to the stock. As much as had been accomplished in previous years, in regard to any particular department, some effort now and then entirely explodes all or nearly all accomplished, and presents an entirely new principle in the labor of instruction, or in the use of an old one. This is peculiarly true, in regard to the mode of imparting to young minds the philosophy of numbers-or what is more familiarly called Arithmetic. Each new work on the subject has led to another with fresh claims to excellence; and the confidence is strong that the present work of Walker will be found as much an improvement on all previous systems of Arithmetic, as the recent more popular ones are upon those used fifty years since. An outline of its distinctive features will be found in the following extracts from the Author's Preface: "The principles of numbers can be only those of increase and diminution; the former invariably under the forms, addition and multiplication; the latter under those of subtraction and division. Why then should rules be so multiplied? "These principles are applied in this work, in Part I. to simple or abstract numbers; in Part II. to parts of simple numbers, or simple fractions; in Part III. to denominate numbers, or denominate fractions, as they are termed, after Mr. Hassler; and in Part IV. they are applied to all quantities indiscriminately; for which the other parts are, as already stated, only preparatory; Part V. embraces the roots. "Throughout the first three parts, the principles, and every application of them, are illustrated and explained; with these parts explanations cease, and the pupil is thrown on his own resources, to analyze and develop for himself, except in Part V. "The illustrations will in all cases guide the pupil in the special application of the principles proposed, and to them alone it is expected the younger classes of pupils will have regard; omitting the explanations, which are abstract reasonings on stated applications of the principles, as presented to the cases and rules, to be analyzed, and presented in substance, when more maturity and greater familiarity in operations under the rules, guided by the illustrations, are attained. "It is intended that the cases and rules should be thoroughly committed to memory; that the illustrations should be before the pupil, to show him how the application required is made; that the explanations should be mastered by analysis by older pupils; and the examples are for practice by all." |