324 On the Composithn and Decomposition of Threes • 



this body in any .Hrcction CF ; we inay be permitted tp 

 consider this force as if it were applied to any other point 

 D^ in the body , \\\\\(z\\ is in the direction of this force. 



For as the several points of the lx)dy which are in the 

 right hne CF can neither approach to\^'ards nor recede 

 from one another, it is evident that no point wha:tever in 

 this line can move without moving all thf, others, in the 

 same manner as if the force were immediately applied to 

 them. 



We may also be permirtcd to consider the force P as if 

 it were applied to any other point G out of the hody, in the 

 direction of the force, provided that this point be invariably 

 attached to the body. 



2. It follows then, that if in the direction of the force 

 P there be found cither in the body a fixed point D, or out 

 of it an immoveable obstacle G, provided that in this lattcf 

 case the obstacle be invariably attached to the body, the 

 force will be destroyed, and the body remain at rest; for 

 we may regard the force as immediately applied to the fixed 

 point, and its effect will be destroyed by the resistance of 

 that point. 



3. Reciprocallv, if the force P applied to the body AB 

 Jae destroyed by the resistance of a single fixed point, this 

 point will be found in the direction of the force ; for this 

 point could not destroy the effect of the force unless it 

 opposed the motion of the point of application C, and it 

 could not prevent this motion unless it were in the right 

 line in which the force tends to move the point of applir 

 cation. 



AXIOMg. 



I. 



4. A point cunnot move several ways at once. 



5. Therefore, when several forces diff'erently directed are, 

 applied at the same time to the same point, this point either 

 remains at rest, or it moves in a single direction, in the 

 same manner as if it were moved by a single ibrce in that 

 direction, capable .of producing the same effect. 



6. Thus, whatever may be the number and direction of 

 forces applied at the same time to the same point, there 

 always exists a single force which can move it, or which 

 tends to move it, in the same manner as all the forces to- 

 gether. This single force is called the resultant, and 

 the several forces which compose the system, and act all 

 together, are called composants. The operation by which 

 >ve seek the resultant of several given composant forces, 



• is 



