as are terminated by Planes, &c, 
greatest attraction : viz. 
~ + Cf(x)' 
299 
0. 
(x*+y*+f(xyr- 
Prop. 36. 
To solve Prop. 32, the force being supposed inversely as 
the mi h power of the distance, and the generating polygon 
being composed of triangles having such a law of density as 
that in the scholium to lemma 3. 
By using the value found in that scholium, and proceeding, 
in other respects, as in the similar propositions already given, 
we find, for the equation of the curve touching the sides of 
the polygon, 
(x 2 + (i +r*)yy 
— + Cry = 0 . 
Prop. 37. 
Let Prop. 32 be yet once more resolved, on the supposition 
that the force is inversely as the mth power of the distance ; 
and the density, in the triangles forming the generating poly- 
gon, either uniform, or as any function of x and T. 
If we make use of the first value of A in lemma 3, we get, 
for the equation of the curve touching the sides of the polygon, 
+ (8-w) U-m) 
(x*+y % )(**+(i+r*)y*)‘ 
rV See . } + C 
0. 
3-5 (x'-ry 1 ) 2 
When r = 0, or the polygon becomes a circle, this equation is 
reduced to 
(x*+y 2 ) m -± 
ner, in Cor. 1, Prop. 33 
- -j- C = 0, as was found in another man- 
