treatise begins with two propositions to the effect that the surface of 

 every still fluid is spherical, the centre of the sphere being the centre 

 of the earth. This book contains in all nine propositions. In the 

 second book, he deals mainly with the question of specific gravity, 

 a question to which his interest was aroused, so tradition says, by 

 the request of the perplexed King Hiero, who wished to know 

 whether or not his crown was alloyed with silver or other metal. 



In his Equiponderance of Planes, Archimedes commences by 

 making certain assumptions, which he, no doubt, regarded as self- 

 evident, and which would be called to-day axioms. By means of 

 these, he proves the law of the lever, which according to Mach 1 he 

 stated as follows: "Commensurable magnitudes are in equilibrium 

 when they are inversely proportional to their distances (from the 

 point of support)." Now one of the axioms which he assumed, and 

 did not therefore attempt to prove, was "magnitudes of equal 

 weight acting at equal distances (from their point of support) are 

 in equilibrium". It is natural for one to ask why both the axiom 

 and the proposition (the law of the lever stated above) might not 

 have been proved directly by experiment, and then both placed on 

 the same level. But the important point is that Archimedes tried 

 to explain the lever in terms of phenomena which he, at any rate, 

 regarded as simpler and better known. That was a great insight, 

 and, as shall be seen, is the type of all scientific explanations. Very 

 little advance upon the results of Archimedes in mechanics was 

 made till centuries later, when that great polymath Leonardo Da 

 Vinci, 1452-1519, shaking off the traditions of Aristotle, continued 

 the investigations begun in this earlier period, investigations which 

 were shortly followed by those of Stevin and the illustrious achieve- 

 ments of Galilei and Newton who prepared the way for the 

 modern development of this science. 



Before concluding this chapter, it will be well to ascertain, if 

 possible, from the material presented what science is. It will be 

 remembered, that, just as it was considered inadvisable to com- 

 mence the discussion of philosophy with a preconceived definition 

 of philosophy, so in the outline of the development of science, it 

 was deemed inadvisable to begin with any arbitrary definition. 

 But now, after history has presented the accounts of the different 



1 E. Mach, Science of Mechanics P. 9. 



34 



