the Quadrature of the Circle. 
221 
r 
= < 
L 
+ 
f 81-1/12 
8 A 
4 - 
16 B 
24 C 
1 
32 D 
i 80 
9.80 
T 
17.80 
25.80 
" 3 ^ 8 ^ , 
J 8Ia/12 _ 
8 A 
J_ 
16B 
24 C 
1 
32 D 
l 5 - 9 - 8 o 
13.80 
rr 
21.80 
29.80 
T 
37.80 * 
C 8 I , ' I 2 
8 A 
4_ 
16 B 
24 c 
[ 
32 D 
J 3 - 3-80 
1 1 .80 
1 
19.80 
27.80 
l 
35.80 ’ 
) 8 - /I2 
8 A 
4 _ 
16B 
24 c 
1 
32D 
^7.27.80 
15.80 
T 
23.80 
31.80 
T 
39.80 * 
Sec. 
Sec. 
■, &c. 
8. All these new series, it is evident, converge somewhat 
swifter than by the powers of 80. For in the first series, 
which has the slowest convergency, the coefficients y, y 24 , 
&c. are each of them less than i ; so that its convergency is 
somewhat swifter than by the powers of 8o. 
g. But another advantage of these new series is, that the 
numerator and denominator of every term except the first, in 
each of them, is divisible by 8 ; in consequence of which the 
arithmetical operation by them is much facilitated, the divi- 
sion by 8o being exchanged for a division by 10, which is ho 
more than removing the decimal point. These series then. 
when the factors which are common to both numerators and 
denominators are expunged, will stand as below, (each of 
which still converging somewhat quicker than by the powers 
of 8o), and we shall have the circumference of a circle whose 
diameter is l, 
f 81^/12 
J 8o 
j 9 a/»2 
400 
A 
9.10 
A 
13.10 
A 
11.10 
A 
15.10 
+ 
+ 
+ 
+ 
2 B 
3C 
17.10 
25.10 
2 B 
3 C 
21.10 
29.10 
2 B 
3 C 
1910 
27.10 
2 B 
3 C 
23.10 
31.10 
+ 
+ 
+ 
+ 
4 P 
33 - 1 ° 
4 P 
37.10 
4 P 
3S-io 
4 D 
39.10 
-, See. 
Sec . 
, Sec. 
See. 
