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

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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.

Contributed by: Izidor Hafner (March 2011)
Open content licensed under CC BY-NC-SA

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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'sElements: 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.

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