PREFACE. When I entered upon the arduous task of simplifying a science of so much importance to the civilized world as Arithmetic, in every department of society, I was aware, that it would be attended with no inconsiderable labour, deep thinking and research: How far I have succeeded to prove this work an auxiliary, to increase the general stock of knowledge already disseminated, (for the youth of our country) a generous, enlightened, and impartial public will determine. At all events, it is the result of much experience, during twenty-five years teaching, and it is the opinion of learned gentlemen to whom the manuscript has been submitted for inspection, that if it be introduced into our schools and academies, it will be found to answer admirably, the END, for which it is intended, and, thereby prove to be a guide and a text book to the merchant, mechanic and man of business, and, a standard system of Arithmetic in the United States. Some persons may think, that books of a similar nature have been sufficiently multiplied; but in answer to this, I may with propriety state, that the only correct evidence of a spirit of improvement in our seminaries of learning, and that education is in a high state of prosperity, is, the continually increasing demand for new school books which exists in every section of our country. I ask then, what friend of our numerous, and flourishing literary institutions can, for a moment wish to check the progress of improvement in our books and systems of instruction;—Indeed it may with perfect safety be mentioned, that when instructers become wholly content with the elements and principles which have long been in use the progress of improvement is entirely at an end. It is a matter of fact that dispatch in business in every department, is no small accomplishment. Therefore, to prepare pupils in the shortest period of time possible for business, and to afford assistance to teachers in the arduous and important work of education were the motives which led me to this production. Let me ask, why is it that boys of common capacity can learn any kind of mechanical business in three or four years, when, in fact, double the time has been devoted to the attainment of only a superficial knowledge of the rudiments of Arithmetic? How is this, I pause for a reply? In the systems generally used in the schools of our country, the questions in the different rules are “mixed” up with examples of Pounds, Shillings and Pence. Certainly this is wrong!! Because the very idea of pounds, shillings and pence is foreign to American students. Not only this, but the derangement of the rules, and the old-fashioned protracted methods of calculation which are adopted in these old Arithmetics, retard the progress of pupils and cause a dislike to their studies. This is a fact, which cannot be controverted, And, that two-thirds of the time usually spent in acquiring a knowledge of this useful art may be saved, by means of a proper system of Arithmetic and a correct mode of instruction is also, a fact well known to every judicious instructer. In no department of mathematical science have I been more deeply interested than in this, and hence, the reason, (as before mentioned) that I have laboured assiduously in preparing and collating a work, to suit the wants of the American people. In relation to foreign currencies, sterling money, and the currencies of other countries of EUROPE are treated of in EXCHANGE: this is precisely as it should be: because, we know that young persons are not lovers of long or hard lessons and that they CAN LEARN with pleasure, when neither their memories are overcharged nor their understandings put on the rack, from the use of tedious and ambiguous examples, which are interspersed throughout systems of Arithmetic said to be designed for American schools. In consequence of this, let us try to remedy this evil: In the first place, is it not well known, that the United States have political and civil institutions of their own, and can these be upheld unless, our children are taught to understand them by books and other means of instruction perfectly suited to the genius and constitution of the country? Again, a proper system of Arithmetic in dollars and cents, is much wanted, in order that pupils may receive from their teachers ample satisfaction for their TIME and MONEY. For it is manifest, that all, that concerns our public happiness, our union and peace within ourselves, ALL which tends to develope our resources, improve and perpetuate our institutions, ALL which may gives us wealth, strength, and glory among nations, depends on a general and systematic course of instruction in our schools. How ready,short, easy and familiar this work may be for actual performance, will appear by inspection. In conclusion, I cheerfully tender my most grateful acknowledgments to RICHARD COTTER, Esq. PROFESSOR OF MATHEMATICS AND NATURAL PHILOSOPHY OF THIS CITY, who has ably and faithfully acquitted himself in its EXAMINATION, and also, for the useful hints he has kindly suggested to me, which I conceive to be of utile im· portance to the work. With these remarks, and an ardent wish, that the “UNITED STATES CALCULATOR; or, ARITHMETIC SIMPLIFIED” may be useful to the youth of my country, I cheerfully submit it to the patronage of an enlightened and independent public. JOHN M'NEVIN. Balto. Jan. 1, 1841. UNITED STATES CALCULATOR; OR, ARITHMETIC SIMPLIFIED. One Two Three Four Five Six Nine 9. ARITHMETIC is that part of the Mathematics which teaches the art of computation by numbers. All operations in Arithmetic are performed by means of the following figures: Cipher Seven Eight 0 1 2 3 4 5 6 7 8 There are five principal rules in Arithmetic, viz: Notation and Numeration may be included in 1, Addition 2, Multiplication 3, Subtraction 4, Division 5. The proper definitions are inserted at the head of each rule. The Arabic numbers, are represented by the characters above written. The Roman letters also express number without limitation, but are chiefly used to mark dates, and the chapters, and sections of books. The following letters are used to express number. I V X L С D M |