C 62 4 ] 
of the lead refinance, with innumerable other cafes. 
But altho’ cafes of this fort do, indeed, moil fre- 
quently occur, and have therefore been chiefly at- 
tended to by mathematicians, others may neverthe- 
lefs be propofed, fuch as actually arife in inquiries 
into nature, wherein both the flowing quantities, to- 
gether with their fluxions, are jointly concerned. 
The inveftigation of a rule for the refolution of 
theie, is what I fhall in this paper attempt, by 
means of the following 
General Proposition. 
Let Q, R,S,T, Sec. reprefent any variable quantities, 
expreffied in terms of x and y (with given coeffici- 
ents), a?id let q, r, s, t, See. denote as many other 
quantities , expreffied in terms of x and y ; It is 
propofed to find an equation for the relation of x 
and y, fo that the fluent o/'Qq + Rr-f-Ss-j-Tt, 
&c. correfponding to a given value of x (or y), may 
be a maximum or minimum. 
Let 
