2q 6 Mr. maseres's Method of 
~ .003,174,603,174, 
- .001,154,401,154, 
.000,444,000,443, 
- .000,177,600,177, 
- Sec. 
- 1 ~ • 2I 4,474,4 I 4,47°, 
Therefore the feries 1 — - + — 
3 5 
tt t 4 / 8 f TO Z 11 
^ 3 rr ~^5 r+ 7/ 6 "^9r b iir 10 ^ i$r l * 
= *7 ^5)525,585,530. 
Jr 3 Ar 4 * 5 * 6 # 7 
7 + 9 ” ' «3~ I 5 + ^ CC ' ° r 
t'* 
-7^77-4+ &c. is equal to 
•785)5 2 5,5 
t 3 r 
t 2 , rr+ 5 r * 
85,530; and confequently the feries 
f t 9 t 11 / I3 t 15 
— sH — i r3+ — n — — r- + See. is in this cafe 
7 r 9 r 11 r iS r 
= ^.785, 525, 585, 530 , -rx •785,525,585,530; that 
is, the length of an arch of 45 °, in a circle whofe ra- 
dius is r, is = r x •785,525,585,530; which number is 
true to three places of figures, the more exadt value of 
that arch being/* x .785,398,163,397, 8cc. 
Art. 14. It has been aflerted in art. 12. that in 
order to obtain the value of the feries 
i 3 r 
* 
3 rr 5 r 
JL ‘I Cl 
y r 6 4 gr* Ilr 10 4 
t ' 3 
l 3 r lz 
t ls 
ypr. r+ Scc.exadt to 3 
places of decimal figures by the mere computation of its 
terms, in the cafe of an arch of 45% we muft compute 
at leaft 500 of its terms. This maybe proved in the 
following manner. The indexes of the powers of t in 
that feries are the odd numbers 1, 3, 5, 7, 9, 1 1, 13, 1 5, 
8cc. 
