[ 320.] 
the ratio of 2Ri) / Qjo A CFH, greater than the 
ratio of D ht¥ + D hfC to A C F H *. 
It will be eafily feen that this Article improves 
conliderably the rule given in Art. 12. But we may 
determine within {fill narrower limits whereabouts 
the required chance muft lie, as will appear from the 
following Articles. 
25. If c and d Hand for any two fractions, when- 
ever the fluxion of c x F t is greater than the fluxion 
of d x Cf (Vid. fig.) f xF/-(-^xC /'will be 
greater than Q t. For in the fame manner with Art. 
6. it will appear that cxF^-j-^xC fis to Q/, 
as the fluxion o f f x F/ x 1 4 - — x 1 — — to- 
I q q 
gether with the fluxion 0 f JxC / xi — — X 
P 
1 -| to the fluxion of O t x 1 — — — — . Now 
q P q 
ft 1 2J * i 2, # 
lince 1 — — — is the arithmetical mean between 
P 1 
n z 
+ /L Xj 
T XI 
11 z 
n z 
— and i — x 1 H ■, it is 
q P q 
plain, that were the fluxion of c x F t equal to the 
fluxion of d x C f 3 rxF t -\-d xC f would decreafe 
in refpedt of its own magnitude at the fame rate with 
i an( i> therefore, flnce at firfl: equal, they would al- 
ways continue equal. But the fluxion of c x F t 
being greater than the fluxion of d x Cf by fuppo- 
fition, and (flnce q greater than) p 1 X 1 — — , 
* This Art. is true, whether p be greater or lefs than q. 
2 following 
