to the other propofed quantities AF, fG\ G'g, 
whereon the cwfBcients e, f, g, depend and’ this 
relation will, evidently, continue the fame, at what- 
ever diftances from the line ^ L, the points c,/, b k 
are taken, as thefe diftances have nothing to'do^n 
the confideration, all the propofed quantities (as well 
the ^’s as i?’s, being (by hypothefisj exprefted 
in terms intirely independent thereof. 
Lemma II. 
Fig. 2 Upon a given right-line B L, fuppofe per- 
pendiculars Bb, Cc, Dd, to beeredled at 
equal diftances j and upon the fame line B L, as 
a bafe, fuppofe a polygon Bbc defghi klL to 
be conftituted, having its angular points b, c, d, &c. 
pofited in the faid perpendiculars ; let y denote the 
diftance of any of thefe perpendiculars (Cf, Dd, 
&c.) from any given point m LB produced; 
and, fuppoling bC\ c D\ dE', ^c. to be drawn 
parallel to A B, let the bafe of any of the little 
triangles b C c, c D d^ ^c. be reprefented by 
and the perpendicular correfponding by x (y be- 
ing given, or the fame, in every triangle, and x 
indeterminate) : then, fuppofing i?, S, T, to 
denote any quantities expre/Ted in terms ofy, y, 
and X, it is propofed to find an equation exhibit- 
ing the general relation of the quantities y, y, and 
X fo that the fum of all the y ^’s (refulting from 
the feveral triangles) may be a Maximum or Mini- 
mum, at the fame time that the fums of all the 
yR'Sy y*S’s, are given quantities. 
Becauib 
