



INTRODUCTION 7 



were called harpedonaptce, which signifies rope- 

 stretchers. 1 It would appear also that the Egyptians, 

 as well as the Hindoos, had dis- 

 covered, before Pythagoras, the 

 relation between the surfaces 

 of squares constructed on the 

 sides of a right-angled triangle. 

 However, the demonstration 

 which they gave of this relation 

 must have been purely intuitive 

 and empirical : it probably con- 

 sisted in dividing the squares so constructed into small 

 squares, all equal, and showing the equality of the sums : 



I 



V X/ 



Fig. 2. 



J 



Fig. 3 



25 = 16 +9 (Fig. 3). This demonstration is not appli- 

 cable to any right-angled triangle whatever ; it neces- 



1 Clement of Alexandria, edit. Pottier, p. 357. 

 2 



