386 HISTORY OF MECHANICS. 



looked so obvious a fact. F. Piccolomini, in his Liber Sc'tentice cte 

 Nature^ published at Padua, in 1597, says, "On the subject of the 

 motion of heavy and light bodies, Aristotle has put forth various 

 opinions, which are contrary to sense and experience, and has delivered 

 rules concerning the proportion of quickness and slowness, which are 

 palpably false. For a stone twice as great does not move twice as 

 fast." And Stevinus, in the Appendix to his Statics, describes his 

 having made the experiment, and speaks with great correctness of the 

 apparent deviations from the rule, arising from the resistance of the 

 air. Indeed, the result followed by very obvious reasoning ; for ten 

 bricks, in contact with each other, side by side, would obviously fall in 

 the same time as one ; and these might be conceived to form a body 

 ten times as large as one of them. Accordingly, Benedetti, in 1585, 

 reasons in this manner with regard to bodies of different sie, though 

 he retains Aristotle's error as to the different velocity of bodies of 

 different density. 



The next step in this subject is more clearly due to Galileo ; he dis- 

 covered the true proportion which the Accelerating Force of a body 

 falling down an inclined plane bears to the Accelerating Force of the 

 same body falling freely. This was at first a happy conjecture ; it was 

 then confirmed by experiments, and, finally, after some hesitation, it 

 was referred to its true principle, the Third Law of Motion, with pro- 

 per elementary simplicity. The Principle here spoken of is this : 

 that for the same body, the Dynamical effect of force is as the Statical 

 effect ; that is, the Velocity which any force generates in a given time 

 when it puts the body in motion, is proportional to the Pressure which 

 the same force produces in a body at rest. The Principle, so stated, 

 appears very simple and obvious; yet this was not the form" in which 

 it suggested itself either to Galileo or to other persons who sought to 

 prove it. Galileo, in his Dialogues on Motion, assumes, as his funda- 

 mental proposition 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, towards the end of his life, proved his assump- 



13 Opere, in. 96. 



