Proposition: Prop. 12.06: Sizes of Pyramids of Same Height with Polygonal Bases are as Bases

(Proposition 6 from Book 12 of Euclid's “Elements”)

Pyramids which are of the same height, and have polygonal bases, are to one another as their bases. * Let there be pyramids of the same height whose bases (are) the polygons $ABCDE$ and $FGHKL$, and apexes the points $M$ and $N$ (respectively). * I say that as base $ABCDE$ is to base $FGHKL$, so pyramid $ABCDEM$ (is) to pyramid $FGHKLN$.

fig06e

Modern Formulation

(not yet contributed)

Proofs: 1

Proofs: 1


Thank you to the contributors under CC BY-SA 4.0!

Github:
bookofproofs
non-Github:
@Fitzpatrick


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