[ 628 ] 
When y is not found in the quantity given, v will 
then be = o ; and, confequently, the expreffion for 
o, equal to nothing alfo. But if y be abfent, then 
will 6 = o, and confequently the value of v = a con- 
flan t quantity. It is alfo eafy to comprehend, that, 
inftead of y and y , x and x may be made fucceffively 
variable. Moreover, ihould the cafe to be refolved 
be confined to other reflri&ions, befides that of the 
maximum or minimum , fuch as, having a certain 
number of other fluents, at the fame time, equal to 
given quantities, flill the fame method of folution 
may be applied, and that with equal advantage, if 
from the particular expreffions exhibiting all the 
feveral conditions, one general expreffion compofed 
of them all, with unknown (but determinate) coeffi- 
cients, be made ufe of. 
In order to render this matter quite clear, let A, 
By C, D, &c. be fuppofed to reprefent any quantities 
exprefled in terms of x, y, and their fluxions, and 
let it be required to determine the relation of x and y, 
fo that the fluent of A x fhall be a maximum , or mi- 
nimum y when the cotemporary fluents of B x, Cx^Dx, 
&c. are, all of them, equal to given quantities. 
It is evident, in the firfl; place, that the fluent of 
A x b B x -f c 4- d D x, &c. (b, c, d y &c. being 
any conftant quantities whatever) mud be a maxi- 
mum, or minimum , in the propofed circumftance : 
and, if the relation of x and y be determined (by the 
rule), fo as to anfwer this Angle condition (under all 
poffible 
