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
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References
Adapted from CC BYSA 3.0 Sources:
 Callahan, Daniel: "Euclid’s 'Elements' Redux" 2014
Adapted from (Public Domain)
 Casey, John: "The First Six Books of the Elements of Euclid"
Adapted from (subject to copyright, with kind permission)
 Fitzpatrick, Richard: Euclid's "Elements of Geometry"