Proposition: Prop. 11.29: Parallelepipeds on Same Base and Same Height whose Extremities are on Same Lines are Equal in Volume
(Proposition 29 from Book 11 of Euclid's “Elements”)
Parallelepiped solids which are on the same base, and (have) the same height, and in which the (ends of the straight lines) standing up are on the same straight lines, are equal to one another.
* For let the parallelepiped solids $CM$ and $CN$ be on the same base $AB$, and (have) the same height, and let the (ends of the straight lines) standing up in them, $AG$, $AF$, $LM$, $LN$, $CD$, $CE$, $BH$, and $BK$, be on the same straight lines, $FN$ and $DK$.
* I say that solid $CM$ is equal to solid $CN$.
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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