The bases of equal cones and cylinders are reciprocally proportional to their heights. And, those cones and cylinders whose bases (are) reciprocally proportional to their heights are equal.

- Let there be equal cones and cylinders whose bases are the circles $ABCD$ and $EFGH$, and the diameters of (the bases) $AC$ and $EG$, and (whose) axes (are) $KL$ and $MN$, which are also the heights of the cones and cylinders (respectively).
- And let the cylinders $AO$ and $EP$ have been completed.
- I say that the bases of cylinders $AO$ and $EP$ are reciprocally proportional to their heights, and (so) as base $ABCD$ is to base $EFGH$, so height $MN$ (is) to height $KL$.

(not yet contributed)

Proofs: 1

**Fitzpatrick, Richard**: Euclid's "Elements of Geometry"

**Prime.mover and others**: "Pr∞fWiki", https://proofwiki.org/wiki/Main_Page, 2016