MATHEMATICAL ELEMENTS 



OF 



NATURAL PHILOSOPHY. 



PART IL 



MECHANICS. 



OF THE MOTIONS OF SOLID BODIES. 



SECTION I. OF MOTION. 



217. Axiom. Like causes produce like 

 effects, or, in similar circumstances, similar 

 consequences ensue. 



218. Definition. Motion Is the change 

 of rectilinear distance between two points. 



319. Definition. A space or surface, 

 of which all the points remain spontaneously 

 at equal distances from each other, is said to 

 be quiescent, or at rest within itself. 



Scholium, The term " spontaneously" is introduced, 

 in order to exclude from the definition of a quiescent space 

 any surface, of which the points are only retained at rest 

 by means of a centripetal force, while they revolve round a 

 common centre; for with respect to such a revolving space 

 or surface, the motions of any body will deviate from the 

 laws which govern them in other cases. 



220. Definition. When a point is in 

 motion with respect to a quiescent space, 

 the right line joining any two of its proxi- 

 mate places is called its direction ; such a 

 point is often simply denominated a moving 

 point. 



221. Theorem. A moving point never 

 quits the line of its direction without a new 

 disturbing cause. 



A right line being the same with respect 

 tO all sides, no reason can be imagined why 

 the point should incline to one side more 

 than another. Let AB be the direction of -A. 

 the motion of A in the plane ABC, ahd let 

 CB and DB be equal, and perpendicular to 

 AB, then the triangles ABC and ABD are equal (8C), and 

 A is similarly related to C and D. Then if A depart from 

 AB, and be found in any point out of it, as E, ED will be 

 greater than EC (l03), and A will be no longer similarly 

 related to C and D, contrarily to the general law of induc- 

 tion (217). 



222. Definition. The times in which 

 a point, moving without disturbance, de- 

 scribes equal parts of the line of its direction, 

 are called equal times. 



223. Theorem. The equality of time* 

 being estimated by any one motion, all other 

 points, moving without disturbance, will de- 

 scribe equal portions of their lines of direc- 

 tions in equal times. 



