SCHOOL ARITHMETIC. ANALYTICAL AND PRACTICAL. BY CHARLES DAVIES, LL.D. AUTHOR OF A FULL COURSE OF MATHEMATICS, PUBLISHED BY A. S. BARNES & BURR, 51 & 58 JOHN STREET. SOLD BY BOOKSELLERS, GENERALLY, THROUGHOUT THE UNITED STATES. 1864. P ADVERTISEMENT. tar attention of Teachers is respectfully invited to the REVISED ONS of Davies' Arithmetical Series FOR SCHOOLS AND ACADEMIES. 1. DAVIES' PRIMARY ARITHMETIC AND TABLE-BOOK. 2. DAVIES' INTELLECTUAL ARITHMETIC. 8. DAVIES' SCHOOL ARITHMETIC. 4. DAVIES' UNIVERSITY ARITHMETIC. 5. DAVIES' PRACTICAL MATHEMATICS. the above Works, by CHARLES DAVIES, LL.D., Author of a Complete Vourse of Mathematics, are designed as a full Course of Arithmetical Instruction necessary for the practical duties of business life; and also to prepare the Student for the more advanced Series of Mathematics by the same Author. The following New Editions of Algebra, by Prof. Davies, are commended to the attention of Teachers: 1. DAVIES' NEW ELEMENTARY ALGEBRA AND KEY. 2. DAVIES' UNIVERSITY ALGEBRA AND KEY. 3. DAVIES' BOURDON'S ALGEBRA AND KEY. Entered according to Act of Congress, in the year one thousand eight hundred and fifty-five, BY CHARLES DAVIES, In the Clerks Office of the District Court of the United States for the Southern District of New York. PREFACE. ARITHMETIC embraces the science of numbers, together with all the rules which are employed in applying the principles of this science to practical purposes. It is the foundation of the exact and mixed sciences, and the first subject, in a well-arranged course of instruction, to which the reasoning powers of the mind are directed. Because of its great practical uses and applications, it has become the guidé and daily companion of the mechanic and man of business. Hence, a full and accurate knowledge of Arithmetic is one of the most important elements of a liberal or practical education. Soon after the publication, in 1848, of the last edition of my School Arithmetic, it occurred to me that the interests of education might be promoted by preparing a full analysis of the science of mathematics, and explaining in connection the most improved methods of teaching. The results of that undertaking were given to the public under the title of "Logic and Utility of Mathematics, with the best methods of instruction explained and illustrated." The reception of that work by teachers, and by the public generally, is a strong proof of the deep interest which is felt in any effort, however humble, which may be made to improve our systems of public instruction. In that work a few general principles are laid down to which it is supposed all the operations in numbers may be referred : 1st. The unit 1 is regarded as the base of every number, and the consideration of it as the first step in the analysis of every question clating to numbers. 2d. Every number is treated as a collection of units, or as made up of sets of such collections, each collection having its own base, which is either 1, or some number derived from 1. 3d. The numbers expressing the relation between the different units of a number are called the SCALE; and the employment of this ter enables us to generalize the laws which regulate the formation of numbers. 4th. By employing the term "fractional units," the same principles are made applicable to fractional numbers; for, all fractions are but collections of fractional units, these units having a known relation to 1. |