Main theorem The Quadrature of the Parabola

archimedes inscribes triangle given parabolic segment.

a parabolic segment region bounded parabola , line. find area of parabolic segment, archimedes considers inscribed triangle. base of triangle given chord of parabola, , third vertex point on parabola such tangent parabola @ point parallel chord. proposition 1 (quadrature of parabola), line third vertex drawn parallel axis divides chord equal segments. main theorem claims area of parabolic segment 4/3 of inscribed triangle.