CURVES WHICH SATISFY GIVEN CONDITIONS. 165 
3L = — 9 m 2 + 27m+«( 3m — 9) 
+2M= 9 m 2 + 3 m+«(-6m- l)+« 2 
— 2N= + 6m +a( — 2) 
— O = 3m+os( — 1) 
6m+33M+a( — 3 n — 13) + a 2 (tenth equation). 
<% 2, 1)= 
— 18mM— 18 m 2 — 
162m 
(i) 
-|D = 
W 
— 
fm 2 + 6m 
(2) 
— 2E 
— m?n 
+ 
4m 2 + ImM— 8m 2 — 4m + 
32m 
(3) 
— 2F =- 
-2m 3 
+ 
8m 2 — 16mM — 6m+ 
£ 
oo 
(4) 
- G = 
— mn 3 
— 
8m 2 + lmM+ 4 m 2 -f 32m— 
4 n 
(5) 
+|H = 
—\m?n 
+ \rrm— 4m 2 
(6) 
+11 = 
—bmn 2 
+15mM+20M 2 — 
60m 
(7) 
-W = 
+ 10m 2 —30m 
(8) 
+2D' = 
■3w 3 
+21m 2 - 
36m 
(9) 
- J' = 
3m 2 — 
9m 
(10) 
— fm 3 — fm 2 M— 6mM 2 — Sm^^tm 2 — -^mM+18M 2 — 2m— 191 m 
0) 
+ “( 
— 3mM - 
-3m 2 + 
6m+ 
51m + 54)+a 2 (m+M 
-15) 
(2) 
+ *(“ 
-§-m 2 
+ 
|m 
- 2) 
(3) 
+a( 
3m -12) 
(4) 
+ «( 
6m 
-18) 
(5) 
+a( 
3m 
-12) 
(6) 
+ a ( 
- 
|m+ 
"IpM )+« 2 ( 
- i) 
(7) 
+ «( 
%mn 
- 
5m— 
-^m 4-20) 
(8) ’ 
-f-a( 
- 
J#m+10) 
(9) 
+«( 
1m 2 
— 
7m +12) 
(10) 
+«( 
- 
M + 3) 
(11) 
+ «( 
— -fmM- 
-2m 2 + ' 
4pM +55) + a 2 (m+M- 
-¥) 
(eleventh equation). 
2 a 2 
