Cotes' Theorem

Geometrical method of factoring a+ xn and x-an, when n is an integer. Describe a circle with radius a, and, fixing a diameter, divide the circumference into 2n equal parts. On the diameter lay off from the center O a distance O P = x; from P draw lines to the divisions of the circumference. Considering the distance from P to the circumference as the first in order, the odd-numbered lines will as factors form a" -x or xa, as P is within or without the circle; the even-numbered lines as factors will form a2+x". The lines can be determined trigonometrically in terms of x, a, and functions of the known arcs. n