To bisect a given circumference.

Let *ADB* be the given circumference.

It is required to bisect the circumference *ADB.*

Join *AB,* and bisect it at *C.* Draw *CD* from the point *C* at right angles to the straight line *AB.* Join *AD* and *DB.*

Then, since *AC* equals *CB,* and *CD* is common, the two sides *AC* and *CD* equal the two sides *BC* and *CD,* and the angle *ACD* equals the angle *BCD,* for each is right, therefore the base *AD* equals the base *DB.*

But equal straight lines cut off equal circumferences, the greater equal to the greater, and the less to the less, and each of the circumferences *AD* and *DB* is less than a semicircle, therefore the circumference *AD* equals the circumference *DB.*

Therefore the given circumference has been bisected at the point *D.*

Q.E.F.