Archimedes’ ‘Quadrature of the Parabola’, Prop1

by Corry Shores
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Archimedes

Quadrature of the Parabola

Proposition 1 [quoting]

If from a point on a parabola a straight line be drawn which is either itself the axis or parallel to the axis, as PV,

and if QQ' be a chord parallel to the tangent to the parabola at P and meeting PV in V,

then QV=VQ'.

Conversely, if QV=VQ', the chord QQ' will be parallel to the tangent at P.

Archimedes. “Quadrature of the Parabola.” In The Works of Archimedes. Ed. T.L. Heath. Cambridge UP, 1897. Obtained at

https://archive.org/details/worksofarchimede00arch