◀ ▲ ▶Branches / Geometry / Elements-euclid / Book-12-proportional-stereometry / Proposition: Prop. 12.11: Volume of Cones or Cylinders of Same Height are in Same Ratio as Bases

Proposition: Prop. 12.11: Volume of Cones or Cylinders of Same Height are in Same Ratio as Bases

Euclid's Formulation

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 $EN$.

Modern Formulation

(not yet contributed)

Table of Contents

Proofs: 1

Mentioned in:

Proofs: 1 2 3

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References

Adapted from (subject to copyright, with kind permission)

1. Fitzpatrick, Richard: Euclid's "Elements of Geometry"

Adapted from CC BY-SA 3.0 Sources:

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