### The quadrature of the parabola

In the treatise The Quadrature of the Parabola, Archimedes determines the ratio between the area of a parabolic segment and that of a triangle having the same base and height. This demonstrates that a parabolic segment is 1/3 of the right-angled triangle with the same base, one side perpendicular to the base and the other tangent to its second extreme. In the Method Archimedes demonstrates this result by separating the two figures into their constituent segments and using the Law of the Lever and knowledge of the centre of gravity of the triangle.