RATIONAL ARITHMETIC. BY MRS. G. R. PORTER. A NEW EDITION. ALTERED AND ADAPTED FOR THE USE OF SCHOOLS AS WELL AS FOR PRIVATE INSTRUCTION. LONDON: JOHN MURRAY, ALBEMARLE STREET. 1852. 181. C.43. PREFACE. A LITTLE BOOK, published some years ago, entitled 'Conversations on Arithmetic,' has been long out of print, and there is reason to believe that a second edition may be advantageously given to the public. On determining to republish this work, I have been naturally anxious to make such improvements and alterations in its arrangement as the experience of others as well as my own may have suggested, in order to extend its usefulness, and to make it as far as possible deserving of public favour. In the first instance I adopted conversations as the form of instruction, considering that through that medium a greater facility for explanation and familiar illustration was afforded than by any other mode of imparting information. But though much easier and more pleasing to the writer, this form has the serious objection, that a book teaching by the aid of such machinery cannot well be employed as a school or class book, and is therefore adapted only for private instruction; and it has been considered that, if direct teaching and rules were substituted for the conversational form used in the former edition, this attempt at teaching rational arithmetic might be made of more extensive use. Under this impression I have remodelled my former work, and have endeavoured by means of direct instruction to give the same explanations as were used in the form of question and answer. I have encountered many difficulties in this task, but trust I have not omitted any necessary explanations, or departed from the spirit, though I have from the letter, of the first edition. An attentive revision has been made of the whole, and, where it has been thought that more simple explanations might have been given, these have been supplied. Many new questions and examples have been added, the answers to which, as well as to those already given, have been carefully examined by competent persons. The following extracts from the first preface will show the purport of this little work, and my reasons for venturing to introduce it into notice. An author should not perhaps offer to the public a new elementary work, without assigning some reason for thus swelling the already numerous list of books written for the purposes of education. Every writer hopes that his individual work will not be found one of supererogation, and believes that what he has to propose will correct established errors in practice, or afford new facilities for acquiring knowledge. However little may be accomplished in these respects, there is perhaps sufficient reason for attempting that little. In this hope, and influenced by this belief, I have written the following work. Having had my attention early awakened to the beauties of the study which forms the subject of these pages, it has ever been a matter of regret with me that arithmetic should be acquired in the unsatisfactory manner in which it is generally taught. There is no branch of early education so admirably adapted to call forth and strengthen the reasoning powers; this object, therefore, independent of the advantages attendant on the thorough knowledge of arithmetic, offers in itself a sufficient motive for engaging the young mind in the pursuit. If its end and aim were only to exercise their mental faculties, the time thus employed in the education of youth would be well bestowed, "not so much to make them mathematicians as to make them reasonable creatures."* To assist in rescuing arithmetic from the degraded rank it at present occupies among intellectual pursuits is a principal object of the following work. I have endeavoured so to simplify the subject, that mothers or instructors who have not previously turned their attention to this interesting and important branch of education may be enabled by its help to teach their pupils the rationale of the science, and make it attractive to them, without finding any difficulty in the task. Whether or not I have succeeded in my attempt can only be discovered by the test of experiment, and from the verdict of enlightened preceptors. It is particularly hurtful to the mind to be hurried into knowledge, nor can it be too strongly urged that but little should be proposed at once, and, until this little has been thoroughly understood and mastered, |