DISCOVERY OF THE LAWS OF MOTION. 51 



It is easy to see, by looking at the proof, that the 

 discoverer had had to struggle, not for intermediate 

 steps of reasoning between remote notions, as in 

 a problem of geometry, but for a clear possession of 

 ideas which were near each other, and which he had 

 not yet been able to bring into contact, because he 

 had not yet a sufficiently firm grasp of them. Such 

 terms as Momentum and Force had been sources 

 of confusion from the time of Aristotle; and it 

 required considerable steadiness of thought to com- 

 pare the forces of bodies at rest and in motion 

 under the obscurity and vacillation thus produced. 



The term Momentum had been introduced to 

 express the force of bodies in motion, before it 

 was known what that effect was. Galileo, in his 

 Discorso intorno alle Cose chestanno in su VAcqua, 

 says, that " Momentum is the force, efficacy, or 

 virtue, with which the motion moves and the body 

 moved resists, depending not upon weight only, 

 but upon the velocity, inclination, and any other 

 cause of such virtue." When he arrived at more 

 precision in his views, he determined, as we have 

 seen, that, in the same body, the Momentum is 

 proportional to the Velocity; and, hence it was 

 easily seen that in different bodies it was propor- 

 tional to the Velocity and Mass jointly. The prin- 

 ciple thus enunciated is capable of very extensive 

 application, and, among other consequences, leads 

 to a determination of the results of the mutual 

 Percussion of Bodies. But though Galileo, like 



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