book two

problems, Props. 11 and 14.

If written in the above symbolic language, the former requires to find a line x such that a(a - x) = x^2. Prop. 11 contains, therefore, the solution of a quadratic equation, which we may write x^2 + ax = a^2. The solution is required later on in the construction of a regular decagon.

More important is the problem in the last proposition (Prop. 14). It requires the construction of a square equal in area to a given rectangle, hence a solution of the equation

x^2 = ab.

In