DISCOVERY OF THE LAWS OF MOTION. 337 



tion, 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 con- 

 ceive 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 Galileo's assump- 

 tion was supported in the later editions of his works. His own proof 

 rests on this principle ; — that if a body fall down one inclined plane, 

 and proceed up another with the velocity thus 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 ex- 

 perimental illustration. In truth, however, Galileo'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 movable body, the impetus, energy, momentum, or propen- 

 sion 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 am- 

 biguity of any one term, as appears to have happened to some mathe- 

 maticians. 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 narrated. 17 When Viviani was study- 

 ing 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 consequence 

 of which was, that Galileo, as he lay, the same night, sleepless through 

 indisposition, discovered the proof which he had long sought in vain, 

 and introduced it in the subsequent editions. It is easy to see, by look- 

 ing at the proof, that the discoverer had had to struggle, not for inter- 

 mediate steps of reasoning between remote notions, as in a problem of 

 geometry, but for a clear possession of ideas which were near each 

 other, and which he had not yet been able to bring into contact, be- 

 cause he had not yet a sufficiently firm grasp of them. Such terms as 

 Momentum and Force had been sources of confusion from the time of 

 Aristotle ; and it required considerable steadiness of thought to com- 

 pare the forces of bodies at rest and in motion under the obscurity and 

 vacillation thus produced. 



18 Galileo, Op. iii. 104. Prinkwater, Life of Galileo, p. 59. 



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