|Book VI Proposition 2|
the triangle ADE is another area.
But equals have the same ratio to the same; [V.7]
as the triangle BDE is to the triangle ADE,
so is the triangle CDE to the triangle ADE.
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.
as BD is to DA,
so is CE to EA. [V.11]
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