Proposition: Prop. 12.11: Volume of Cones or Cylinders of Same Height are in Same Ratio as Bases
Cones and cylinders having the same height are to one another as their bases.
* Let there be cones and cylinders of the same height whose bases [are] the circles $ABCD$ and $EFGH$, axes $KL$ and $MN$, and diameters of the bases $AC$ and $EG$ (respectively).
* I say that as circle $ABCD$ is to circle $EFGH$, so cone $AL$ (is) to cone $EN$.
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Table of Contents
Proofs: 1 2 3
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Adapted from (subject to copyright, with kind permission)
- Fitzpatrick, Richard: Euclid's "Elements of Geometry"
Adapted from CC BY-SA 3.0 Sources:
- Prime.mover and others: "Pr∞fWiki", https://proofwiki.org/wiki/Main_Page, 2016