o 
.. . , [ 395 ] 
Now, in order to 
reduce the forego- 
ing rule to practice, 
we muff find the 
value of the area 
of the figure de- 
fcribed and the fe- 
veral parts of it fe- 
parated, by ordi- 
nates perpendicu- 
lar to its bafe. For 
which purpofe, fuppofe A H — i and H O the 
fquare upon AH likewifecrr i, and Cf will be— y t 
and Af~ x , and Hfy=z r, becaufe y, x and r denote 
the ratios of C f A f and Ilf refpedively to A H. 
And by the equation of the curve y — x p r q and (be- 
caufe Aff-J H — AH) r x — i. Wherefore 
y — x p x i-x\ q ~ x p — qx -\-qX q— 1 X x — q 
X q-f X g —2 x x + Sec. Now the abfcifTe being 
* 3 P ' /.q-i 
x and the ordinate x the correfpondent area is x 
(by prop. io. caf. i. Quadrat. Newt.) * and the ordi- 
P+-* # /> + 2 
nate being qx the area is qx ; and in likeman- 
~P + 2 
* *H S very evident here, without having recourfe to Sir Ifaac 
Newton, that the fluxion of the area AC f being yx—x f x — 
P + i p+2 
1 x * + ? * x x &c. the fluent or area itfelf is x ^ > ^~ I 
x* 
x X? + 3 &C. 
p+ 
P + 2 
P + 3 
ner 
