



68 OF UNDISTURBED MOTION. 



other plane, is called the result of the two 

 motions. 



226. Theorem. The result of two mo- 

 tions, with respect to a quiescent space, is the 

 diagonal of the parallelogram of which the 

 two sides would be described by the separate 

 motions ; and any motion may be considered 

 as the result of any other motions thus com- 

 posing it. 



XB c -"^^^ -^» -^j ^^^ ^ ^^ three quiescent 



points, and let Z, Y, and X be three 

 -/ points in another plane which moves in 



the direction AZ, or BY ; then the point 

 A has a rectilinear motion ZA with respect to the plane 

 ZYX. Now, while AZ is described by Z, let A have a 

 motion in its own plane equal to AB ; then it will have 

 two motions with respect to ZYX, by the joint effect of 

 which it will arrive at X in that plane ; and if the motions 

 are both equable, it may be shown, by the properties of 

 similar triangles, that it describes the diagonal ZX. But 

 it is of no consequence to the relative motion of A and 

 ZXY which, or whether either, be imagined to be abso- 

 lutely at rest : therefore, in general, the result of two mo- 

 tions, in a quiescent space, is the diagonal of the parallelo- 

 gram of which the sides would be described by the sepa- 

 rate motions : and the motion, thus produced, is precisely 

 the same as if it were derived from a simpler cause. 



Scholium 1. The existence of two or more motions 

 at the same time, in the same body, is not at first compre- 

 hended without some difficulty. But it is, in fact, only a 



