OF THE BOOTS OF CEETAm SYSTEMS OF TWO EQUATIONS. 
725 
3bi 
3cj =S zlz^x^z^w^, 
3ak = S x^x^y^x^y^^ 
3ci =^^y,z,zlzl, 
3aj =S z^x^xlxl, 
?>h'k=^ x,y,ylyl, 
Gal x\x^y^z^X 3 , 
6bl ^^yly^z^^y^, 
Gel 
=8 
z\z^x^y^z^. 
9P 
-Gbi 
=8 
y\yl^l 
9g' 
— Gcj 
= 8 
<^ 2^39 
9h^ 
— Gak 
= 8 
x\xiyl 
9P 
— Gef 
= 8 
fXzl 
9j^ 
-Gag 
=8 
-2 ^2 ^2 
9k^ 
-Gbh 
=8 
x\ylyl 
9fg 
-3ck 
= 8 
xyj.z^zl 
9gh 
— 3ai 
=8 y, 2 , 22 ^ 2 ^ 1 , 
9hf 
-3bj 
=8 
z.x^x^y^yl, 
9jk 
— 3af 
— 8 x-^x^y^y^z.^.^ 
9ki 
-3bg 
= 8 y\y^z^zyx^, 
9ij 
— 3ch 
= 8 
z\ z.yx^^y^. 
9fi 
— 3bc : 
=8 
yly^z^zi, 
9gj 
— 3ca : 
r=8 
Z\ 22^2'^35 
9hk 
— Sab : 
=8 
3 ( fj +gk + hi —P)=S .r,y 122^2:^323, 
3 ( 2 fj — gk —hi -{-\^)=^ x,y,x^y^zl 
3 ( 2 gk— hi — fj +P)=S 3/,2 i_^2^2^, 
3 ( 2 hi — fj — gk+P)=S z.XiZ^x^yl, 
3 ( 6 fl — 3 ki— bg) —^xyjiylzl, 
3 ( 6 gl — 3 ij — ch) =Sy,2i2lx*, 
3 ( 6 hl — 3 jk— af ) =821^1^2^^, 
5 B 
MDCCCLVII. 
