T
H
E

E
L
E
M
E
N
T
S
Book III   Proposition 32
Next, since
    ABCD is a quadrilateral in a circle,
    its opposite angles are equal to two right angles. [III.22]

But
    the angles DBF, DBE are also equal to two right angles;
therefore
    the angles DBF, DBE are equal to the angles BAD, BCD,
of which
    the angle BAD was proved equal to the angle DBF;
therefore
    the angle DBE which remains is equal to the angle DCB in the alternate segment DCB of the circle.
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