[ 3^0 ] 
ratio if q be greater than />, it is evident inuft be 
greater than the ratio of equality. Wherefore, if 
from the fecond feries you fubftraft the two firft 
terms which together are lefs than two, the remainder 
islefs than the former feries j and of confequence, the 
former feries fubftradted from the latter cannot leave 
a remainder fo great as two. And therefore in this 
cafe, that is, when q is greater than />, by the pre- 
ceding article, the ratio, of HD/6 — A D h to H O 
P ? 
cannot be fo great as 2 a b . 
n 
4 
3. The curve A D H being as before divided into 
two parts AD b and HD£, let the ordinates C / 
and F t be placed on each fide of D b and at the 
fame diftance from it, and let 2; be the ratio of h / 
or h t to A H. Then if y y x and r be relpedtively 
the ratios of Cf A / and H/ to A H, by the nature 
f q J 
of the curve y = xr . But becaufe the ratio of 
A b to A H is a, and that of h j to AH is z y the 
ratio of A h — hf(—Af) to A H is tf—z. Where- 
fore — zz=x. And in like manner b 4- z-=.r. But 
p 9 1 
y—xr, and^ is the ratio of Cf to AH. Where- 
fore the ratio of C /to A H is p x And 
in like manner the ratio of F/ to AH is X ^ 3 A 
And confequently C) is to F / as is to 
a -f z ]f> X b — 
^ y/ greater than ^>, a 4- X b — 2J 7 is greater 
tnan a — zF x and the ratio between them in^ 
creates as z increaies. For the hyperbolic logarithm 
of 
