To construct an equilateral triangle on a given finite straight line.
Let AB be the given finite straight line.
We start with a line segment AB. This is our given, and we will construct an equilateral triangle with AB as one of its sides.
With center A and radius AB, describe the circle BCD.
With center B and radius BA, describe the circle ACE.
Let C be the point where the circles intersect.
Join CA and CB.
Triangle ABC is equilateral.