[ 6 2 6 ] 
manifeft, that the whole required fluent cannot' be & 
maximum or minimum , unlefs this part, fuppofing the 
bounding ordinates EL, GN to remain the fame, is 
alfo a maximum or minimum. Hence, in order to 
determine the fluxion of this expreffion Rr 
&c. £^q"+ R"r' &c.) which muff, of confequence, 
be equal to nothing, let the fluxions of ^ and q' 
(taking a and u as variable) be denoted by and. 
q u alfo let R d and ~ r u denote the refpedtive flu- 
xions of R and r j and let, in like manner, the flu- 
xions of q", R"y r", &c. be reprefented by"^/3’, 
q w, Rfi, rW, &c. refpe&ively. Then, by the com- 
mon rule for finding the fluxion of a redlangle, the- 
fluxion of our whole expreffion + R'r' + 
££ 'q llj r R"r" &c.) will be given equal to u '-\- 
q R r u -\- r R <x &c. -f- -f- q Qf 3* -fi 
R'fw + r"Rl 2' &c.= o. 
But u -\- w being = G N — EL, and /3 — a = 
G A — R_ L ^ con ft; an t quantity), we therefore have 
w — — u, and fd = d : alfo u being (= i r p') = 2 ^ 
— 2 EL, thence will u'—zd: which values being 
fubftituted above, our equation, after the whole is. 
divided by d, will become 
2 ^q + q 4L“b 2 R' r -\- r r, &c. — 2 + q 
2 R r + r R, = O i 
6r, % } — + R" r—R'-r &C. = 1 1,+ 'LL 
+ tl+LI, 
2 
But 
