From the extreme points of the right line A, B, with radii less than
the length of the line describe two arcs intersecting each other at
C and D, and through the points of their intersection draw the line,
which will be perpendicular to the given right line at the middle.
[Illustration: _Fig. 2_]
In this way, too, may any line be divided into too equal parts with
facility and exactness.
PROBLEM III. _To erect a perpendicular at or near the end of a given
right line._
[Illustration: _Fig. 3_]
Take any point, D, on the given right line A, B, as a centre, and to
the required point C, as a radius, and describe an arc C, E, F. Take
a portion of this arc, say E, and make from C, E, equal to E, F. Join
F and C. Now with E, C, for a radius, describe the arc G, E, H, and
make from E to H equal to from E to G. Then through H from C draw the
perpendicular required.
There are other methods of accomplishing this, but we will not
introduce them here, as the one now given is sufficient.
We will now proceed to the formation of geometrical figures which
enclose space.
That which is bounded by one line is called a _circle_; and a right
line dividing it into two equal parts is called its _diameter_; from the
centre of which to either end is called the _radius_: and the boundary
line is termed the _circumference_ from the Latin words _circum_,
around, and _fero_ to carry. That is: a line carried around. Thus we
see an area or space is enclosed by one line. An area may be enclosed
by two lines; but one, or both of them, must be curved; as two right
lines cannot enclose a space. But three can; and the figure is called a
_triangle_.