Parabolic segment area

A parabolic segment is the region bounded by a parabola and line. To find the area of a parabolic segment, Archimedes considers a certain inscribed triangle. The base of this triangle is the given chord of the parabola, and the third vertex is the point on the parabola such that the tangent to the parabola at that point is parallel to the chord. Move points A and B and look at the values of the areas. The blue triangle area is always 1/8 of the red one and the green triangle area is 1/8 of the blue one!