STATEMENT OF LEIBNIZ'S PHILOSOPHY 87 



divisible. Its division is due to motion. Its forms arise 

 solely from the combinations and separations of its parts, 

 which also are due to motion. ' All the variety of matter, 

 or the diversity of its forms, depends on motion 1 .' 'I 

 frankly avow that I acknowledge in corporeal things no 

 other matter than that which can be divided, shaped 

 [figurees], and moved in all kinds of ways, that is to say, 

 that which mathematicians call quantity, and which they 

 take as the object of their demonstrations ; and in this 

 matter I consider only its divisions, shapes [figures], and 

 motions ; and, in short, regarding this I will accept 

 nothing as true which is not deduced from it with as 

 much certainty as belongs to a mathematical demonstra- 

 tion. And inasmuch as by this means all the phenomena 

 of nature may be explained ... it seems to me that in 

 Physics no other principles ought to be accepted, or even 

 desired, than those which are here expounded V 



Conservation of Motion (or Momentum), its Direction being 

 left out of account. 



Again, according to Descartes, the quantity of motion 

 in the world (or in any material system complete in 

 itself and apart fr^m all external influences) is constant. 

 The motion (or momentum), whose quantity is thus con- 

 stant, is in each particular case directly proportional to 

 the mass and the velocity of the moving body, and it may 



a portion of matter, I mean the whole of what is transferred to- 

 gether, although this may be composed of several parts which 

 themselves have other motions. And I say that motion is the 

 transfr rence and not the force or activity which transfers, in order 

 to show that motion is always in the moving object and not in that 

 which moves it ; for it seems to me that these two things are not 

 usually distinguished with sufficient care. Further, I mean that 

 motion is a property of the moving thing and not a substance ; 

 just as form is a property of the thing which has a form, and rest 

 is a property of that which is at rest.' 



1 Principia, Part ii. 23 (Veitch's tr.). 



2 Ibid. Part ii. 64 (tr. from Abbe Picot's French). Descartes's 

 object is to show that all the motion in the world is one, and thus 

 to get rid of the later Scholastic theories which referred each parti- 

 cular motion to some unexplained principle in the moving body. 



