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Book VI   Proposition 2
Therefore
    each of the triangles BDE, CDE has the same ratio to ADE.
Therefore
    the triangle BDE is equal to the triangle CDE; [V.9]
and
    they are on the same base.

But equal triangles which are on the same base
    are also in the same parallels. [I.39]
Therefore
    DE is parallel to BC.
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