THE PRINCIPLES AND PRACTICE OF ARITHMETIC AND MENSURATION: WITH THE USE OF LOGARITHMS. ADAPTED FOR THE USE BOTH OF PUBLIC AND PRI BY J. WHARTON, SCHOOLS WITH THE SANCTION OF THE COLLEGE OF PRECEPTORS. LONDON: FRINTED FOR LONGMAN, BROWN, GREEN, AND LONGMANS, PATERNOSTER-ROW. PREFACE. THESE pages are intended as a first step towards a method of teaching Arithmetic, which, by abrogating the use of rules and inducing a knowledge of principles, may gradually lead pupils to trust to their own intellect for the discovery of methods, and thus more fully prepare them for bringing their knowledge into real use than can be done by any amount of mere drilling. Recent treatises on the subject have increased almost without limit the numbers of examples in the more elementary parts, and have in a great measure neglected the treatment of fractions and decimals; but these, in fact, ought to be made the foundation of all arithmetical knowledge. By destroying, also, at one stroke, all need of rules for every variety of proportions, and bringing under the same head a multitude of other rules, it is hoped that much complicity will be avoided. It is earnestly recommended to allow pupils to pass on to fractions as soon as they have acquired a knowledge of the processes of Multiplication and Division in abstract and concrete quantities, and that at the same time they should begin to learn Algebra and to work Equations. The mental energy acquired by such studies will be found to amply repay all the attention bestowed upon them. The absence of rules will enforce on Tutors the necessity |