AND TEACHER'S ASSISTANT, INTENDED AS A KEY AND SUPPLEMENT TO THE DIFFERENT WORKS ON ARITHMETIC. FOR THE USE OF SCHOOLS AND ACADEMIES. BY CHARLES WATERHOUSE, TEACHER OF MATHEMATICS. SECOND EDITION, REVISED AND ENLARGED. PORTLAND. WATERHOUSE & CO.-WM. HYDE.-R. H. SHERBURNE. S. H. COLESWORTHY. 1842. MAVAND COLLEGE LILUNY GIFT OF GEORGE ARTHUR PLIMPTON Entered according to Act of Congress, A.D. 1842, In the Clerk's Office of the District Court of Maine. PRINTED AT THE AMERICAN OFFICE. NO. 1, UNION STREET, PORTLAND. PREFACE. It is well known that common works on Arithmetic abound with curious and abstruse questions more perplexing than beneficial, but if partially explained serve as an inducement rather than an obstacle to the study so solitary in its character. These questions the inquisitive and ingenious student is anxious to solve, and after puzzling a while, applies to the teacher for assistance. To teachers, these applications are necessarily too great a tax on their time, especially when having a large number of pupils under their care. Besides, in the hurry of business, it is often very difficult for persons of good retentive abilities, that have attained to the knowledge of Mathematics, not to be expected of our primary school teachers, to recollect, at the moment, all the principles by which are solved some of the difficult questions that may be taken from any of the many works on arithmetic; the judgment of some to the contrary notwithstanding. Even the Professor in College, who is confined to one or two branches, on which his powers are concentrated, makes free use of his translations, and if these are useful to him, certainly similar helps ought not to be denied the common teacher, who has several branches to look after. And the various studies taught in our common schools with the difficulties that teachers labor under, forbid the idea of illustrating the principles of intricate questions, without being partial in the application of time or energies-And pupils by not being thus furnished, lose the knowledge of Mathematical principles they should have for assistance through life, and never obtain what they might have for a convenience. Sometimes also, questions are found in works containing no rule or precedent for solving them. Likewise, difficult questions are much used by wiseacres and the ill-disposed to annoy teachers and injure schools by engaging the attention of the teacher which might be devoted, at particular times, to more useful purposes. Hence, whatever tends to promote the usefulness of the instructor, must commend itself to all. Also, it is believed that every judicious attempt to facilitate the study of a science so essential to the interests of all, will be received with indulgence by an enlightened community, and meet the entire approbation of a generous public. When considering the preceding facts, and in order to give advanced scholars the privilege of extending their knowledge to a full development of the elementary principles in the higher operations of Arithmetic; also with the view of enabling teachers to lay demonstrations of the dogmatical rules, and an explanation of the abstruse matter before their class studying this science, I composed this Desideratum. It is presumed that it would be studied to good advantage, in connexion with other works on Arithmetic, by the Teachers' class in Academies. Particular attention has been paid to render it concise and free from those mistakes which are commonly to be met with in our various text-books on Arithmetic. Therefore, it is hoped that if the tongue of the captious caviler should blazon defects, for which others might search in vain, that the eye of the candid critic will not see objections in it which reason and truth would long hesitate to approve. It is not presumed however, that it is without imperfections, the same at least as may always be met with in any and all the works of man. In this production, although availed of the best Authors which could be obtained, I followed none particularly, except Bonnycastle's method of demonstration, And every item deemed intricate, rare, useful, and interesting, occupies its proper place in this work, and matter considered of a superfluous and common nature was carefully excluded. Since the utility of a work like the present, if faithfully prepared, is so obvious as to require no comment, its author solicits the candid consideration of the public in presenting it, with full confidence that it will serve to lessen the labor of instructors and facilitate the improvement of their pupils. N. Pownal (Me.) A. D. 1842. THE AUTHOR. This treatise may be considered as an Appendix to the works of the following authors on Arithmetic, and as containing precedents for the solution of their difficult questions, viz.: Messrs. WELCH, WALSH, SMITH, PIKE, Beecher, KennE, HALL, DABOLL, LEAVITT, Colburn, ROBINSON, BURNHAM, ROSE, ADAMS, STANIFORD, Olney, Leonard, ROOT, EMERSON, BAILEY, TRACY, DAVIES, BONNEYCASTLE, TYLER, and GREENLEAF. C. W. |