Practical arithmetic, uniting the inductive with the synthetic mode of instruction: also,illustrating the principles of cancelation. For schools and academies. By James B. Thomson, A.M. Day's school algebra,Legendre's geometry, &c New Haven: Loomis & Peck, Philadelphia, J.C.Derby & co.,Auburn,N.Y. PREFACE. IT has been well said, that "whoever shortens the road to knowledge, lengthens life." The value of a knowledge of Arithmetic is too generally appreciated to require comment. When properly studied, two important ends are attained, viz: discipline of mind and facility in the application of numbers to business calculations. Neither of these results can be secured, unless the pupil thoroughly understands the principle of every operation he performs. There is no uncertainty in the conclusions of mathematics; there should be no guess-work in its operations. What then is the cause of so much roping and fruitless effort in this department of education? Why this aimless, mechanical" ciphering," that is so prevalent in our schools? The present work was undertaken, and is now offered to the public, with the hope of contributing something towards the removal of these inveterate evils. Its plan is the following: 1. To lead the pupil to a knowledge of each rule by induction; that is, by the examination and solution of a large number of practical examples which involve the principles of the rule. 2. The operation is then defined, each principle is analyzed separately, and illustrated by other examples. 3. The general rule is now deduced, and put in its proper place, both for convenient reference and review; thus combining the inductive and synthetic modes of instruction. 4. The general rule is followed by copious examples for practice, which are drawn from the various departments of business, and are calculated both to call into exercise the different principles of the rule, and to prepare the learner for the active duties of life. |