186 SCIENCE IN GRECO-ROMAN ANTIQUITY 



but it possesses a certain power (Phys., 208 b, 10). 

 This fact explains why the fall of heavy bodies is 

 accelerated ; the force of the weight increases in 

 proportion as the body approaches its position of 

 equilibrium. 1 



The movements enumerated above, rectilinear down- 

 wards for heavy bodies, rectilinear upwards for light 

 bodies, circular for celestial bodies, are, as natural 

 movements, in opposition to violent movements, which 

 result from an external constraint and which are not 

 directed towards the position of equilibrium of a body ; 

 such, for instance, as the throwing of a projectile and 

 the towing of a vessel. 



Further, whether the movement be natural or 

 violent, it can only be either rectilinear or circular 

 or composed of both, " for all that which is in motion 

 is moved either circularly or rectilinear ly or both " 

 (Phys., 261 b, 25). 



In postulating this principle Aristotle foresees one 

 of the most fruitful theorems of modern kinematics 

 which may be formulated thus : in its most general 

 form, an infinitely small movement of a solid body 

 is composed of an infinitely small rotation around a 

 certain axis and of an infinitely small translation parallel 

 to this axis. 2 However, by applying this principle 

 without any consideration of the infinitesimal, the 

 Aristotelian dynamics was bound to lead to manifest 

 errors. Consider, for example, a stone which, thrown 

 into the air by means of a sling, falls back to the 

 ground. To the disciples of Aristotle, the trajectory 

 described by the stone is not a parabola, but it is 

 composed of two straight lines which are joined by 

 a circular arc. 



Having once established the distinctions between 



1 1 6 Jouguet, Lectures de mecanique, I, p. 3. 



2 13 Duhem, Systeme, I, p. 171. — 24 Sageret, Systhne, 

 p. 214. 



