521] 
AND ON THE CONSTRUCTION OF A DOUBLE-SIXER. 
379 
48—2 
that is, 
*J'M X _ {m 1 — b) (m l — c) _ m 1 — a 
V57 ( m —b) (m — c) m — a’ 
We have thus for m, a quadric equation satisfied by m=m 1 , so that throwing out the 
factor m — m lf the equation is a linear one, viz. we find 
ma — ab — ac + be 
TOj = 
m - a 
or, what is the same thing, 
and thence also 
viz. M x is determined rationally in terms of m, Vili; this is of course as it should 
be, since the point 6' is uniquely determinate. 
Point 6 by means of the conic 2361 / 4 / 5 / . 
In precisely the same manner the coordinates are m 1? — ^M lf where m lf 
denote the same quantities as before. 
Point 4 by means of the conic 2341 , 5 / 6 / . 
The equation of the conic is 
Fx+Gy + H =^~~ , (2, 3), 
where 
Fb 
(50 
Fm x + G JM X + H = —, (60 
m! v 
Fm - G Vilf + H = -—(10 
/vyj ' / 
m 
which give without difficulty 
abcF= — a — c + P, 
Vif abc G = (m — b) (— m + P), 
abc H = ab+ ac +be — bP, 
where P — 2a — c- 
terms of m only. 
2 (a — c){b — c) 
m + m x — 2 c ’ 
a quantity which will presently be expressed in 
And then 
Fd+G\/®+H =