74 SCIENCE IN GRECO-ROMAN ANTIQUITY 



paraboloid of revolution is equal to one and a half times 

 the cone having the same base and axis as this segment. 

 Two segments cut off from a paraboloid of revolution 



Right angle 



Pa ra b o I a 



Ellipse 



Fig. 7. 



by any planes are to each other as the squares of their 

 axes. To prove these demonstrations Archimedes 

 uses the method of exhaustion, which consists in 

 limiting the quantity sought between two known 



