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Proposition: 1.37: Triangles of Equal Area I

(Proposition 37 from Book 1 of Euclid's “Elements”)

Triangles which are on the same base and between the same parallels are equal to one another.

• Let $ABC$ and $DBC$ be triangles on the same base $BC$, and between the same parallels $AD$ and $BC$.
• I say that triangle $ABC$ is equal to triangle $DBC$.

Modern Formulation

Triangles (\(\triangle{ABC}\), \(\triangle{DBC}\)) on the same base (\(\overline{BC}\)) and standing between the same parallels (\(\overline{AD}\), \(\overline{BC}\)) are equal in area.

Table of Contents

Proofs: 1

Mentioned in:

Proofs: 1 2

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

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@Calahan

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References

Adapted from CC BY-SA 3.0 Sources:

1. Callahan, Daniel: "Euclid’s 'Elements' Redux" 2014

Adapted from (Public Domain)

1. Casey, John: "The First Six Books of the Elements of Euclid"

Adapted from (subject to copyright, with kind permission)

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