C 766 ] 
and, this value being added to that of the former 
part (found above), and the whole being divided by 
, - . — A M -f- 2 v / 1 
77 , we thence obtain — — 
AAxN x 
-, or ~ 
’ n 
x — co-f. i^x M + fin. ^x 2 N for that part of the 
value fought depending on the two terms affedted 
with q and r. From whence the fum of any other 
two correfponding terms will be had, by barely fub- 
flituting one letter, or value, for another : So that, 
f — log. 1 — x 
* x 
n ' 
— co-f. <^x M + fin. 2 N 
— co-f. 5^ x M + fin. i^x 1 N' 
— co-f. C x M" 4 - fin. ^ x 2 N 
In 
K &C. + &C* 
will truly exprefs the fum of the feries propofed to 
be determined} M, M' ? M See. being the hyperboli- 
cal logarithms of I 2ccX- f- xx, 1 — 2 /2 x -j- xx, 
1 — 2 y X 4- X X, &c. N, N', N" &c. the arcs 
X y/ i — « 
whofe lines are 
V 
Mi 
\/ 1 — z fi * 4 
XX 
2 & X -p xx 
y y/i — yy — ^ & c . anc j ^ gr &c. the mea- 
y/ i — 2 y x 4 x x 
fures of the angles exprefled by 360 
n 
Tf )0 
XW.2X — X 717, 
n 
3 x ^ x 777, &c. And here it may not be amifs to take 
notice, that the feries — A- , 
m 1 vi -f n 7 n 4- 2 71 
+ 
,m + 2 n 
4 * 
&c. thus determined, is that expreffing the fluent of 
OC ,,m " — ' * /» 
-j correfponding to one of the two famous 
Cotefian 
a 
