PREFACE. IN the construction of this Arithmetic, the Authors have had two principal objects in view; one, to make a book expressly for the use of scholars in elementary schools who are to be examined in Arithmetic under the Revised Code the other, to supply to more advanced scholars the means of acquiring an intelligent knowledge of the higher parts of the subject. In the first part of the book care has been taken to supply methods by which a scholar may learn to overcome every difficulty likely to be met with, and each step has been made the subject of a separate lesson, which directs the attention to one point only. Questions for solution are given to teach the application of every rule, and examples are introduced, to be worked at sight, to give readiness in the performance of useful calculations. An endeavour has been made to supply a book from which scholars may acquire a thorough knowledge of arithmetic-not merely to work sums, but to turn questions into sums, to work them out, and to understand the answers. The sums are also set in a variety of ways, that the scholars may not be at a loss how to proceed under different circumstances. In the second part of the book, the methods employed refer to elementary principles and not to rules. An attempt has here been made to render arithmetic an intellectual exercise, as well as a branch of useful knowledge. Rules have, in almost all cases, been dispensed with, and the understanding is employed in preference to the memory. It is hoped that the chapters on the rule of three, and on percentage, will be particularly valuable in this respect. The Authors have not been satisfied with imparting a knowledge of arithmetic -their aim has been to supply methods which are not readily forgotten when once understood. They have endeavoured to show that all arithmetic consists of the four elementary rules and a few other ideas, and that when these have been acquired, the solution of all arithmetical questions may be arrived at by the application of a little common sense. STEP BY STEP. STANDARD II. * For STANDARD I. see ARITHMETICAL COPYBOOK No. I. by the Authors. ARITHMETIC is the science of number. All numbers can be represented by the following ten figures: 0 Nought 1 One 5 Five 2 Two 3 Three 4 Four 6 Six 7 Seven 8 Eight 9 Nine 1. NOTATION. Notation is the art of writing numbers in figures. To write numbers less than one hundred. Write the figure that stands for ones or units, and on the left of it write the figure that stands for tens; thus, sixtyfive is written 65, where the 5 stands for 5 ones, but the 6 stands for 6 tens or sixty. Write in figures. (8) Sixty (1) Twenty-five. (2) Eighty-six. (3) Forty-two. (4) Thirty one. (5) Seventeen. (6) Twenty-five. (7) Eighty. four. (9) Twelve. (10) Seventy-two. (11) Eighteen. (12) Ten. To write hundreds. When hundreds are to be written, three figures must be used-the first for ones and the second for tens, as before, and the third for hundreds. To write one hundred and sixty-five, read one, sixty-five--165. B |