T
H
E

E
L
E
M
E
N
T
S
Book III   Proposition 1
    Let a straight line AB be drawn through the circle at random,
and
    let it be bisected at the point D;
from D
    let DC be drawn at right angles to AB and let it be drawn through to E;
    let CE be bisected at F.

I say that F is the center of the circle ABC.
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