[ 299 3 
C j has moved till it coincides with D h and AC f 
becomes A D b. In like manner, from Art. 3. in 
the Effay, it appears that the ratio of H D h to H O is 
P q + 1 — s 
a 
X I + 
P <7 
— y — _L. 
q + 2 p ~ 
p p—l q 
x 5+s x P 
q + 1 
4 - &c. 
From hence it follows that the ratio of the difference 
p q 
between AD/j and HD h to II O is <? b multiplied by 
n 
the difference between the feries 
+■' 
+ 
q X q — 1 X p' : 
P q + 2 q p -f 1 X p + 2 xp q 1 + 3 q 
p + I ' p + I 
4* &C. 
and the feries 
+ 
P x q 
p X p — I X q : 
£ + * ’ q+LXpq + 2p 
4 - &C, 
}+IXj-|- 2 X^ q + 3 p 
the former feries being to be fubffraded from the 
latter, if H D b is greater than AD h, and vice verfa . 
2. The ratio of any term in the former of the two 
foregoing feries to that which next but one follows 
the correfpondent term in the latter is * 
pq + 2 p w p *i v p±± 3 P v p q v p q + 4 -P 
pxq x q p + q * Pq — q * pq+ 2 q pq — ^q 
x OjtJ. x X t!=ll X tmt &c . taking 
pq + 39 pq— 3 ? pq + ^q pq—\q & 
twice as many terms and four over as there are units 
in the number which expreffes the diftance of the 
term in the former feries from its firff term j which 
Qji 2 ratio 
