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the triangle ADE is another area.
But equals have the same ratio to the same; [V.7]
therefore
as the triangle BDE is to the triangle ADE,
so is the triangle CDE to the triangle ADE.
But
As the triangle BDE if to ADE, so is BD to DA;
for being under the same height, the perpenticular drawn from E to AB, they are to one another as their bases. [VI.1]
For the same reason also,
as the triangle CDE is to ADE, so is CE to EA.
Therefore also,
as BD is to DA,
so is CE to EA. [V.11]
