272 NEW SERIES for the 
Let the fums of the correfponding fides of thefe equations 
be taken, and obferving that the feries 
i I I I 
ia gil gad cagA gail. ig 
pitane ia tania Stania a 
2 4 rs cy ae as 
is found in each fum, let it be rejected from both; and the re- 
fult will be 
( I 
oes 
t= 4 I I Zit cog Ehonl I I 
tana cee ries ber be oe iv 
wea: 
the number of terms of the feries in the parenthefis being x, 
and hence we have 
I I I I I I I 
- = saat ~ tan—- 4-4 - tan = a+, tant a+ 
pepe tan 2 2 4 4 
Qn 
a 
Sei aaviaa oe = tan 4, 
I I an 2" 
6. Now, 2tan{a4 is the perimeter of a figure formed by 
drawing tangents at the ends of the arch z, and. producing 
them till they meet; and 4 tan +a is the perimeter of a figure 
formed by bifecting the arch a, and drawing tangents. at its ex- 
tremities and at the point of bifection, producing each two ad- 
sear : —- Aa: 
joining tangents till they meet ; and in general 2" tan = the 
perimeter of a figure formed in the fame way, by dividing the 
arch 
