sect, in.] DISSERTATION SECOND. 105 



plete, the preceding proposition being assumed in them 

 without proof. It is probable that he satisfied himself of 

 the truth of it, on the principle, that the distances of 

 forces from the centre of motion must always be measured 

 by lines making the scune angles with their directions, and 

 that of such lines the simplest are the perpendiculars. 

 His demonstration is regarded by La Grange as quite sa- 

 tisfactory. ' 



Galileo extended tiie theory of motion still farther. He 

 had begun, while pursuing his studies at the university of 

 Pisa, to make experiments on the descent of falling bodies, 

 and discovered the fact, that heavy and light bodies fall to 

 the ground from the same height in the same time, or in 

 times so nearly the same, that the difference can only be 

 ascribed to the resistance of the air. From observing the 

 vibrations of the lamps in the cathedral, he also arrived at 

 this very important conclusion in mechanicks, that the 

 great and the small vibrations of the same pendulum are 

 performed in the same time, and that this time depends only 

 on the length of the pendulum. The date of these observa- 

 tions goes back as far as the year 1583. 



These experiments drew upon him the displeasure of 

 his masters, who considered it as unbecoming of their pupil 

 to seek for truth in the Book of Nature, rather than in the 

 writings of Aristotle, when elucidated by their commenta- 

 ries, and, from that moment began the persecutions with 

 which the prejudice, the jealousy, and bigotry of his con- 

 temporaries continued to harass or afflict this great man 

 throughout his whole life. 



That the acceleration of falling bodies is uniform, or, 

 that they receive equal increments of velocity in equal 

 times, he appears first to have assumed as the law which 



1 Mecanique Analytique, Tom. I. Sect. 1. § 6. 



