In an essence, using normal straightedge and compass construction, we can add, subtract, multiply, divide and find a square root. This means that we can find the real roots of a quadratic equation with rational coefficients because the quadratic formula consists of only these operations. The easy and fast way to do this would be http://www.concentric.net/~pvb/ALG/rightpaths.html" [Broken]. We can also deduce that we can't solve cubic equations because the cubic formula also includes finding a cubic root. However, with neusis construction we can find the real roots of cubic equations because it can find a cube root. Does anyone know how we could solve the general cubic equation using neusis? Preferably an extension to Lill's Method. PS: This was my topic for my http://en.wikipedia.org/wiki/Extended_essay" [Broken], and I've already handed it in. This is just further (personal) research. JPM.