192] GENERAL TRILINEAR EQUATION OF THE SECOND DEGREE. 145 
Now observing the equations 
{a, h, g^cc, ¡3, y) = ~ , 
{h, b, /$>, /3, 7) = p> 
(;9> f o & 7) = ^ , 
we have 
(®> •••$«. A 7) (?, >7. f)=y (f + >7+t) = 0, 
(a, ... fi, 7) =p ( a + ^+ 7) = p > 
and the equation of the conic gives therefore 
(a, ,, r) 2 + ~=0, 
and we have as before 
£ + v + £ = 0. 
To find the axes we have only to make 
r\ = Zf + Mr? + N£\ 
a maximum or minimum, £, 77, £ varying subject to the preceding two conditions; this 
gives 
(a, h, 77, £) + \L% + g = 0, 
(/¿, &,/$£, 77, 0 + + /i = 0, 
(#> /, c Vi 0 + + fi = 0, 
and multiplying by f, 77, £, adding and reducing, we have 
K 
P 
+ Ar 2 = 0, 
which gives 
A = 
K 
Pf 2 
Substituting this value, and joining to the resulting three equations the equation 
C. III. 
£ + 77 + £= 0, 
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