The book begins with a simpler proof of the law of the lever in Proposition 1, making reference to results found in Quadrature of the Parabola. Archimedes then proves the next seven propositions by combining the concept of centre of gravity and the properties of the parabola dealt with in book one of On the Equilibrium of Planes. More importantly, he infers that two parabolas equal in area have their centre of gravity equidistant from some point, and later substitutes their areas with rectangles of equal area.[1]