On the Composition and Decomposition of Forces, 325 



is called the composition op forces, and that by which 

 we find the composants when we know the resuhant, i$ 

 called the decomposition of forces*. 



II. 



7. Two forces equal and directly opposite, applied at the 

 same time to the same point, destroy each other and are 

 in equUihrio. Reciprocally, when two forces are in equili- 

 brio, they are equal and directly opposite. 



8. If, therefore, several forces differently directed are 

 applied to the same point, to produce an equilibrium, that 

 is to destroy the effect of their resultant, we must apply to 

 this point a single force equal to their resultant, and di- 

 rectly opposite to it; or else we must apply several forces 

 the resultant of which may be equal and directly opposite 

 to the resultant of the first. 



9. Reciprocally, when several forces, differently directed/ 

 ^nd applied to the same point, are in equilibrio, their re- 

 sultant is nothing, or, which comes to the same, any one 

 of these forces is equal and directly opposite to the result- 

 ant of all the others, or lastly the resultant of any number, 

 of forces is equal and directly opposite to the resultant of 

 all the others. 



;.:.,,;,; m. 



10. If several forces applied to the same point have all 

 the same direction, and all act the same way, the effect 

 produced upon this point is the same as would be produced 

 by a single force equal to their sum, acting the same way^ 

 and in the same direction 5 consequently this single force i^ 

 their resultant. 



11. Hence, to produce an equilibrium with all these 

 forces, we must apply to the same point, and in an oppo- 

 site direction, a force equal to their sum; for this force 

 will be equal and directly opposite to their resultant. 



12. It follows then, First, that when two unequal 

 forces are applied to the same point, but in opposite di- 

 rections, the resultant will be in the direction of the greater, 

 and equal to their difference. For the greater of these twd 

 forces may be considered as coniposed of two forces, di- 

 rected the same way, one of which is equal to the less and 

 the other equal to their difference ; now of these two latter 

 forces, the first is destroyed by the less (7) ; therefore, there 

 remains to move the point, only the difference, which acts 

 in the same direction as the greater. 



13. Secondly, That if ever so many forces be applied 

 to the same point, some of which act one way and the 



* English author* call thi» resoluliijn of forces, 



X 3 0th CTJ} 



