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ENTERED, according to Act of Congress, in the year 1850, by J A. M. E S T. EN OS,
in the Clerk’s Office of the District Court of Wisconsin.
1T has become a generally received truth, that Intellectual Arithmetic is among the first studies that should be presented to the juvenile mind. It is also a truth worthy of general reception, that the young grasp combinations of numbers with greater ease, when properly presented, than any other branch of science. This, together with the fact that whatever is taught a child at first should be UNCHANGING TRUTH, is ample evidence in favor of this branch as the FIRST STUDY OF EVERY CHILD. The following Arithmetical Analysis is designed to present the subject in its most practical light—developing the general principles of numbers in a simple, yet strictly philosophic and logical manner, The arrangement of the text, though in some respects differ: ent from any other work on this branch, is nevertheless believed to be a more natural arrangement, and at the same time to dictate a more simple analysis of the Elements of Arithmetic ; a want of which has, unquestionably, led pupils to be content with a superficial knowledge of the principles of the science. Multiplication is placed immediately after Addition, from the fact that it is only a different mode of applying the same general principle. Fractions are introduced immediately after Division, and the relation and relative size of one part to another are clearly elucidated. The questions throughout are of a practical character, or given with reference to securing the attention of the pupil, and holding it for a long time, on a single subject, thus strengthening the reasoning powers, and capacitating them for more powerful mental effort. The mode of solving the questions is the one long used by the Author, and has received the commendation of many of the most distinguished teachers in the United States, and has been in substance adopted by them. The first sections, and the first questions of each section, are formed of small numbers, the following ones rising in regular and systematic gradation, to greater degrees of complexity. Thus the mind of the pupil is gradually led out and strengthened, and the foundation of a healthy and unchanging mental progression firmly implanted in the mind. Exercises rationally performed serve a far better mode of awakening the faculties of children to invigorating effort, than by recourse to demonstrations of mere abstract propositions; and the present work has been prepared with direct reference to this important principle. The notes are designed chiefly for the use of young teachers, or those who have never been called to teach this branch. These, together with the ANALYSIs of a large number of questions, it is believed will render the method of procedure so simple that teachers need have no fears in instructing a class, even though they have never pursued the study in school. In submitting this little work to the consideration of his fellow laborers, the author would only add that, in its preparation, great pains has been taken, and most of the questions presented have been put to the practical test in the school room, before being incorporated into the work itself. He believes the arrangement, system, and sufficient simplicity of its pages will secure the largest portion of its success. With this brief statement of the general plan of the work, it is most respectfully dedicated to the friends of education, trusting to its merits alone for adoption and use.