QUADRATURE of the CONIG SECTIONS, &c. 281 
the adjacent tangents until they meet, (Art. 6.); therefore 
22" tan’ < will be the fquare of that perimeter. Let the pe- 
rimeter itfelf be denoted by P, then, fubftituting P* in the 
equation inftead of 2% tan “, and 2 (1— a) inftead of the 
gs ae 
feries to which it is equivalent, and bringing pz t0 one fide, 
we get 
RD ee a 
| marat 3 ( z 
I BE inis & I4 ty Tay OT aX Ev ia'T 
— = 4 —(- tan’ — 4+ — tan’ — — tan’ = —tan —@... 
oe { C 3 sue citys an’ ae tat =f 
| : naa 
15. THis is true, whatever be the value of 2, the number of 
terms of the feries in the parenthefis. Let us now conceive 
the feries to be continued indefinitely, then, as upon this hypo- 
thefis, n may be confidered as indefinitely great, + will become 
4” 
lefs than any aflignable quantity, and therefore 2 (x ch 
3 4" 
will become fimply + moreover, P will in this cafe become a, 
(Art. 7.), and P* will become .a*. Thus, upon the whole, we 
fhall 
