T
H
E

E
L
E
M
E
N
T
S
Book VI   Proposition 30

And, since
    BC is equal to CD,
let
    CE be subtracted from each;
therefore
    the remainder BF is equal to the remainder AD.

But
    it is also equiangular with it;
therefore
    in BF, AD the sides about the equal angles are reciprocally proportional; [VI.14]
therefore
    as FE is to ED,
    so is AE to EB
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