A KEY TO THE COLUMBIAN CALCULATOR: DESIGNED FOR THE USE OF TEACHERS, AND TO ASSIST THOSE WHO HAVE NOT THE BENEFIT OF A TUTOR'S AID: CONTAINING, ALSO, A GREAT VARIETY OF INTERESTING AND VALUABLE MATTER, EXPLAN- BY ALMON TICKNOR, AUTHOR OF "THE COLUMBIAN CALCULATOR," "YOUTH'S COLUMBIAN CALCU- "If a man's wit be wandering, let him study the mathematics."-BACON, STEREOTYPE EDITION. POTTSVILLE, PA.: PUBLISHED BY BENJAMIN BANNAN. AND FOR SALE BY BOOKSELLERS THROUGHOUT THE UNITED STATES. 1849. HARVARD 46*130 Entered, according to Act of Congress, in the year 1848. BY ALMON TICKNOR, in the Clerk's Office of the District Court of the United States, in and for the Eastern District of Pennsylvania. STEREOTYPED BY REDFIELD & SAVAGE 13 Chambers Street, N. Y. 10-16-34 Misses Flora & Leva Lott Doner INTRODUCTORY REMARKS. THE utility or benefit of a "KEY" to a treatise on Arithmetic may very justly be doubted; but the practice has become so general of having a Key to almost every primary work, as to render it compulsory on the part of authors to publish one, however reluctant they may be to comply with the requisition. If the teacher is a good arithmetician previously to his acquaintance with a Key (and unless this is the case, he most certainly is unqualified to give instruction in the science), he may not be materially injured by the use of one; but in nine cases in ten, where the teacher is deficient, and compelled to resort to his Key for information, he will from this very circumstance, and constant habit, neglect his study and opportunity of instruction, and place his sole reliance on his Key; whereas, if he would apply himself assiduously to the study of his science, so far from its proving an injury, it would be a benefit: and this is the design of the author. It is not intended to supersede the necessity of investigation, illustration, and calculation, nor to indulge the teacher in negligence and idleness, but as an aid or assistant in cases where the question may not appear quite clear, if any such there be (which was not intended), or when the correctness of the solution is doubtful. With permission, we will again urge upon the teacher the very great advantage to be derived from a frequent use of the black-board, accompanied with explanations and illustrations, examinations and reviews, as the only way to make an arithmetician. |