In a circle the angles in the same segment are equal to one another
be a circle, and let the angles BAD
be angles in the same segment BAED
; I say that the angles BAD
are equal to one another.
For let the centre of the circle ABCD
be taken, and let it be F
Now, since the angle BFD
is at the centre, and the angle BAD at the circumference, and they have the same circumference BCD as base, therefore the angle BFD is double of the angle BAD. [III. 20]
For the same reason the angle BFD is also double of the angle BED; therefore the angle BAD is equal to the angle BED.
Therefore etc. Q. E. D.