DYNAMICS. 31 



forces, to the directions of which they are perpendi- 

 cular. 



69. If any number of forces act on a body, pro- 

 portional to the sides of a rectilineal figure, and also 

 parallel to them, in such a manner that the angle 

 which the direction of each force makes with that 

 of the contiguous force, be the supplement of the 

 angle which the corresponding sides of the figure 

 make with one another, these forces will be in equi-, 

 librium. 



This proposition is true, whether the sides of the recti- 

 lineal figure be all in one plane or not. If they 

 inclose a space, that space may be extended either 

 in two or in three dimensions. 



70. If there be an equilibrium among any num- 

 ber of forces, which are in different planes, but ap- 

 plied to the same point ; if, through that point, 

 three straight lines or axes, be drawn at right angles 

 to one another, (one of them in a plane perpendi- 

 cular to that of the other two^, and if every force 

 be resolved into parts in the directions of the three 

 axes, then shall the sums of the opposite forces, in 

 the direction of each axis, be equal to one ano- 

 ther. 



This theorem furnishes three independent equations. 

 a. If F, F', F", F'", &c. be the forces; a, a', a", a'", 

 &c. the angles which they make with one of the 



three 



