546 
[622 
622. 
ON A SYSTEM OF EQUATIONS CONNECTED WITH MALFATTI’S 
PROBLEM. 
[From the Proceedings of the London Mathematical Society, vol. vii. (1875—1876), 
pp. 38—42. Read December 9, 1875.] 
I consider the equations 
X, = by- + cz 2 - Ifyz - a (be -f 2 ), = 0, 
Y, = cz 2 + ax- — 2gzx — b (ca — g-), = 0, 
Z, = ax 2 + by- — 2hxy — c (ab — h 2 ), = 0, 
where the constants (a, b, c, f g, li) are such that 
K, — abc — a/' 2 — bg 2 — ch 2 + 2fgh, = 0. 
Hence, writing as usual (A, B, C, F, G, H) to denote the inverse coefficients 
(be -f 2 , ca - g 2 , ab - h 2 , gh - af, hf - bg, fg - ch), 
we have (A, B, G, F, G, H\x, y, zf — the square of a linear function, = (cnx + (3y + yz) 2 
suppose; that is, 
(A, B, C, F, G, H) = (a 2 , fi 2 , 7 2 , ¡3y, ya, a/3). 
It is to be shown that the three quadric surfaces X = 0, Y = 0, Z = 0 intersect in a 
conic ® lying in the plane aax + b/3y + cyz = 0, and in two points I, J; or more 
completely, that 
the surfaces Y, Z meet in the conic ® and a conic P, 
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X 
X, Y