In the Wikipedia article on lever mechanics from the Archimedes codex where
"The first proposition states:
The area of the triangle ABC is exactly three times the area bounded by the parabola and the secant line AB."
The wikipedia proof ends prematurely in my view:
"In other words, it suffices to show that $EF:GD = EH :JD$. But that is a routine consequence of the equation of the parabola. Q.E.D."
I cannot see this is obvious - in fact it seems counterintuitive since the parabola equation is quadratic while the other dimensions are linear.
Please could you see if there is a explanation for the Q.E.D bit.