THE PRACTICAL CALCULATOR: A TREATISE ON ARITHMETIC, COMPREHENDING ALL THE USEFUL RULES, WITH A COMPENDIUM OF BOOK-KEEPING, SUITABLE FOR SCHOOLS, PRIVATE PU PILS, &c. BY C. W. THORNHILL, PRINCIPAL AT MOOR LANE HOUSE ACADEMY, SOUTHWELL. London: J. AND C. MOZLEY, PATERNOSTER ROW. DERBY: J. AND C. MOZLEY. NOTTINGHAM: G. BATTERS, AND ALL BOOKSELLERS. It may be enquired what necessity there is to publish another work on Arithmetic, when there are at the present time such a multidinous class of works in circulation, on this subject. A few words in explanation, why this work is presented to the public, may not be unacceptable. The Author, who has for several years seen the necessity for some improvement in this branch of education, compiled this for his own use among his private pupils. The success that has attended the private use of the mauuscript of these sheets in the Author's establishment, induces him to recommend it to the public, with the hope that, in so doing, he may be conferring some benefit upon the cause of education, by facilitating the progress of the pupil in one of the most important and useful branches of knowledge. A cursory glance at the work will show its arrangements, but it may briefly be noticed here, that its chief characteristics are its brevity and simplicity. The examples given with each rule are adapted to the capacity of pupils of all ages, with a view that this treatise on Arithmetic may be useful to the young, and prove a valuable acquisition as a text book, for those of maturer years. The Author solicits the indulgence of the discerning public; for it is needless to add, that in working so great a number of examples, errors may occur. With the hope that these may be few and unimportant, for great care has been employed in solving the questions, and neither labour nor expense has been spared to render it generally useful. Moor Lane House, Southwell. C. W. THORNHILL. ARITHMETIC. ARITHMETIC) is the art of computation, or the science of numbers. It is divided into two parts, Theoretical and Practical. 1. Theoretical Arithmetic is the science of the properties of numbers &c., considered abstractedly, with the demonstration of the several rules. 2. Practical Arithmetic is the art of computing, i. e. certain numbers are given to find certain others, whose relation to the former are known. Thus, two numbers 10 and 5 are given, we find their sum to be 15; their difference 5; their product 50; and their quotient 2, Numbers are expressed by characters called figures) or digits, (c) as 1, 2, 3, 4, 5, 6, 7, 8, 9, 0. A unit signifies but one, as one tree, one apple, &c. A number signifies simply either one or several units, as one box, four hats, &c. All the operations of Arithmetic are comprised of two fundamental rules, namely, "Addition, and Subtraction; of which there are simple and compound. NOTE. A Cipher (s) when standing alone signifies nothing, but when it is placed on the right hand of the other figures, it increases their value in tenfold proportion. Thus 2 with a cipher annexed to it becomes 20 twenty, and with two ciphers 200 two-hundred, &c. (a) Arithmetic, from apibμntixn, the art of numbering.-(b) Figure, from figura, a figure.-(c) Digit. from digitus, a finger.-(d) Unit, from unus, one.- -(e) Number, from numerus, a number. (f) Multiplication is a compendious method of Addition, thus 3 times 4 equal 12; which signifies the number 3 added four times into itself equal 12 3+3+3+3=12. Division is a compendious method of performing subtraction thus, 12, divided by 3, equal 4, signifies that the number 3 may be taken 4 times from the number 12; as 12-3-9, and 9-3-6, and 6-3-3, &c. (g) Cipher, from (Ar.) siforon, a cipher. |