20 Proceedings of Eoyal Society of Edinburgh. [sess. 
Taking now the six points 1, 2, 3, 4, 5, 6 whose coordinates are 
• • • • ? and calling the origin 0, we have as the 
equations of the planes 012, 023, 034, .... 
Avih\ + y\h x 2 1 + = °> 
AvA + yh x s\ + = 0 > 
and therefore the condition that the intersection of 012, 045, the 
intersection of 023, 056, and the intersection of 034, 061 will lie in 
the same plane is 
fed 
feel 
feel 
fell 
fell 
M2! 
Mel 
• 
Mel 
|%« 4 | 
te 
3* 
to 
tel 
tel 
tel 
Ids'll 
feel 
feel 
1^2%' 
fell 
fell 
Mel 
Mel 
• 
Mil 
Mil 
fey 
l*4%l 
fe^el 
fe^sl 
tel 
tel 
The four determinants here, however, are simplifiahle after the 
manner of a similar determinant above. They are, in fact, all seen 
to he of the type 
m w w 
IVfcl \Vy\ M.l 
KVfs\ Mvl \ x 0c\ , 
and this multiplied by 
x<t Xp x y 
y* Vp v y 
Z a Zp Z y 
Kv^yl te 2 «l 
te*.l ■ 
V-i/tH ■ foml 
i.e., . \xpy s z,\ ; 
produces 
