DESIGNED TO IMPART TO LEARNERS A CLEAR AND AN ADEQUATE TO ACCOMPANY THE APPARATUS. Br OLIVER A. SHAW. BOSTON: T. R. MARVIN, PRINTER, 24, CONGRESS STREET. 1832. Educ. 1.118-32-7 Educ T 118. 32. 786 1859, Sept. 15. Entered according to Act of Congress, in the year 1832, In the Clerk's Office of the District Court of Massachusetts. THE VISIBLE NUMERATOR. THIS apparatus is designed to illustrate to the Eye, and thus to convey to the Mind, a clear and an adequate idea of the general principles of Arithmetic. It is, in a word, designed to take the same place in Arithmetic, which the Diagrams occupy in Geometry. Its nature and use are founded in the soundest principles of Mental Philosophy, as advanced and maintained by Locke, Reid, Stewart, Brown, and others. Consisting of a series of solids, so arranged as to impart with rapidity a satisfactory knowledge of a most important branch of Education, this simple apparatus will, in the opinion of many of the most distinguished Mathematical Professors in our country, who have examined it, prove an essential aid in the Art of Teaching, by communicating in a few hours, as much real science, as it has usually cost months, and even years, fully to acquire. Each set of the Visible Numerator is accompanied by ample directions for its use, and is adapted to pupils of every age. Families, therefore, will find this Apparatus an invaluable source of instruction for their children, and its introduction into the domestic circle, cannot fail to render a science, which has too often inspired aversion and disgust, the subject of daily amusement and satisfaction. "This apparatus is very simple, and we cannot but look upon it as one of the improvements of the age."-Magazine of Useful Knowledge, for May, 1831. "This apparatus should be used in every family and school where elementary instruction is given."-New York Evening Journal. "We have been exceedingly gratified in examining an apparatus, intended for illustrating the general principles of Arithmetic, invented by Mr. Oliver A. Shaw, a practical teacher, of Richmond, Va. It has received the decided approbation of many gentlemen of literature and science, but it needs them not, to commend it to any person, who has opportunity to examine it, and witness its use and application for a few minutes. By this means all the fundamental rules of Arithmetic may be taught with great facility; and, what is far better, the reason of the process is explained to every common capacity. The invention is perfectly simple, and every one is surprised that it has not been thought of before."-Education Reporter, of July 21st, 1831. The following testimonials of gentlemen belonging to New York, and others from different parts of the country, who have examined the Visible Numerator, are annexed, together with a letter from Mr. Walter R. Johnson, Principal of the High School in Philadelphia, and Professor of Mathematics in the Franklin Institute of that city: Mr. Oliver A. Shaw, Philadelphia, May 2, 1831. Dear Sir,-Having been favored with a view and explanation of your method of elucidating the elements of arithmetical calculation, by means of sensible objects, I am fully of opinion, that it is superior to any of the devices designed for similar purposes, which have hitherto fallen under my notice. I am persuaded that by the use of the simple means which you apply, the mind of the pupil will be early led to attach the right value to figures according to their places; and to comprehend, with perfect clearness, the reason of every step demanded by the nature of the operation which he is to perform by means of figures. By the method of teaching yet extensively in use, the progress of the scholar is chiefly impeded by the mere technical expressions employed about this subject, which, if not left wholly without elucidation, are often explained in terms equally technical, and equally need ing explanation. Your Apparatus, embracing the combined view of numbers and magnitudes, and their relation to each other, gives an intuitive perception of the truth and propriety of every process required in the solution of a problem. Knowing from long observation, that Arithmetic may be rendered one of the most engaging of pursuits for the youthful mind, I feel assured, that with the aid of such facilities as are presented in this method, no scholar of ordinary capacity need be embarrassed by any of those appalling obstacles, which have too often rendered the whole subject a matter of perplexity and disgust. I am, dear sir, with high respect, your friend and servant, WALTER R. JOHNSON. |