a2 + 2ab + b2
Inductive Inference: The square of the sum of two quantities is equal to the square of the first, plus twice the first by the second, plus the square of the second.
(2) Nature.
This corn sent me as a sample produced heavy, full ears, and many of them; hence (inductive inference), if I plant corn like this sample under like conditions, I will receive in return heavy, full ears, and many of them.
(3) Geography.
Cities like New York, located on the coast, possess a larger foreign element than the inland cities like Philadelphia.
(4) Grammar.
A noun is the name of anything, as the examples, “George Washington” and “house” would indicate.
In deriving a generalization from one or two examples the prime essential is to select types which are truly representative. Often the example used is a special type and in consequence does not exemplify all of the essential characteristics of the group. To teach the nature of a parallelogram by using a rectangle only, is an easy way to commit this error; or one may affirm that the class can easily cover the work, when the judgment is based entirely on knowledge concerning the brightest one of the grade.
Type work when judicially used is a positive time saver and a very present help in times of perplexity. Let the skillful teacher use types and examples extensively yet cautiously.