54 INVESTIGATION of fome’ 
fides of the figure, is — Nxr'+2xGa+Gb +Ge + Gad’. 
But fince the angles GaA, GSA, Ge A, GdA, are right ones, 
a circle paffes through the points A, a, 4, G, c, d. having GA 
for its diameter. And becaufe the angles CGT, QGC, LGQ; 
are equal, this circle is equally divided by the points a, 4, ¢, d. 
Confequently the fquares of the chords drawn from thefe 
points to the point A, are together = N X Ss, that is, Ac (Ga) 
RO EE pe GR 
4+ Aa (Gc) + Ad (Gb) + Ab (Gd) = Nx p= 
N X : Wherefore the fum of the fquares of the perpendicu- 
lars drawn from A to the fides of the figure, is = N Xr +2N 
x : — Nx 3. But the fum of the fquares of thefe perpen- 
AC’, AB’, AT. AS | AL | AE’ AQ’ 
4r° Ar 4r Ate 4r 4r° 4r 
diculars is = 
AR’ Therefore AC’ + AB’ +, &c. => NX67r+= N X27% 
x3r= AG +. AB +, &c. X 37°... Whence this propofition: 
Ir a circle be divided into any-even number of parts, and 
from the points of divifion chords be drawn to any point in the 
circumference, the fum of the fourth powers of thefe chords is 
equal to the fum of their fquares, multiplied by.thrice the fquare 
of radius. 
WHEREFORE 
