[ ro ] 
feveral fums (whether of the /^’s, y R*s, or j 5’s, 
will depend intirely upon the difference of the 
particular triangles 25-3, c D' d i f t 6 , J G'gy &c. 
aliigned. 1 
Since, therefore, the values of the 7 ^s, yR\ yS'Sy 
^c. may be varied, at pleafure, by altering the fpe- 
cies of any number of correfponding triangles (2^3, 
cD'dy ^t 6 yfG'g', 7 ^ 8 , hTi-y 5 ?;- 10 , 
while the other triangles, and the values depending 
on them, remain the fame, it is manifeft, that, when 
the fum of the y ^s, anfwering to| all the triangles,, 
is a Maximum or Minimum, the fum of any num- 
ber of them, taken at pleafure (other things re- 
maining the fame), will likewife be a Maximum or 
Minimum ; and, confequently, that the fum of as 
many ^s will, at the fame time, be a Maximum or 
Minimum, becaufe y is every-where the fame, or a 
conftant quantity. 
Hence, if the confirudion of the preceding Lem- 
ma be retained (fuppofing all the ^s, R's^ S’s, 
&c. to be here expreffed as before, in terms of 
^Cy cD'y and ‘D' dy &c.) it is plain that the 
fum of all the i^’s, (or of the depending 
on the faid particular triangles (and confequently of 
all the y ^s in general), will be a Maximum or Mi- 
nimum, when the general relation of y, jy x, (or of 
J^Cy CD'y D'dy) is exprelTed by the fame equation 
g-{-er -j~/s -f- g t = o, there determined : in which 
q, r, j, /, reprefent the fluxions of Ry S, Ty di- 
vided by that of x (= a = D' d)y aS wherein the 
coefflcients Cyfygy will be conflant quantities ) be- 
caufe it is proved that their values depend intirely on 
the triangles/G'^, hliy kL ly which remain the 
fame, 
