47 ° 
Mr. Hellins on the Rectification 
A =j- 4/ ( 1 + eeyy)+ ~ H. L. {ey + 4/(1 + eeyy) ) =0*3497,6260, 
B = 
C = 
D= 
y(i+eeyy)i —A 
4 ee 
yi(i-{-eeyy)l — 3B 
6 ee 
y s (* 4 — 5C 
8 ee 
= °' 01 34 ’ 3 2 34 > 
= 0-0009,0892, 
= 0-0000,7272, 
E s— 3 ,7 ( | + gg xy)^ — 0-0000,0632, 
loee 
F = 
G = 
3 
y>( 1 + eeyy) 1 — 9E 
i2ee 
y 1 ( 1 -f ee y y)k — xiF 
and thence 
14.ee 
= 0*0000,0038, 
= 0-0000,0003; 
+ 
A = 0-3497,6260, 
- 1 - C = 0-0003,4084, 
3-5 
3 - 5-7 
2. 4.6. 8 
E = 0-0000,0173, 
2.4.6 
3 - 5 * 7-9 
|B = 0-0067,1617, 
D =3 0-0000,2273, 
G = 0-0000,0001, 
2.4.6.8.10.12 
2.4.6.8.10 
and the sum 
and the sum= + 0-3301,0318, 
— 0-0067,3904, 
0-0000,0014, 
0-0067,3904. 
diffe sums e is ftheSe } °'3433 j^ 6 i 4 = z, the length of the arch of an 
hyperbola, from the vertex to the ordinate, of which the trans- 
verse and conjugate semi-axes are ^ and 1, and the ordinate 
And, since like parts of similar hyperbolas are to each other as 
their semi-axes, we shall have, by multiplying 0-3433,6614 by 
30, the semi-conjugate of the hyperbola proposed, 10-3009,842 
for the length required. 
Having in this example shown how to adapt these theorems 
to hyperbolas that have a conjugate semi-axis different from i* 
