22] ON ALGEBRAICAL COUPLES. 
129 
The couple may be said to have the two linear moduli, 
a (7 + ^) ( x + ^y), - (7 + ) (« + py); 
/v jjj 
as well as the quadratic one, 
— (7 + AS) (7 + fiB) (as + \y) (x + fiy), 
the product of these, which is the modulus, and the only modulus in the 
systems. 
B. 
i~ — — Bi + -— (7 + 8 A -f- ¡Jb)j, 
A,/jL 
a =ji=7 i+&j, 
f = (A + y 7 + A/aS) i — yj, 
( 1 
X + A T = - (7 + AS) (x + /xy) (xj + y,y-), 
A 6 
Z + /aF=^( 7 + fiB) (x + A y) (x l + A y,). 
C. 
D. 
{!= rX Xfi + yX+ ^ )i ~^ j ' 
ÿ = (y + % + X 7 + M+^-S) • + 
>' = 7 1 ‘ + Sj, 
A + /a 
A/a 
/- = (A + /a 7 + A/aS) i — yj, 
i 1 
F+ A } = — (7 + AS) (x + Ay) (Xj + /aî/x), 
1 A 
i Z + /A F = - (7 + /aS) (a? + /¿y) (X 1 + Ayj. 
V /A 
t 2 = — St + — (7 + S A + /a) j, 
j* = 7 1 ’ + fy’, 
= — A/a Sa -f- (7 f A + /aS)^', 
( 1 
Z + AF= - (7 + AS) (x + /Ay) («X + Ayx), 
A 6 
Z + /aF= - (7 + fiB) (x + A y) («X + fiyd). 
\ A. 
remaining 
C. 
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