of the Hyperbola, 
ns 
Coeff. of 2d term 1—205, 
3^ — (3-3 — 1 ) B -j- 1.3 A — 4*.+ 
4 th + (5-5 — 1 ) c — 3-5 b + 8£ — ioy, 
5th — (77 “ l)D + 57C— 12y-f- 14J, 
6th + (9-9 *— 1 ) E — 7.9D -f* 16$ — i8g, 
&c. &c. 
And, putting each of these coefficients = 0, (since the whole 
series is now known to be == 0,) writing 2.4 for its equal 3.3 
— 3, 4.6 for 5.5 — 3, 6.8 for 7.7 — 1, &c. we obtain from 
these equations 
a ; 
B = 
C = 
D = 
E = 
&c. 
±3 A 
2.4 
2 1 
x 
2 > 
£ 
2.2 s 
3-5 
4.6 
5-7 
6.8 
5 ? 
B - - + , 
3 ' 3 - 4 * 
C _ X 4. 2 i 
4 + 4 - 6 ’ 
£2-D 
8.10 
2. J, 91 
5 + 5 - 8 ’ 
&C. 
the law of continuation being very evident. 
The value of A, which is not discovered by this process, 
was found in Art. 30, and is == £ -f- H. L. 2. And the deci- 
mal values of these coefficients are as below, viz. 
A == 0*44314718, 
B = 0-05680519, 
C — 0-02183137, 
D = 0-01154452, 
E = 0*00714200, 
&c. &c. 
33. Thus, by the common application of Sir Isaac Newton’s 
doctrine of fluxions and infinite series, without any assistance 
