finding the Value of an infinite Series , 8cc. 199 
X * 
~ . 036 , 940 , 836 , 940 , x -===p 
A: 6 
- . 028 , 416 , 028 , 415 , X 
X I 
- . 022 , 732 , 822 , 731 , X ==p 
- <kc. ; and confequently the product of this latter feries 
into the tangent t will be equal to the product of the 
former feries 1— — + fir 
3 5 
X 3 X 4 X s ' , * X , o • . 
— + + -+ See. into 
7 9 11 I 3 »5 
the fame quantity, that is, to the product of the feries 
tt t* t 6 t 
^-r-r+TZi *+ 
3 r r ' 5 r 4 7 r 6 ‘ 9 r 8 1 1 r 10 13 r 12, 1 5 r J 
gent /, or to the original feries 
, l L 
t~ 1 : * + 
3 r r 5 r 4 7 r° 9 r 
t+ 
1 1 r i0 13 r 12, i5^ I+ 
+ &e. into the tan- 
+ 8cc. which ex- 
preffes the magnitude of the arch of which t is the 
tangent.. 
Computation of an arch of 30 degrees . 
Art. 9. Now let t be the tangent of 30°, which is 
rr I 
,or x, = — r , or- • 
: -- , and ~ will be 
2 ’ 1 -\-x 
rr 
r r 1 1 
- r x — • Then will 1 1 be = — ; and 
a 3 3 
I o i 
Therefore 1 + „v will be =1+-=- + - 
f 3 
=6V and 
I 
4 4 
*4 
Therefore — ~ will be -T , and 
1 + a! 
J+7T " 16 
? and = 
and * 5 = > and 
rra 3 
, and xl 
*3?+ 
. Confequently the, differential feries will in this 
cafe 
