It is divided by its midpoint into two smaller arcs, of which one consists of
those points M on the arc for which the arc AM is greater than MB, the other of
points for which AM is smaller than MB.
9. Two points of a circle are diametrically opposite (A, B, Fig. 6) if the line
which joins them passes through the center. This segment is called a diameter. It
is clear that a diameter has a length twice that of a radius.
A circle is clearly determined when we are given one of its diameters. Its center
is then the midpoint of the diameter.
A diameter AB divides a circle into two arcs, which are, respectively, the por-
tions of the circle situated in the two half-planes determined by line AB. These two
arcs are equal: we can make them coincide by superimposing the two half-planes
in question (6). Thus we have two semicircles.
In the same fashion, a disk is divided by a diameter into two equal parts, which
can be superimposed in the same manner as the semicircles.