[ ” ] 
fame, let the perpendicular (or ordinate) Cc be 
taken at what diftance you will from the given point 
A ; that is, let y ftand for which you will of the 
diftances A AC^ A Dy ^ E, L 
Corollary. 
If the fides of the polygon bed e f g hy &c. be 
diminifhed, and their number increafed in infinitum^ 
the fum of all the y will (it is well known) be 
exprefled by the fluent of the fum of all the 
y R’s, by the fluent of y R, &c. whence it follows, 
that, to have the fluent of j^(anfwering to a given 
value of y) a Maximum, or Minimum, and the 
fluents of jiRyySy&c. at the fame time, given 
quantities, the relation of y, and x, muft be de- 
fined by the equation g er -\-f ^ ^ = o, above 
exhibited ; y, r, j, ^c. being the refpedive fluxions 
of Ry Sy &c. divided by that of Xy (or x ) ; this 
quantity x, or x, (in finding the faid fluxions) being, 
alone, confidered as variable. Hence we have the 
following 
General Rule, 
For the refolution of Ifoperimetrical Problems, of 
all orders, take the fluxions of all the given ex- 
preflions, (as well that refpedting the Maximum, 
or Minimum, as of the others whofe fluents are 
to be given quantities), making that quantity (x) 
alone variable, whofe fluent (x) enters not into 
the faid expreflions j and, having divided every- 
where by the fecond fluxion (s)y let the quanti- 
ties hence ariflng, joined to general coefficients, 
C 2 
