194 SCIENCE IN GRECO-ROMAN ANTIQUITY 



To demonstrate this relation it is sufficient to replace, 

 in the example given, the weight of 4 lbs. by an arrange- 

 ment of two weights of 2 lbs. each, then there will be 

 symmetry round the fulcrum and consequently equi- 

 librium (Fig. 33). 



After having established the law of the lever, 

 Archimedes used it in the investigation of the centre 

 of gravity of various surfaces such as triangles, trapez- 

 iums, and segments of a parabola. He demonstrated, 

 for instance, that the centre of gravity of a triangle is 

 the point of intersection of the medians. In fact, if 



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Fig. 33 



a triangle be placed on the blade of a knife in such a 

 manner that the latter coincides in each position with 

 one of the medians, the triangle is in equilibrium. 

 Consequently, it will also be in equilibrium if it be 

 suspended by the point of intersection of the medians. 

 By a similar method, but making use of new hypo- 

 theses, Archimedes demonstrates in a masterly fashion 

 a series of propositions in hydrostatics, which are still 

 renowned. Amongst other things, he proves that a 

 body plunged in a fluid of equal density to its own is 

 entirely immersed, but remains suspended in the fluid ; 

 and that a solid floating in equilibrium on the surface 

 of a liquid displaces a weight of this liquid equal to 

 its own weight. It can be clearly seen that, in 

 mechanics, Archimedes did not, like Aristotle, deduce 

 his principles from the general laws of motion. He 



