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(whofe values will depend on the 
values given, and may be either politive or ne- 
gative), be united into one fum, and the whole 
be made equal to nothing j from which equation 
the true relation of x and jv, and of a* andy, will 
be given, let the number of reftridtions be what 
it wilL 
For an example of the general Rule here laid 
down, let the fluxions given be and x; the 
yy 
fluent of the former, correfponding to any given va- 
lue of y, being to be a Minimum, and that of the 
latter, at the fame time, equal to a given quantity. 
Here, taking the fluxions of both expreflions (making 
X, alone, variable), and dividing by x, the quantities 
refulting will be and i j fo that, in this cafe, 
_ yy 
We have — -f* ^' = o, and therefore x = y — ^ « 
(fuppofing a — — I f). From whence, by taking 
the fluents, x — i or = 4 ^y, an equation 
anfwering to the common parabola. 
If the abfciffe of a curve be denoted by x, and the 
ordinate by y, it is known, that the feveral fluxions 
of the abfcifle, curve-line, area, fuperficies of the 
generated folid, and o f the folid itfelf, will be repre- 
.fentcd by X, V X X -j- y y, y 2 y V ^x -f- y y, 
and />y^ x refpedlively : if, therefore, the fluxions of 
thefe different expreflions be taken as before (making 
^ alone. 
