192 SCIENCE IN GRECO-ROMAN ANTIQUITY 



foreshadows the principle of virtual velocities. " For," 

 said he, ' ' the properties of the balance are reduced to 

 those of the circle ; the properties of the lever to those 

 of the balance ; and the greater part of the other 

 peculiarities of mechanical movements are reduced to 

 the properties of the lever" (Quastiones mechanics, 

 848 a, 11). 



Aristotle, however, was not able to deduce from the 

 principle which he discovered all the rigorous conse- 

 quences which arise from it. He applies it to problems 

 which are too complex for the means by which he 

 attempts to solve them. Already as regards the lever 

 he had been confronted with the following difficulty : 

 " the line described in a movement of the lever through 

 the point of application of the force of resistance is 

 a circumference of a circle ; it does not coincide with 

 the vertical line along which this force or resistance 

 acts." x Aristotle perceived the problem, but he did 

 not succeed in solving it. He contented himself with 

 supposing that a balance is more accurate the longer 

 its arms are, for then the circular arc described ap- 

 proximates more nearly to a vertical line. 2 



3. ARCHIMEDES AND STATICS 



The method adopted by Archimedes is very different 

 from that of Aristotle. Archimedes limited the domain 

 of theoretical mechanics to the study of problems of 

 equilibrium, and in this manner he succeeded in estab- 

 lishing the foundations of statics and hydrostatics. 

 He did not dream of seeking his fundamental hypOr 

 theses in kinematics, for the laws which govern the 

 displacement of bodies in space do not seem to be 

 reducible to the intelligible and clear conceptions of 

 reason. On the other hand, the phenomena of equili- 

 brium can be interpreted by means of very simple rules, 



1 11 Duhem, Origines, I, p. 9. 



*- 1.6 Jouguet,. LeQtures de mfranique,, I, p. 35,. 



