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. DẠY, LYON & CO.–H. J. LITTLE & CO. S. H. COLESWORTHY. 1842. Entered according to Act of Congress, A.D. 1842, By CHARLES WATERHOUSE, In the Clerk's Office of the District Court of Maine. PRINTED AT THE AMERICAN OFFICE. No. 1, UNION STREET, PORTLAND. 3-19-40 MJ Turtle 7-21-08 36926 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, |