AN ELEMENTARY AND PRACTICAL ARITHMETIC, IN WHICH HAVE BEEN ATTEMPTED VARIOUS IMPROVEMENTS IN ARRANGEMENT AND NOMENCLATURE, AS WELL AS IN THE MEANS OF SECURING THOROUGH DISCIPLINE IN THE PRINCIPLES AND APPLICATIONS OF THE SCIENCE. BY JAMES B. DODD, A. M., MORRISON PROFESSOR OF MATHEMATICS AND NATURAL PHILOSOPHY, IN NEW YORK: PUBLISHED BY PRATT, WOODFORD, & CO. HARVARD COLLEGE LIBRARY BY EXCHANGE JAN 8 1937 Entered according to act of Congress, in the year 1849, by JAMES B. DODD, In the Clerk's Office of the District Court of Kentucky. Stereotyped by JAMES & CO., PREFACE. In this work an effort has been made to treat the subject of Arithmetic with that strictness of method which is appropriate to the nature of every branch of mathematical science. By a new arrangement of several subjects, consequent upon a regard to what has seemed the most natural order of instruction, a wider range of application has been assigned to general Rules. Decimal Fractions, for example, include Federal Money; and the Reduction of quantities to different denominations, whether Integers, Vulgar Fractions, or Decimals,—usually forming three divisions of Arithmetic, requiring half a dozen Rules,-is presented under two consecutive Rules in Reduction descending, and ascending. Other simplifications in the structure of the work, will be noticed by the intelligent Arithmetician, and need not be here specified. They will all be found to facilitate the acquisition of the science, in the only way in which any science can be effectually acquired-by apprehending its general principles, and carrying those principles into their particular applications. Some changes in nomenclature have been introduced, from a belief, strengthened by the concurring opinions of numerous literary and scientific friends of the author, that such changes would be useful, and would thus be likely to succeed. For "denominate number," applied to such an expression as 3 bushels of grain, for example, is substituted monomial quantity, or simply monomial: and for "compound number," or "compound denominate number," applied to such an expression as 3 bu. 2 pk. 5 qts. of grain, is used polynomial quantity, or simply polynomial. These terms, monomial and polynomial, are literally appropriate to the designation of the quantities to which they are thus applied; and, having the advantage of greater brevity and precision than those for which they are substituted, they will be found to introduce real improvements in the composition of the Rules relating to such quantities. |
