Infinite Series * 1 6 1 
equation which finds the approximate to x will be a quadratic 
or an equation of n dimenfions. 
3. The approximations found by this method will converge 
more or lefs, according as the approximations given are more 
or lefs near to one value of each of the unknown quantities 
than to the remaining ones, &c. 
Thefe principles were printed in the Medit. Algebr. in the 
years 1768 and 1769, 
LEMMA. 
1 5. Let kab (fig. 3.) be a circle, whofe center is 0 ; and P 0 per- 
pendicular to the plane of the circle; and the force of any cor- 
pufcle in the circle on the particle P vary as the corpufcle 
divided by the (#) power of its diftance from the particle ; to 
find the attra&ion of the circle kab on the particle P. 
From the fuppofita the force of any ring contained between 
the neareft concentric circles led and hef of which the center 
is o 9 on the particle P, will be as /the area of the ring divided 
by the nth power of the diftance Vh; and confequently if 
Vo n A, obzzv, hl=zVy and p « periphery of a circle of which 
the radius is l ; the attraction of the ring on P will be as 
- p * ■ *— , and the force of it in the dire&ion Vo as ~ x 
I 
(A 4 + w*) a 
— . » of which fluxion the fluent is 
n n -j- j ' 
(A* + ^) r (A*+V)' r 
— ; and thence the force of the circle kab on the 
M 't * 
i — « x ( A ’-+^) 2 
particle P will be as = 1 * - - — - ) • 
1 i _ i - nPO 1 V i - «A" V 
Vol. LXXXI; Z 
Cor. 
