Proposition: 1.39: Triangles of Equal Area III
(Proposition 39 from Book 1 of Euclid's “Elements”)
Equal triangles which are on the same base, and on the same side, are also between the same parallels.
* Let $ABC$ and $DBC$ be equal triangles which are on the same base $BC$, and on the same side (of it).
* I say that they are also between the same parallels.
Modern Formulation
Triangles (\(\triangle{BAC}\), \(\triangle{BDC}\)), which are equal in area and stand on the same base (\(\overline{BC}\)) and on the same side of the base also stand between the same parallels (\(\overline{AD}\), \(\overline{BC}\)).
Table of Contents
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Proofs: 1
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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"