Eukleides, Základy, Kniha II. Věta 5

If a straight line is cut into equal and unequal segments, then the rectangle contained by the unequal segments of the whole together with the square on the straight line between the points of section equals the square on the half.
This proposition is set up to help in the solution of a quadratic problem of the following form. Find two numbers x and y so that their sum is a known value b and their product is a known value c\sub{2}. In terms of the single variable x, this is equivalent to solving the quadratic equation, x(b – x) = c\sub{2}.