Natural Geometry

At a time when the desirability and importance of imparting technical education to all classes are generally admitted, an effort to render such education easier to both teacher and pupil is worth consideration. Intelligent reasoning is the basis of all such education. And of such reasoning mathematical is the most important, and perhaps the most difficult, to the young and uneducated.
There are two ordinary methods of learning mathematics: one, the Euclidian, which follows a road to a goal that the traveller does not see until he arrives at it; and the other, the method of most books on arithmetic and mensuration, which shows the goal without pointing out the road that leads to it. There is no novelty in applying concrete reasoning to the solution of mathematical propositions.