36 INVESTIGATION of fome 
WHEREFORE, the fum of the cubes of the perpendiculars, 
drawn from the point D to the fides of the figure, is = Nx 734 
6+ x DM + DV + DH’ + DN’ =NXr +67 x DS 
This is Prop. 23. Srewart’s Theor. When DG =7, the fum 
of the cubes of the perpendiculars is = N X 5 x nm=N x 
Sen 73, This is Prop. 22. Dr Srewart’s Theor. 
Wuen DG =, , or D coincides with A, she fum of he cubes 
AC’ 
-of the petpaneiculats is) egiral, tac — a ae am i &c.; 
and, confequently, we get AG’ 7 AB. ok AT Ae, Be 58 
— “.2@Br=NX20 Xr = 
XN Sr 9ENGEX 20178!= 
N X lor? X SOT ATE 4, 
Ir, therefore, the circumference of a circle be divided into an 
even number of equal parts, and from the points of divifion 
chords be drawn to any point in the circumference, the fum of 
the fixth powers of thefe chords is equal to the fum of their 
fquares, multiplied by ten times the fourth power of radius. 
7+DM' 7 i. =artt 1277 DM +2>x DM", 
FEDV' Fr DV = art+327°x DV + 2x DV, 
77 DH hr DA = art-+ yar x DA +2 DA’, 
7--DN'+r—DN = oe 127°x DN +2 DN. 
WHEREFORE 
