64 OF UNDISTURBED MOTION. 



from a metaphysical principle of the minimum of action^ 

 which is of a very complicated and almost fanciful nature ; 

 and the intricacy of his theory tends only to envelope the 

 subject in unnecessary obscurity; while the fundamental 

 laws of motion appear to be easily demonstrable from the 

 simplest mathematical truths, granting only the homoge- 

 neity or similarity of matter with respect to motion, and 

 allowing the general axiom, that like causes produce like 

 effects. If, however, any person thinks differently, he is 

 at liberty to call these laws experimental axioms, collected 

 from a comparison of various phenomena : for we cannot 

 easil} reduce them to direct experiments, since we can 

 never remove from our apparatus the action of all disturb- 

 ing causes ; for either gravitation, or the contact of sur- 

 rounding bodies, will interfere with all the motions which 

 we can examine. 



222. Definition. The times, in which 

 a point, moving without disturbance, describes 

 equal parts of the Hne-of its direction, are 

 called equal times. 



223. Theorem. The equality of times 

 being estimated by any one undisturbed mo- 

 tion, all other points, moving without disturb- 

 ance, will describe equal portions of their 

 lines of direction in equal times. 



ACE BDE G Let A and B be moving 



' ^ ' ' ' ' ' in the same line, and while 



A describes AC, let B describe BD ; then while A de- 

 scribes CE=:AC, B will describe DF=BD. For sup- 

 pose AC :i:2BD, and let AGz=2AB, then AB and BG 



