BG, the 
iere the 
mig that 
pectively 
It may be added that, taking (x 1} y 1} z 4 ), (x 2 , y 2) z 2 ), (x 3 , y 3> z 3 ), (x 4 , y 4 , z 4 ) as the 
coordinates of the four points of intersection of the three conics, the first conic is 
given by means of these four points and the fifth point (y =0, z = 0); and similarly 
for the other two conics; whence, denoting the determinants formed with any four 
columns out of the matrix 
tfj 2 , 
2/i 2 > 
Zy\ 
y&, 
Z\Xi, 
Xiy 4 
#2 2 , 
yi, 
z.?, 
y*z2, 
Xojy 2 
yl 
y&, 
z 3 x 3 , 
X 3 y 3 
x 4 2 , 
yi> 
zi, 
y+z 4 > 
z 4 x 4 , 
X 4 y 4 
by 1234, 1235, &c., we easily find the equations of the three conics, viz. these may 
be written 
x 2 , 
f > 
, 
yz » 
zx , 
xy 
1456 ( 
0 , 
+ 3456, - 2456, 
+ 2356, 
+ 2364, 
+ 2345) = 0, 
2356 (- 
• 3456, 
0 , 
+ 1456, 
+ 3156, 
+ 3164, 
+ 3145) = 0, 
3456 ( 
2456, 
- 1456, 
0 , 
+ 1256, 
+ 1264, 
+ 1245) = 0, 
the exterior factors 1456, 2356, 3456 being introduced in order to bring the equations 
into the above-mentioned form, wherein the sum of the quadric functions is = 0. 
[Yol. x. pp. 88, 89.] 
2743. (Proposed by M. Jenkins, M.A.)—Show that if p be a prime number and 
m and n any positive integers, the highest power of p contained in ~t n \ may 
II (to) II (n) J 
be obtained by expressing m + n and either to or n in the scale of p; the number of 
times that it would be necessary to borrow in subtracting the latter number from the 
former being the index of the power of p required.