106 DISSERTATION SECOND. [fart i. 



they follow, merely on account of its simplicity. Having 

 once assumed this principle, he showed, by mathematical 

 reasoning, that the spaces descended through must be as 

 the squares of the times, and that the space fallen through 

 in one second is just the half of that which the body would 

 have described in the same time with the velocity last ac- 

 quired. 



The knowledge which he already had of the properties 

 of the inclined plane enabled him very readily to per- 

 ceive, that a body descending on such a plane must be 

 uniformly accelerated, though more slowly than when it 

 falls directly, and is accelerated by its whole weight. By 

 means of the inclined plane, therefore, he was able to bring 

 the whole theory of falling bodies to the test of experiment, 

 and to prove the truth of his original assumption, the uni- 

 formity of their acceleration. 



His next step was to determine the path of a heavy bo- 

 dy, when obliquely projected. He showed this path to 

 be a parabola ; and here, for the first time, occurs the use 

 of a principle which is the same with the composition of 

 motion in its full extent. Galileo, however, gave no name 

 to this principle ; he did not enunciate it generally, nor 

 did he give any demonstration of it, though he employed 

 it in his reasonings. The inertia of body was assumed in 

 the same manner ; it was, indeed, involved in the uniform 

 acceleration of falling bodies, for these bodies did not lose 

 id one minute the motion acquired in the preceding, but, 

 retaining it, went on continually receiving more. 



The theory of the inclined plane had led to the know- 

 ledge of this proposition, that, if a circle be placed verti- 

 cally, the chords of different arches terminating in the 

 lowest point of the circle, are all descended through in the 

 same space of time. This seemed to explain why, in a 

 circle, the great and the small vibrations are of equal du- 



