Archimedes Mechanical Demonstration
Any segment of a section of a right angled cone (i.e., a parabola) is four thirds of the triangle that has the same base and equal height.
Seg CBA is 4/3 of ∆CBA. Mechanically, seg. CBA is in equilibium with ∆CFA when the segment is placed at H and the triangle at W (its center of gravity) and the balance point is at K. WK is 1/3 of KH. ∆CBA is 1/4 ∆CFA.