RoBKKTS — The Symbolical Expression of Eliminants. 75 



We can now make E{Ai, B^) a starting-point, and from it find all elimi- 

 nants included in the formula E[A,„, B^) by an operative process as follows : — 



E{A„ B,) = - By 



s. 



ni 



E{A„ B,), 



(29) 



Ar, Ai 



E{A„B,) = B,'c ' c ' E{A,B,), 



-^6 » ^5 _ At 



--^ns -jr0.i -j-^' 



E(Ao,B,) = -B^e ' c " c ' E{A„B,); 



and so on by the method above indicated. 



In order to find E{Ai, Bt), we must first find the value of E(B,, A.t), just 

 in the same way as when seeking the value of E^A,, Bi) we first found the 

 value of E(B„ A,). 



We have then, by a similar process of reasoning, 



^4 



(30) 



E(Bt,A,) =-A,c 



_Ai 



A, 



E{B„ A,), 



flo 



E{A„B,) = B,e- E{B„A,). 



E(A,, Bi) is then in its turn made a starting-point for the evaluation of all 

 eliminants included in the formula E(A„„ Bi). 



The generality of the method is now obvious, and the application of it to 

 any two given binary quantics will present no difficulty. 



