and let AD, DB be joined.
Then, since AC is equal to CB, and CD is common, the two sides AC, CD are equal to the two sides BC, CD; and the angle ACD is equal to the angle BCD, for each is right; therefore the base AD is equal to the base DB. [[I. 4](elem.1.4)]

But equal straight lines cut off equal circumferences, the greater equal to the greater, and the less to the less; [[III. 28](elem.3.28)] and each of the circumferences AD, DB is less than a semicircle; therefore the circumference AD is equal to the circumference DB.

Therefore the given circumference has been bisected at the point D. Q. E. F.