Archimedes’ ‘Quadrature of the Parabola’, Prop19

by Corry Shores
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Archimedes

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

https://archive.org/details/worksofarchimede00arch