[ 3 1 1 ] 
J 3’ The ratio of the fluxion of t - ” ~ 2 l x to the 
pq 1 
fluxion of i -j- 
n z 
X 
and the ratio of the fluxion of i 
p — j 
to the fluxion of i — 
nZ zj a 
P q 1 
is i 
n % 
*■+3 
f— i 
I — n z 
P q 
This will immediately appear from Art. 7. 
14 * While z is increafing from nothing till ~ 
becomes equal to unity, thefe two ratios are* at 
niit greater than the ratio of equality, and in- 
creafe as z increafes, till they come to a maxi- 
mum. Afterwards they decreafe untill they be 
come firA equal to the ratio of equality, and then 
lefs. > This is proved by finding the hyperbolic 
logarithms of thefe ratios. The hyperbolic logarithm 
of the firA is the feries - 1 Lz~± v „ „ , 
■ q P x 11 z -r 
t P 1 n — 
+ ~ 77 
X 
w 2 . q — I p — j 
n 3 2 3 
JL £ i 1 P 1 » — 2 
+~- 
* 4 
n* z 
P 
+ 
X 
3 
X 
4 
S 
