﻿540 On the Ewpressibility of a Determinant. 



or 



(D + 2) 4 



-CD + «)»{f + fe + ^ + 5 + ^ + 32+^/+ 4-} 



<- P7 a ya /3 afi y ajSy i 



/3 2 ' r 2 



a 2 "*" yS 2 + y 2 + /8V "*" 7V "*" a 2 /3 2 



ipy a jot, (3 afi 7 ' a/37 



+2^+2^+2^ 

 + {s« 4 +2^+a 2 /SV+l 



By utilizing the facts that 



«+-=A + 2, ^+i=B + 2, y+-=C + 2, 

 a p y 



this is readily transformed into 



(D + 2) 4 



- (D + 2) 3 (A + 2)(B + 2)(C + 2) 



+ (D + 2) 2 { 2(A + 2) 2 (B + 2) 2 - 22(A + 2) 2 j- \ 



-(D + 2){S(A + 2) 3 (B + 2)(C + 2)~8(A + 2)(B4-2)(C + 2)} 

 + {2(A + 2) 4 - 22( A + 2) 2 (B + 2) 2 



+ (A + 2)(B + 2)2(C + 2) 2 } = 0; i 



and by applying the 2 to the four letters A, B, C, D, it ! 



becomes 



■(A + 2) 4 +2(A-f2) 2 (B + 2) 2 (C + 2) 2 + 8(A + 2)(B + 2)(C + 2)(D+( 

 . -2(A+2) 3 (B + 2)(C + 2)(D + 2)-22(A + 2) 2 (B + 2) 2 =0 



