of the conic Sections, 461 
shown to be = o, it will thence follow, that all the terms denoted 
by C, D, E, &c. will vanish, and there will be left % = ey — d. 
13. And in like manner it will appear, that the value of % 
in Theorem IV, Art. 5, when y becomes immensely great, is 
also ~ ey — cl. For, in this case, H. L. — -^ 1 becomes 
= 0; and each of the expressions ~ -—-4^-, &c. also 
becomes = o ; and, consequently, % ^ 1 ) But, since 
e is a finite quantity, the expression e <f(yy -f 1) = ey -f- 
~T y Tff 3 ^ c * w “ en y immensely great, becomes barely 
= ey. Therefore, in this case, we have z = ey — d. 
14. Corollary. And hence it appears, that the series in 
these two theorems are equal to each other, and, consequently, 
that the constant quantity to be subtracted from each of them, 
by way of correction, is the same. 
15. The first term of the series which expresses the value 
of % in Theorem V, Art. 7, is s/{uu — 1), which, by the nota- 
tion there used, is always =: ey. And, when y becomes im- 
mensely great, the terms YL'i'ldiL, l r'>, J 'l ™-'} ... , &c . 
which enter into the values of B, C, D, &c. vanish ; but A be- 
comes = the quadrantal arch of the circle , of which the radius is 
A 
■,C= 4 B, 
— A, D = — 
2.4 3 6 
1 ; and thence we have B = 
C = A, &c. and these values being written for B, C, D, 
&c. in the series, we have, in this case, z~ey — A -f 
2.2,4 
•A 
A + A ’ &c - And > since this series 
always gives the correct value of 2, we have now discovered the 
value oi d, the constant quantity to be subtracted from the 
MDCCCII. q o 
tj 
