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Book VI   Proposition 3
For,
    with the same construction,
since
    as BD is to DC, so is BA to AC
and also,
    as BD is to DC, so is BA to AE:
for AD has been drawn parallel to EC, one of the sides of the triangle BCE; [VI.2]
therefore also,
    as BA is to AC, so is BA to AE. [V.11]
Therefore
    AC is equal to AE, [V.9]
so that
    The angle AEC is equal to the angle ACE. [I.5]
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