DISCOVERY OF THE LAWS OF MOTION. 49 



the same force produces in a body at rest. The 

 Principle, so stated, appears very simple and ob- 

 vious ; yet this was not the form in which it sug- 

 gested itself either to Galileo or to other persons 

 who sought to prove it. Galileo, in his Dialogues 

 on Motion, assumes, as his fundamental proposi- 

 tion on this subject, one much less evident than 

 that we have quoted, but one in which that is 

 involved. His Postulate is 15 , that when the same 

 body falls down different planes of the same height, 

 the velocities acquired are equal. He confirms 

 and illustrates this by a very ingenious experiment 

 on a pendulum, showing that the weight swings to 

 the same height whatever path it be compelled 

 to follow. Torricelli, in his treatise published 1644, 

 says that he had heard that Galileo had, toward 

 the end of his life, proved his assumption, but 

 that, not having seen the proof, he will give his 

 own. In this he refers us to the right principle, 

 but appears not distinctly to conceive the proof, 

 since he estimates momentum indiscriminately by 

 the statical Pressure of a body, and by its Velocity 

 when in motion; as if these two quantities were 

 self-evidently equal. Huyghens, in 1673, expresses 

 himself dissatisfied with the proof by which Gali- 

 leo's assumption was supported in the later editions 

 of his works. His own proof rests on this prin- 

 ciple ; that if a body fall down one inclined plane, 

 and proceed up another with the velocity thus 



15 Opere, iii. 96. 

 VOL. II. E 



