Publisher's Synopsis
Excerpt from School Algebra
The present volume is issued in the hope that it will assist the teacher in the effort to get pupils to Mink and that it will induce pupils to place the subject of Algebra on a rational instead of an arbitrary basis, to work from principles rather than from rules.
In the first part of the work we have pursued what is termed the inductive method, but we do not wish this understood as that method which infers general principles from an accumulation of particular cases. This is the inductive reasoning of the natural sciences. But we believe it is never legitimate in mathematics. Induction, as we use the term, means that method which proceeds from the particular to the general. By particular cases, which gradually increase in generality, the mind of the learner is prepared to appreciate the gen eral case, but this general case must so present itself to the learner's mind that he sees that the truth stated must be so and cannot possibly be otherwise.
It will be noticed that we have not thought it necessary to complete one subject before taking up another, but subjects have sometimes been treated in an elementary way at first and more completely at some subsequent part of the book. We believe that by this plan students can follow the work more easily and with more profit, and at the same time we are enabled to treat some subjects, especially Factors, Multiples, and Fractions, more fully than is ordinarily done.
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