Proof of Proposition 28, Book XI, Euclid's Elements

This Demonstration shows a proof by dissection of Proposition 28, Book XI of Euclid's Elements:
if a parallelepiped is cut by a plane through the diagonals of the opposite planes, then the solid is bisected by the plane.

THINGS TO TRY

SNAPSHOTS

  • [Snapshot]
  • [Snapshot]
  • [Snapshot]

DETAILS

The blue and the orange prisms are only symmetrical; to prove that they are equivalent, certain propositions are needed [2].
[1] D. E. Joyce, "Euclid's Elements: Introduction."
[2] Euclid, Elements, T. L. Heath, trans., as The Thirteen Books of Euclid’s Elements, 2nd ed., Book 3, New York: Dover Publications, 1956 pp. 332–333.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.