QUADRATURE of the CONIC SECTIONS, &c. 285 
be put under this form 
NG Ne tN BR Tes &e. 
I 
a = tan a 
where T(x) is put for + 5 tan = 4, and T (2) for ztan t a, and T,3) 
Pat aie 
for g tanya, &c., then, as the formula given at the conclufion 
of the laft article, becomes by fubftituting tan’ = a for oa 
. 1—cofta 
and tan x4 FOR ot art 14 co 14 cofta , and fo on, 
fi 1-+cofa 
| 4 1—cola +5 6 
I 
Ba aie 
| — Gea ue tng et oan eat, &c.) 
L 
it may be otherwife ol thus, 
( r1+cofa, 1 
tm \4 1—cola ", 6 
pao t Veh Tot Ta) sts be), 
where it is to be obferved, that the fymbols T(2), T(3), T(4), 
denote the very fame quantities in both feries. 
Now, as we have found (Art. 8, and g.), that each term of 
the feries of quantities T(2), T(3), T(4), &c. is lefs than A of the 
term immediately before, but greater than a third proportional 
to the two terms immediately before it, taken in their order, it 
Nn 2 is 
