Page:Popular Science Monthly Volume 34.djvu/375

Rh in Fig. 1. The question, "Where was the particular point?" or, the point being marked, where he must make the circles touch, brings the correct solution (Fig. 2).

Many mistakes of like nature occur in the first lessons. In every such case the pupil must be led, by questioning, to see what is incorrect. He should not be told or shown, but thrown back upon himself; for, in inventional geometry, the knowledge is to be gained by growth and experience, through the powers he possesses and the method of acquirement peculiar to his mind. Occasionally the pupil is not a little baffled, and the skill of the



teacher is put to its best test to gain the solution without showing or telling him. Telling or showing is the method of the instructor—not of the teacher. The following problem (Fig. 3), "Given a circle, and a tangent to that circle, it is required to find the point in the circumference to which it is a tangent," is one of