f 6 30 ] 
» x n y m y p 
propofed the fluxionary quantity - - ^3^- ; wherein 
the relation of x and y is fo required, that the 
fluent, correfponding to given values of x and y , 
fhall be a maximum , or minimum. Here, by taking 
the fluxion, making y alone variable (according to the 
rule) and dividing by y, we fhall have — 
= v. And, by taking the fluxion a fecond time 4 
making y alone variable, and dividing by y } will be 
m x n y m — 1 v p 
had r — . — ±. — Now from thefe equations to 
A ‘ 
exterminate v, let the latter be divided by the former ; 
• m 
-j and therefore ay*— v ( a being a 
fo fhall 
my 
py 
conftant quantity). From whence y p y — - 
a l - 1 
xx p— 1 j and consequently 
m-\- p 
>» 4 -P 
y p 
a\ P-* 
P 
p—r . — 1 
X X P—<- . 
p — n — 1 
Let there be now propofed the two fluxions x n y m x 
and xfyiy, the fluent of the former being required 
to be a maximum , or minimum , and that of the 
latter, at the fame time, equal to a given quantity. 
Then the latter, with the general coefficient b pre- 
fixed, being joined to the former, we ffiall here have 
x n y m x 4* bxfyiy. From whence, by proceeding as 
before, bx p yi = v, and mx n y m ~ l x fl- qbtfy^'y — v. 
From 
