The third book, "On the Construction of Solid and Supersolid Problems", is more properly algebraic than geometric and concerns the nature of equations and how they may be solved. He recommends that all terms of an equation be placed on one side and set equal to 0 to facilitate solution. He points out the factor theorem for polynomials and gives an intuitive proof that a polynomial of degree has roots. He systematically discussed negative and imaginary roots of equations and explicitly used what is now known as Descartes' rule of signs.