6^# -J- 2x 3 
(i — *) J x (j+ *) 5 
6 x 
magnitudes, = 
[ 396 ] 
t | ' 
; and, rejeding the infinitely fmall 
Therefore the moment wherewith the four points 
g, g\ y, y , caufe the point / to turn, will, by lubfti- 
tuting in the place of the letters their analytical va- 
(yX 
lues, b e. (odu — rdu)xSxyx — ; or putting, in- 
deed of ^andr, the values above found, we fhall 
have for the moment ( — z'z — — zz jxdaxSx yx 
\ a ay 
6 x 6 a 5 \ , 1 N-n 
= — — x y x d u x [z 4 - z) x (z — z). But 
s 3 s*a ' 
z -J- z = y M -j~ g m = 2 y G = 2 y V ■, and z — z 
— y M — g m — 2 G M — 2C N — 2 x u. There- 
fore (z' -f- z) x (55' — z) = 4. Vu x y ; and the mo* 
• 6 a 5 _ , ba^S rr > 
ment is — — x ± V uxx xy du — — —x/l Vu xxxdxu. 
s 3 y s 3 
But in the circle D g I we have y d u = a d x, and 
, . (Sab . 6 a.S _ . 
the moment is — — x^v u xxxy d * = — x 4, Vuxdx 
V aa — xx. But the integral o f x 1 d x V aax x is 
x 
a af d x V aa — xx {a a — x x) % and when 
x — a , this integral is \ aa f d x V aa — xx , or, cal- 
ling the ratio of the circumference to the diameter 77 
we fhall have f d x V aa — xx, or the area of the qua- 
drant whereof a is the radius, = ~ a ?r x ; a — a 1 x. 
6^ S ** 
Therefore the integral of — - x 4 . V u x x x d x 
y/ aa 
