216 Mr. J. J. Sylvester on Poncelet's approximate 



1 T 



vf v/J T 



1 i VI I 



F=^J + iVl-i-i = 3v/];-l = -060660 

 G= ^-l^^-^T^^^ 



H=iv/i = *353553 

 Q=4v4= -353553 

 N*=F 2 +G 2 + H 2 =iJL+S + i-7v'i 



= ^-iv / 24 : 5 

 = 2-625-2-474874 

 = •150126 

 N = -387461, N + Q=-741014, N-Q=-033908. 



33908 



N + Q"" 37051" 



The last of these quantities is less, the first two greater than 

 the corresponding coefficients in M. Poncelet's form. 



Ex. 4 and 5. The inequality system, \/x 2 + y 2 > z > y > x, is 

 represented by the triangle K N Q, and the corresponding deter- 

 mining matrix will be 



V\ V\ I 



1 * Vi I 



Vi Si s\ I 



• 



So, too, the inequality system, \/# 2 + y 2 < z < y > x, has for 

 its locus the triangle Z K N, its determining matrix 



•* V\ I 



\ \ ^\ I 

 11 

 It would be superfluous to go on multiplying numerical ex- 



