of the Hyperbola. 131 
put = e , and if ~ be written instead of y, in Theorems II. and 
IV. in pages 453 and 454 of the Philos. Trans, for 1802 ; then, 
(as appears by pages 4 6b and 467 of the same Vol.) the cor- 
responding value of % may be obtained from either of the 
following equations, viz. 
2 1 2.4 2.4.6 
D -f 
3 - 5-7 
2.4. 6. 8 
E, &c. 
Mt + i) 
2. z 4 - d=< 
I + — A' — 
B' -f 
2.4.6^ 
C' — 
3-5 
2.4.6.8c 7 
[_ • ze 2 4.C 
in the first of which equations 
A = ^y(i+0 + ^H.L.(/ < + 4 /(i + < )), 
( i + c) T — A 
D', &c. 
B = 
4ec 
Q — « *(i + c) z — 3B 
6cc J 
D 
S 3 
e a (i+e)^— 5 C 
See 3 
e * ( 1 + ef - — 7D 
10 CC 
&C. 
in the second. 
&c. 
A' — H.L. (-*/ 1 +e) — -v/V), 
