man of any respectable standing in society, that no scholar should be permitted to leave school, to become an apprentice either to a merchant, a mechanic, or even to a farmer, without a thorough knowledge of the principles and forms of Book-keeping; as on his knowledge of this art essentially depends the security of all the fruits of his indus try through life. Many mechanics and farmers have lost half their earnings by neglecting to make a regular entry of their daily transactions peculiar to their employment; and even wealthy merchants |