PRACTICAL ARITHMETIC: EMBRACING THE SCIENCE AND APPLICATIONS OF NUMBERS BY CHARLES DAVIES, LL. D., PROFESSOR OF HIGHER MATHEMATICS IN COLUMBIA COLLEGE; AND NEW YORK: A. S. BARNES & Co., 111 & 113 WILLIAM STREET, 1866. K134164 MARVARD UNIVERSITY LIBRARY 77x130 ADVERTISEMENT. THE attention of Teachers is respectfully invited to the REVISED EDITIONS of Dabies' Arithmetical Series FOR SCHOOLS AND ACADEMIES. 1. DAVIES' PRIMARY ARITHMETIC. 3. DAVIES' PRACTICAL ARITHMETIC. 4. DAVIES' UNIVERSITY ARITHMETIC. 5. DAVIES' PRACTICAL MATHEMATICS. The above Works, by CHARLES DAVIES, LL.D., Author of a Com plete Course 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 Professor DAVIES, are commended to the attention of Teachers: 1. DAVIES' NEW ELEMENTARY ALGEBRA AND KEY. 2. DAVIES' UNIVERSITY ALGEBRA AND KEY. 8. DAVIES' BOURDON'S ALGEBRA AND KEY. Entered according to Act of Congress, in the year one thousand eight hundred and sixty-two, BY CHARLES DAVIES, In the Clerk's Office of the District Court of the United States for the Southern PREFACE. ARITHMETIO embraces the science of numbers, together with al the rules which are employed in applying the principles of th 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 uses and applications, it has become the guide and daily companion of the mechanic and man of business. In the present work, a few general principles are laid down, to which 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 is the first step in the analysis of every question relating 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 series of numbers expressing the relation between two different units of a number, is called the SCALE; and the employment of this term enables us to generalize the laws which regulate the formation of numbers. 4th. By employing the term "fractional unit," 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. 5th. The presentation of the fractional units to the minds of young pupils, by means of a diagram, as exhibited in the Primary and Intellectual Arithmetics, has greatly simplified the operations in fractions; and they may now be placed before Denominate Numbers, where, in a purely scientific arrangement, they properly belong. |