finding the Value of an infinite Series , Sec, 201 
are not exadt) 0.906,900. Therefore the produdt of the 
r . tt a t 6 < 8 
lenes 1 + 
3 r r 5 r + 7 r & 97" 
tangent / is equal to 0.906,900, x t — 0.906,900 xr 
/ I0 £ 12 / T 4 
-7^0 + —^,--—;+ 8tc. into the 
II r I3r i5r 4 
— 0.906,900, x r x 
= 0.906,900 x r 
1.732,050,8 
x .577,350,2 = 0.523,598,8 x r; that is, the feries 
t- 
+ 
r t‘ 
+ 
$rr S r 7 r ' u 9 r II r 1 3' 1 5 r 
+ &c. (which ex- 
prefles the magnitude of the arch of which t is the tan- 
gent) is in this cafe = 0.523,598,8 x r, or an arch of 30* 
is equal to 0.523,598,8 x r. 
Art. 10. This value of an arch of 30° is exadt in the 
fix firft places of figures, and errs only an unit in the fe- 
venth figure, which fhould be a 7 inftead of an 8, the 
more exadt value of that arch being 0.5 2 3, 5 9 8, 7 7 5, 5 9 8, 
8cc. And thus by the help of only eight terms of the 
differential feries 
a- 
bx 
T> x XX D ti X 3 D 111 * 4 Div^-5 dv^ 6 D VI X^ 
1 + * i +^ 3 14- #1* r+^ 5 rr^ n^ 7 
have obtained the value of the feries 
.*S 
&c. we 
t t t t t t t r r 
t- — +„ — To “t — r»— rm;+ Sec. in the cafe of 
$rr $ r 4 7 r 6 9 r ur 137* 15 r 4 
an arch of 30 degrees, exadt to fix places of figures. 
This degree of exadtnefs is the fame with that which we 
fhould attain by computing twelve terms of the feries 
7— r 4 + 8tc. itfelf, as will 
t- 
+ 
: + 
3 rr Sr 4 7 r 6 gr b 11 r l ° 13^* 15 
appear from the following calculation 
Vol. LXVII. Dd 
Art. 
