INVENTIONAL GEOMETRY. 



361 



in Fig. 1. The question, " Where was the particular point ? " or, 

 the point being marked, wliere 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 show- 

 ing 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 



