T
H
E

E
L
E
M
E
N
T
S
Book III   Proposition 5
Now,
    each of EF, EG was proved equal to EC;
therefore
    EF is also equal to EG,
the less to the greater: which is impossible.

Therefore
    the point E is not the center of the circles ABC, CDG.

Being what it was required to prove.
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