Converging Series for the Circle . 485 
Where it is evident, that the laft number, or the value 
of d, is the fitted: of thole produced in this cafe, and from 
which it appears, that the arc of 45 0 is equal to the dif- 
ference between the arc of which the tangent is and 
quadruple the arc of which the tangent is j. Or that 
A — < 
+ T X : 1 
3-5 
— + 
r + 
5*5 
1 
7*5 
1 
9-5° 
1 
2 39 X * 1 3-239' ' 5- 2 39 + 7- 2 39'‘ ‘ 9- 2 39“ 
8cc. 
■See. 
Which is the very theorem that was invented by Mr. 
machin, as we have before mentioned. 
5. Take now t-\, and the exprellion 
6t 
67T wiu S iv ' e 
C 
91 
3°5 
d 
111 
1921 
e 
1 1767 
Of which numbers none, it is evident, are fit for our 
purpofe. 
S f f a 
6. Again, 
