MECHANICS AND PHYSICS 193 



by a method similar in all points to that adopted by 

 Euclid in his Elements. 



This being so, Archimedes only required that the 

 two following propositions should be granted : 



1. Two equal weights applied at equal distances 

 from the fulcrum are in equilibrium. 



2. Two equal weights applied at unequal distances 

 (from the fulcrum) are not in equilibrium and the more 

 distant weight descends. 



These and similar postulates were considered by 

 Archimedes to be self-evident and independent of all 

 experience. If a rod supposed to have no weight 

 rests freely at its middle point on a fulcrum, and if 



/ / 



Fig. 32. 



two equal weights are suspended from its extremities, 

 it would appear a priori that the whole system is in 

 equilibrium, for as the system is symmetrical there 

 seems no reason why a movement should take place 

 in one direction more than in another. It seems 

 therefore evident, by virtue of the law of adequate 

 reason, that the hypothesis is independent of all 

 experience. 1 



When this hypothesis is admitted, the law of 



equilibrium is easily established in the case of a lever, 



namely ph = VI, the relation in which the greater force 



P is exerted at the shorter arm I of the lever (Fig. 32). 



1 Mach ) La Mecanique, Hermann, Paris, 1904, p. 18. 



