18 THE FOUNDATIONS OF SCIENCE 



appear more " self-evident " to minds unused to 

 experimental investigation. We see clearly from 

 this first illustration that a physical " explanation " 

 is merely a restatement of our result in terms of 

 others more familiar to the particular minds which 

 are dealing with the problem at the time. 



It is to Archimedes, also, that we owe the first 

 clear ideas about the phenomena of floating bodies. 

 Before his work on weights in relation to volumes, 

 the conceptions which we call density and specific 

 gravity were unknown. He showed that when a 

 body floats in a liquid, partially or wholly immersed, 

 its own total weight must be equal to the weight 

 of that part of the liquid which it displaces. 



Very little advance in mechanics was made from 

 the time of Archimedes till, nearly two thousand 

 years later, first that universal genius Leonardo da 

 Vinci (1452-1519) and then Simon Stevin of Bruges 

 (1548-1620) again took up the problem of the lever, 

 and dealt also with the inclined plane and the general 

 conditions of equilibrium of three forces acting in a 

 plane. Here again the form of the proof is that of 

 Euclidean geometry, the chief axiom being the in- 

 stinctive recognition that an endless chain, lying 

 along an inclined plane, hanging down from its top 

 and passing beneath it and so round, will not con- 

 tinue in perpetual motion. This is the real advance, 

 the increased insight into what is or is not experi- 

 mentally possible. 



