12 Apr 2014

Archimedes’ ‘Quadrature of the Parabola’, Prop19

Corry Shores
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Quadrature of the Parabola

Proposition 19 [quoting]


If Qq he a chord of a parabola bisected in V by the diameter PV, and if RM he a diameter bisecting QV in M, and RW be the ordinate from R to PV, then

PV = 4/3 RM.

For, by the property of the parabola,

PV : PW = QV2 : RW2

= 4RW2 : RW2,

so that PV=4PW,

whence PV =4/3RM.


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



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