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.
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.