Proposition: 1.40: Triangles of Equal Area IV
(Proposition 40 from Book 1 of Euclid's “Elements”)^{1}
Equal triangles which are on equal bases, and on the same side, are also between the same parallels.
 Let $ABC$ and $CDE$ be equal triangles on the equal bases $BC$ and $CE$ (respectively), and on the same side (of $BE$).
 I say that they are also between the same parallels.
Modern Formulation
Triangles which are equal in area (\(\triangle{ABC}=\triangle{DCE}\)) as well as stand on equal bases (\(\overline{BC}\), \(\overline{CE}\)) and on the same side of their bases stand on the same parallels (\(\overline{AD}\parallel\overline{BE}\)).
Table of Contents
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"
Footnotes