[713 
714] 
37 
w»5 ,m 6 
/¿5 ^ 6 ’ 
set —*üi- 
/¿g î)î 6 
714. 
VARIOUS NOTES. 
ie foregoing 
[From the Messenger of Mathematics, vol. VII. (1878), pp. 69, 115, 124, 125.] 
An Identity. 
The following remarkable identity is given under a slightly different form by 
Gauss, Werke, t. ill., p. 424, 
/1\3 /1 3\3 /1 3 5\3 
®' + (îi) -,+ (liais) 4<, + te 
1 + 
= 1 + 
x + 
2 
5 
4 
1.2 
1 5 \ 2 
4 • 4 
X 3 + 
1 5 1\2 2 
lTaTs) a!, + &c j • 
= deficiency, 
curve which 
particuliers 
f give rise 
minution of 
icy will be 
On two related quadric functions. 
Assume 
then 
<fjx = a 2 (c — x) — x (c 2 — b~ — cx), 
y]rx = № (c — x) — x (c 2 — a 2 — cx) : 
a- 
c — x) (c — xj 
Ò 2 
c — x) (c — x)‘ 
6 2 
fx, 
(j)X. 
In the first of these for x write then 
a 2 (c - x) \ _ a 2 (c - x) 
6 2 
^ ( C 2 _V _ (c 2 - Ò 2 - cæ) 2 (c - ^) 2 ^ (c 2 - & 2 - ca) ! 
a 2 6 
<f> («).