PRINCIPLES AND METHODS 



in 



fact, it does not rest on any group of axioms or pro- 

 positions previously demonstrated. It is complete in 

 itself, but it lacks generality, since the sides of the 

 triangle must be whole numbers of a certain value. 

 Let us take, on the other hand, the theorem which tra- 

 dition attributes to Pythagoras. We see immediately 



Fig. 9. 



how different the demonstration is. The large square 

 (Fig. 9) constructed on the hypotenuse, is divided into 

 two rectangles ; the question being to demonstrate the 

 equality of their areas with those of the squares con- 

 structed on the sides of the right angle. Auxiliary 

 figures, viz. pairs of triangles, intervene ; this being 



