finding tbs Value of an infinite Series , 8cc. 203 
~rx - Jr * [1.023,709,255,024,- .116,809,630,442, 
» «5 
+ Sec# 
-f* “X. 906,899, 624,582, 
= rx x •9 o 6 > 899,62 4 ,582, 
= r x *5775350,2 x .906,899,624,582, = (if we neglect 
the fix latter figures of 906,899,624,582, which we 
know to be not exadt) r x *5775350,2 x 906,899, 
-rx .523,598,319,029,8 ; of which the firfl: fix fi- 
gures *523,598, are exadt. 
Computation of an arch of 45 degrees. 
Art. 1 2. Now let the tangent t be equal to the radius 
r, or the arch (whofe magnitude is exprefled by the 
jf t S f t 9 f l 5 
feries/ + — ■ -—5+ — rs+r^— — a + &c.) be an 
arch of 45 0 . This feries will, in this cafe, become equal 
tor-— +-7 — -+ - — ^c. of which the firft 
eight terms will give the value of the whole exa£t to 
only one figure, as will appear by the following com- 
putation. Thele terms are equal tor x the eight terms 
I- ~+ y “ J + + r 3 ~Ts » that is > to r x the ei s ht terms 
1. 000, 000, 000, 000, -.333, 333, 333, 333, 
+ .200,000,000,000, - .142,857,142,857, 
+ .111, hi, in, .111,- .090,909,090,909, 
+ .076,923,076,923,- .066,666,666,66 6, 
