 Given a line segment AB containing point C (see  figure 6),  the problem is to produce AB to D such that the product AD\(\times\)DB is equal to the square of CD. Let AC \(= a\), CB \(= b\), and BD \(= x\), which yields AD \(= a + b + x\) and CD \(= b + x\). Thus, the problem to find BD such that AD\(\times\)DB = (CD)\(^2\) is algebraically equivalent to finding \(x\) such that: \((a + b + x)\times(x) = (b + x)^2\). Or, solving for \(x\), the problem is to find \(x\) such that, given \(a\) and \(b, x = b^2 / (a\)—\(b)\).