OF THE POSITIONS OF EQUILIBRIUM. 355 



or by taking the analytical equivalents, it becomes 



- , 



and from this, by working out the proportion, we get 

 4xz 



hence, by subtraction, we have ,.,'< j 

 ws ns w;w; 



but because Emus is a parallelogram, it follows, that ws E?n; 

 therefore, it is 



Again, the triangles wgn and WGS are similar to one another; but 

 we have shown above, that KEW is similar to wng; therefore, KEW 

 is similar to WGS, and we have 



EK : EWZ : : ws : SG ; 

 taking therefore the analytical values, we obtain 



2: ~ 



P P 



consequently, by reduction, we have 



2p 5 



But by the nature of the figure, SG is manifestly equal to EG ES ; 



z 2 

 now ESZZ mn^nx, and EG ^ZDG -J- DE; that is, EG fa-j 



consequently, we have 



s G f- a -| # ; 



let these two values of SG be compared with each other, and we get 



~~Tp "IfIf" 1 '"*' (279). 



and finally, by reduction, we obtain 



~~ 10 

 Now, the value of a;, as we have determined it from equation (278), is 



2A2 



