92 



STATICS OF KIGID BODIES 



into its final position. For let us take any two other particles jR, S 

 in the body (not in the same straight line with Q), and let R' } S f be 

 their final positions. Since the body is supposed to be perfectly 



FIG. 46 



rigid, it follows that all distances between particles of the body 

 remain unaltered. Hence the distances QR, RS, SQ are respectively 

 equal to QR' t fi'S', S'Q. Thus the triangles QRS, QR'S', being 

 equal in all respects, can be superposed, and the motion of super- 

 position of these triangles is the motion required and is a motion 

 of pure rotation about Q, since Q does not move. 



Since the position of a rigid body is fixed when any three points 

 in it are fixed, it follows that the rigid body can only have one 

 position in which the three points Q, It, S have given positions. But 

 after the motion we have described, the three points Q, R, S are 

 placed in their final positions. Hence the whole body must be in 

 its final position, and this proves the theorem. 



67. Axis of rotation. 

 In a motion of rotation, 

 let P be the point which 

 remains fixed. Take any 

 plane A through P, and 

 let B be the position of 

 the plane A after the 

 rotation has occurred. 

 These two planes both pass through P, and must therefore 



FIG. 47 



