C 62 9 ] 
poflible values of b, c , d, &c.) it will alfo appear 
evident, that luch relation will likewife anfwer and 
include all the other conditions propounded. For, 
there being in the. general expreffion, thus derived, as 
many unknown quantities b, r, d , &c. (to be deter- 
mined) as there are equations, by making the fluents 
of B x, C x, D x, &c. equal to the values given j. thofe 
quantities may be fo afligned, or conceived to be 
fuch, as to anfwer all the conditions of the faid 
equations. And then, to fee clearly that the fluent 
of the firft expreffion, A x, cannot be greater than 
arifes from hence (other things remaining the fame) 
let there be fuppofed lome other different relation of 
x and v, whereby the conditions of all the other 
fluents of B x, Cx, D x, &c. can be fulfilled; and 
let, if poffible y this new relation give a greater fluent 
o f Ax than the relation above afligned. Then, be- 
caufe the fluents b B x, cCx> dD*,&c. are given, 
and the fame in both cafes, it follows, according tc* 
this fuppofition, that this new relation mull give a 
greater fluent of A x -j- b B x cC x -\- d D x, &c, 
(under all poflible values of b , c y d y ©V.) than the 
former relation gives : which is impofjible ; becaufe 
(whatever values are afligned to b y c, d, &c.) that 
fluent will, it is demonftrated, be the greateft pof- 
Able, when the relation of x and y is that above de- 
termined, by the General Rule. 
To exemplify, now, by a particular cafe, the me- 
thod of operation above pointed out, let there be 
^ propofed 
