98 PHYSICAL SCIENCES IN ANCIENT GREECE. 



fulcrum. The proposition is, that two bodies so 

 circumstanced will balance each other, when the 

 distance of the smaller body from the fulcrum is 

 greater than the distance of the other, in exactly 

 the same proportion in which the weight of the 

 body is less. 



This proposition is proved by Archimedes in a 

 work which is still extant ; and the proof holds its 

 place in our treatises to this day, as the simplest 

 which can be given. The demonstration is made 

 to rest on assumptions which amount in effect to 

 such Definitions and Axioms as these : That those 

 bodies are of equal weight which balance each 

 other at equal arms of a straight lever; and that 

 in every heavy body there is a definite point called 

 a Centre of Gravity, in which point we may sup- 

 pose the weight of the body collected. 



The principle, which is really the foundation 

 of the validity of the demonstration thus given, and 

 which is the condition of all experimental know- 

 ledge on the subject, is this ; that when two equal 

 weights are supported on a lever, they act on the 

 fulcrum of the lever with the same effect as if they 

 were both together supported immediately at that 

 point. Or more generally, we may state the prin- 

 ciple to be this ; that the pressure by which a 

 heavy body is supported continues the same, how- 

 ever we alter the form or position of the body, so 

 long as the magnitude and material continue the 

 same. 



