OF UNDISTURBED MOTION. 67 



its inertia, or sometimes, very improperly, its vis inertiae. 

 But the properties of matter, as such, belong to physical 

 rather than to mathematical science : and we are, at pre- 

 sent, considering; the motions of a supposed inert point 

 only. 



224. Theorem. If any number of points 

 move in parallel lines, describing equal spaces 

 in equal times, they are quiescent with respect 

 to each other ; and if all the points of a plane 

 move in this manner on another plane, either 

 plane will be in rectilinear motion with re- 

 spect to the other. 



Let A, B, and C describe in a given A D^ 



time the equal parallel lines AD, BE, /\ 

 CF, then AB=D.E, EF=BC, and ^M 



DF=:AC (109), and the points are c p 



mutually quiescent (218, 219). It is also obvious, that if 

 two points have equal and parallel motions, the vt^hole of 

 the plane will also have a similar motion. 



225. Definition. If a plane be in rec- 

 tilinear motion with respect to another plane, 

 in contact with it, and if, besides this general 

 motion of the plane, any point be supposed 

 to have a particular motion in it, this point 

 will have two motions with respect to the 

 other plane, one in common with its plane, 

 and the other peculiar to itself; and the joint 

 effect of these motions, with respect to the 



F 2 



