HISTORICAL NOTE. 101 



The definitions preceding the laws introduce the notions of mass, and of 

 impressed moving force as an action on a body by which its state of motion 

 changed, and as proportional to what we now call momentum generated in a 

 given interval. The scholia attached to the laws contain a demonstration of the 

 theorem of the parallelogram of forces, and an account of the determination 

 of masses by direct experiment with the ballistic balance. The latter is 

 given as a verification of the Third Law. 



We have already alluded to the application which Newton made of his 

 theory to the problems of celestial mechanics. It was in this connexion that 

 he introduced the Law of Gravitation. The application to ordinary terrestrial 

 mechanics was not considered by him in detail, and thus it happened 

 that when d Alembert propounded his principle (Article 107) it was accepted 

 as a new principle. It is virtually included in the Third Law. 



It has been the task of modern criticism to disentangle in Newton s 

 theory the definitions, and the postulates. That the Laws of Motion are of 

 the nature of postulates is clearly recognised in Newton s word Axiomata, 

 but it is now held that they also partake of the nature of definitions. 

 According to the account we have given, there is an essential physical 

 discovery presented in the Newtonian theory : the discovery that bodies 

 possess the properties we associate with the word &quot; mass &quot; ; these properties 

 are concisely expressed in Postulates I IV of Article 87 ; the rest of the theory 

 is of the nature of definition. In particular the theorem of the parallelogram 

 of forces is a consequence of the definition of force as a vector. 



