as are terminated by Planes , &c. 
*57 
plied by 2 n is me -!= == nit 7== by putting tt for 
r J Va z +b z Va z -\-b z 
nr. If we substitute this value in the expression for a regular 
polygon, it becomes A = 27? £ 1 — ===== j , the well known 
expression of Newton. 
§• II. 
Of the Attraction of Pyramids, and generally of any Solids what - 
ever that are bounded by Planes . 
The simplest case of the attraction of such bodies as we are 
to consider, is that of a pyramid with the attracted point at 
the vertex : and it fortunately happens, that on this simple 
case the action of any body whatever may be made to depend ; 
which is the reason of my placing the general problem in this 
section, though I afterwards treat separately of prisms. 
This facility, in the case of pyramids, results from what 
was shewn in Cor. 1. Prop. 1, viz. that if we put x for a and 
mx for 6, in the functions <p [a, b, r), % (a,b, r), ip ( a , b , r), they 
will become <p (1 ,m,r), % (1, m, r) (1 , m, r), into which x 
does not enter. 
Prop. 7. 
Let figure 5 represent a pyramid with a triangular base 
umv, the vertex p of the solid being in a line pm, perpendi- 
cular to the triangle at the angular point m. It is required to 
find the action of the pyramid on a point at that vertex. 
Draw the perpendicular mr, also pg, po parallel to mr, rv. 
Join pr, and let r'm' be parallel to rm. Call pm', x; r'm', y; 
then y = mx, m being the tangent of the angle rpm. The 
attraction of a triangular section of the solid, made by a plane.. 
