AS TAUGHT IN THE TROY EPISCOPAL INSTITUTE; By W. F. WALKER, A. M., PRINCIPAL. Out of the olde fieldes, as men saithe, Cometh all this newe corne fro yere to yere ; And out of olde bookes, in good faithe, Cometh all this newe science that men lere. Chaucer. TROY, N. Y.: ELIAS GATES, 225 RIVER-STREET. NEW-YORK: COLLINS, KEESE AND COMPANY, 254 PEARL-STREET. 1841. PREFACE. A NEW ARITHMETIC! Why? Its brief history furnishes the answer. During the four years last past, the author had under his especial charge this department in the Institute of which he was Principal, and a large portion of the time exclusively performed its duties. As text books for his classes, many of the various popular works on the subject were, at different times, successively tried, and as many as were tried, were, for some cause, after a while, rejected;-some because the systems were too new, that is, too juvenile, as one reason; and in addition, with most of the others, as embracing too much, more than belongs properly to the subject; and, all dissatisfied, on one main account, which was, the almost total deficiency of expositions of principles, independent of numbers. A consequence of the use of these books was found to be, in so far as reliance was placed on the books, confinement of the mind, rather than invigoration and development, and a reliance on formulas and rules, rather than on the great principles on which they were based; a stopping behind, rather than a looking within the veil. The mind of the pupil was therefore confused; his views were all dependent and indistinct; his powers of analysis were never exercised vigorously; and his judgment was not made the arbiter of his work. Uncertainty as to results, unless the formulas and rules of his books were applied to square them, almost always characterized him. Therefore, when a practical question was presented, it was not uncommon for him to ask, To what rule does this belong? Instead of being made to see and know that but two principles can apply to numbers, and that they, variously applied, solve every question connected with them; and that the modes of application are always discoverable by an analysis to which the given question points; he felt that with each step of advancement a new principle was to be acquired, and so in learning a multiplicity of new things, out of two only which are as old as quantity itself and the first exercise of mind, became bewildered and disheartened. The author then commenced writing and culling for his classes, bringing out the true and the necessary, and rejecting all else, with no idea of inflicting on the public the result of his efforts, further than they might be extended through his pupils. But the labouriousness of writing and transcribing so much as was required daily, caused him to throw his matter in the first part into form, and put it in press, to supply the wants of his own school. When so far committed, in connection with the press, reasons multiplied rapidly for going on with what had been thus begun, and bringing out the whole subject. To their variety, number, and force, the author yielded; and, as a consequence, now offers to the public a new Arithmetic, embracing old principles, as applied to their various purposes in connection with numbers, in the Troy Episcopal Institute, while he had that institution in charge. |