IN VENTIONAL GEOMETR Y. 



363 



into four equal angles without using more than four circles ? "' 

 (Fig. 5). 



" Can you construct a square on a line without using any other 

 radius than the length of the line ? " (Figs. 6, 7, 8, and 9). 



Such problems as that solved in Fig. 10, " Can you place four 

 octagons to meet in one point and to overlap each other to an 

 equal extent ? " delight the eye by beauty of form, and teach the 

 puftil the basis of geometrical design. 



Figs. 11 and 12, solutions to " Can you fit a square inside a cir- 

 cle, and another outside, in such positions with regard to each 

 other as shall show the ratio the inner one has to the outer ? " 



Y. 



and " Place a hexagon inside a circle, and another outside, in such 

 positions with regard to each other as to show the ratio the inner 

 one has to the outer," illustrate one way in which comparative 

 area of figures is treated. 



We have spoken of the pleasure a class experiences in putting 

 their solutions upon the blackboard, and in examining the draw- 



