MECHANICS AND PHYSICS 199 



a very special class of phenomena ; and for this reason 

 his method, in the course of time, proved less fruitful 

 than the dynamical conceptions of Aristotle. 



At first sight it may seem surprising that Archimedes, 

 after having invented and perfected so many ballistic 

 machines, did not attempt to study their theory. 

 This abstention may be accounted for by the logical 

 difficulties raised by the idea of motion. The argu- 

 ments of Zeno of Elea on this point had produced 

 in the minds of the ancient philosophers an uneasiness 

 which was never dispelled. 



For example, the space in which a body moves is 

 motionless : how are we to understand the relationship 

 of a moving body to something motionless ? Look at 

 the arrow in flight. It follows an immovable line 

 which is its trajectory, and it must at each instant 

 coincide with a portion of this trajectory since it 

 traverses it. Now it cannot do this without itself 

 coming to rest for an instant, however short, therefore 

 its whole movement is a sum of instants of rest. 



To the Greek geometers it did not appear possible 

 to avoid the objections raised by Zeno, and this 

 perhaps was the reason that Archimedes did not 

 attempt to establish the foundations of rational 

 dynamics. 



4. LATER DEVELOPMENTS 



It would be a mistake to consider the works of 

 Aristotle and Archimedes as isolated examples of their 

 kind. 1 The statics of Archimedes, in particular, by 

 its subtle analysis and marvellously clever solutions, 

 the interest of which is not apparent to the uneducated, 

 bears wituess to a science already far advanced, and in 

 no way resemble the uncertainties of a science newly 

 born. Moreover history confirms this supposition, 

 since it places prior to Archimedes the mechanical 

 1 n Duhem, Origin$$, II, p. 280 st seq. 

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