50 HISTORY OF MECHANICS. 



acquired, it cannot, under any circumstances, ascend 

 to a higher position than that from which it fell. 

 This principle coincides very nearly with Galileo's 

 experimental illustration. In truth, however, Gali- 

 leo's principle, which Huyghens thus slights, may 

 be looked upon as a satisfactory statement of the 

 true law; namely, that, in the same body, the 

 velocity produced is as the pressure which produces 

 it. "We are agreed," he says 16 , "that, in a move- 

 able body, the impetus, energy, momentum, or pro- 

 pension to motion, is as great as is the force or 

 least resistance which suffices to support it." The 

 various terms here used, both for dynamical and 

 statical Force, show that Galileo's ideas were not 

 confused by the ambiguity of any one term, as ap- 

 pears to have happened to some mathematicians. 

 The principle thus announced, is, as we shall see, 

 one of great extent and value ; and we read with 

 interest the circumstances of its discovery, which 

 are thus narated 17 . When Viviani was studying 

 with Galileo, he expressed his dissatisfaction at the 

 want of any clear reason for Galileo's postulate 

 respecting the equality of velocities acquired down 

 inclined planes of the same heights; the conse- 

 quence of which was, that Galileo, as he lay, the 

 same night, sleepless through indisposition, dis- 

 covered the proof which he had long sought in 

 vain, and introduced it in the subsequent editions. 



16 Galileo, Op. iii. 104. 



17 Drink water, Life of Galileo, p. 59. 



