AND ON DEFINITE INTEGRATION. 477 
Now, if we describe the curve A P, P, &e., &c., 
whose equation is Y=f(or), w being measured 
along the line AB,, and Y perpendicular to it ; 
and at equal intervals AB,; AB, &c., &c. 
draw the corresponding ordinates P,B,; P,B., 
&e., &c. Then, from equation (10), we have 
- f}e (+h) =A, +(A+H’)) f (ow) -f(ey)}+ 
(B+ an'+ mS #(0x)—f(ay)} +(Bh’+AN"+ 1°) 
; f (ow) ~ f (ey) h+(D+B0 +A 4h \f f (aw) 
Til 
—f (ay) + BiG) OLE tec eh eee tees ae ss (11) 
where A, is the area of the curve B, P, P. B,. 
Hence it appears, that if we, now, sum the 
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