Proof: By Euclid
(related to Proposition: 3.21: Angles in Same Segment of Circle are Equal)
 For let the center of circle $ABCD$ have been found [Prop. 3.1], and let it be (at point) $F$.
 And let $BF$ and $FD$ have been joined.
 And since angle $BFD$ is at the center, and $BAD$ at the circumference, and they have the same circumference base $BCD$, angle $BFD$ is thus double $BAD$ [Prop. 3.20].
 So, for the same (reasons), $BFD$ is also double $BED$.
 Thus, $BAD$ (is) equal to $BED$.
 Thus, in a circle, angles in the same segment are equal to one another.
 (Which is) the very thing it was required to show.^{1}
∎
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References
Adapted from (subject to copyright, with kind permission)
 Fitzpatrick, Richard: Euclid's "Elements of Geometry"
Footnotes