PRELUDE TO THE EPOCH OF GALILEO. I -~> 



diligently prosecuted after his time. Pappus and 

 others, among the ancients, had solved some new 

 problems on this subject, and Commandinus, in 

 1565, published De Centro Gravitatis Solidorum. 

 Such treatises contained, for the most part, only 

 mathematical consequences of the doctrines of 

 Archimedes ; but the mathematicians also retained 

 a steady conviction of the mechanical property of 

 the Center of Gravity, namely, that all the weight 

 of the body might be collected there, without any 

 change in the mechanical results; a conviction 

 which is closely connected with our fundamental 

 conceptions of mechanical action. Such a princi- 

 ple, also, will enable us to determine the result of 

 many simple mechanical arrangements; for instance, 

 if a mathematician of those days had been asked 

 whether a solid ball could be made of such a 

 form, that, when placed on a horizontal plane, it 

 should go on rolling forwards without limit, merely 

 by the effect of its own weight, he would probably 

 have answered, that it could not; for that the 

 center of gravity of the ball would seek the lowest 

 position it could find, and that, when it had found 

 this, the ball could have no tendency to roll any 

 further. And, in making this assertion, the sup- 

 posed reasoner would not be anticipating any wider 

 proofs of the impossibility of a perpetual motion, 

 drawn from principles subsequently discovered, but 

 would be referring the question to certain funda- 

 mental convictions, which, whether put into Axioms 



