STATEMENT OF LEIBNIZ'S PHILOSOPHY 89 



Now it follows from this, that, while the quantity of 

 motion in the world, or in any isolated system of bodies, 

 is constant, its direction is variable. For, as all space is 

 body and is therefore a plenum, moving bodies must con- 

 tinually impinge upon others ; and if a moving body be 

 supposed to impinge upon a body at rest, of such mass 

 that the moving body is unable to overcome the resistance 

 of the other and to make it move, then the direction of 

 the moving body is changed ; it rebounds in the direction 

 from Which it came or is deflected in some other way. 

 But, as the moving body has been unable to impart any of 

 its motion to the body at rest, the quantity of its motion 

 remains unchanged, while its direction changes it being, 

 of course, understood that the action of all other bodies, 

 except the two in question, is left out of account 1 . 



Leibniz's Theory of Motion. Conservation of Force. 



Now, according to Leibniz, motion is simply change of 

 position. It is not a positive quality belonging, for the 

 time being, to the moving body ; but motion and rest are 

 entirely relative to one another. If the relative position 

 of any two bodies changes, we may regard either as 

 moving and the other as at rest 2 . And, in general, rest 

 is merely an infinitely small degree of motion ; nothing 



first created them, and now preserves all that matter, manifestly 

 in the same way and on the same principle o~n which He first 

 created it, He also always preserves the same quantity of motion 

 in the matter itself.' 



1 Cf. Principia, ii. 41 : ' Each thing, whatever it is, always con- 

 tinues to be as it is in itself simply, and not as it* is in relation to 

 other things, until it is compelled to change its state by contact 

 with some other thing. From this it necessarily follows that 

 a moving body, which meets on its course another body so firm 

 and impenetrable that it cannot move it in any way, entirely loses 

 the determination it had of moving in this particular direction, 

 and the cause of this is evident, namely, the resistance of the body 

 which prevents it from going further ; but it does not necessarily 

 on this account lose any of its motion, since it is not deprived of its 

 motion by the resisting body or by any other cause, and since 

 motion is not contrary to motion/ 



2 Cf. Animadversiones ad Cartes ii Principia (1692?), Part ii. 25 

 (G. iv. 369 ; Duncan's tr. p. 60). 



