This is one of the most useful and most used simple constructions. Erecting a perpendicular line on a right line is the first step in many of the other more complex constructions and is no end of necessary in all phases of drawing both field and permanent fortifications of the nineteenth century. It is highly recommended that anyone interesting in pursuing this subject beyond a few brief glances at the material commit this construction to memory by persistent practice.

Given a right line AB construct a line that is perpendicular to Line AB.

Select any point (C) on Line AB. Using Point C as center describe two arcs of circles of any radius that cut Line AB on both sides of Point C at Points E and F.

Opening the compass to a length equal to the distance between Points E and F and using Points E and F as centers, describe two arcs of circles above Point C that intersect at Point G.

Produce a right line that passes through Point C and Point G.

Line CG will be perpendicular to Line AB.

~ An Instructive Animation Wherein the Foregoing Construction is Visually Explained ~