6 INTRODUCTION 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. O Figure 6 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.

Purchased from American Mathematical Society for the exclusive use of nofirst nolast (email unknown) Copyright 2008 American Mathematical Society. Duplication prohibited. Please report unauthorized use to cust-serv@ams.org. Thank You! Your purchase supports the AMS' mission, programs, and services for the mathematical community.