By J. R. YOUNG, “The rules of Arithmetic are formed generally for the use of those who have not arrived PREFACE, In this little book I have endeavoured to expound, 'upon simple and rational principles, the rudiments of the SCIENCE OF ARITHMETIC. With rules I have given reasons : and although the work is designed chiefly for schoolboys and young persons, yet, contrary to the usual practice, I have chosen to regard the learner less as an arithmetical machine than as an intellectual being. I venture to hope, that what I have here done may meet with some degree of countenance from Schoolmasters and Teachers; and that it may also prove acceptable to the solitary and self-dependent student. This is not an unreasonable hope: for, although so-called Treatises on Arithmetic are very numerous, the number of books really deserving of the appellation is but few. As I have reserved no room here for even the most summary analysis of the following pages, I must leave them to the candid examination of those who may be interested in the progress of this class of educational books. I trust no fault will be found with me for the familiar and colloquial form of exposition I have adopted: any attempt at elevation of style, in works of this kind, is wholly misplaced. I have imagined my own pupils before me; and I have addressed them as I was formerly in the habit of doing in oral instruction. My sole aim has been to be intelligible, and to invest the subject with what interest I could consistently with the preservation of scientific accuracy: but if there be one part more than another, to which I would invite special attention, it is the subject of Decimals, towards the end of the book. J. R. YOUNG. LONDON, March, 1852. *** A Key to the work is in preparation : besides solutions in full to all the Exercises, it will contain some additional instructions for the otherwise unassisted learner. CONTENTS. Tables of Weights, Measures, &c. Addition, Subtraction, &c. of Compound Quantities Erratum.- Page 37, last line but one, for “less," read “ greater ;' The following Corrections may be made with the pen :- Page 138, Exercises line 2, for “8,” read “8;” p. 147, line 3, for“ 58352-74,” read “68352-74;" p. 168, last line, for “3800," read “ £3800;" and p. 177, foot-note, for The dividend at p. 160 has been made to differ from the number; and the second, or right-hand ngure, telis us now many ones, or units there are in the number, besides the tens : one, you are to remember, is also called unit, or unity. (3.) From what has now been said, you see that the word number does not mean the same thing as the word figure: there are only ten different figures, or single marks, but by joining two or more of these together, we may write down as many numbers as we please. The single figures themselves are also called numbers, as well as sets of two, three, or more figures : thus, 5, 7, 6, &c., are numbers of one figure each ; 57, 75, 76, &c., are numbers of two figures ; and 576, 756, &c., are numbers of three figures. The number 57 is fifty- seven, the number 75 is seventy-five, the number 76 is seventy- * Arithmetic may be defined as the science which teaches how to per- form computations by numbers. It would perhaps be of but little use to a beginner to give a formal definition of Arithmetic in the text. B |