Pantometria — A Geometrical Treatize of Measuring

The First Book

The First Chapter.

How perpendiculars upon any straight line are created.

To create a perpendicular or plumb line on line AB at point C: Open your compass, place one foot in C, and make a mark on either side of the line at D and E. Now, extend the compass to the width of the distance between these two points (or slightly more). Placing one foot in D, make an arc above and below C. Then, move the compass to E (keeping it set to the same width), place one foot there, and cross the arcs previously made above and below C, marking two points (or labels F and G). Use a ruler to draw a line through points F, C, and G. Thus, you make your plumb or square line FCG. In this same manner, any line may be divided in half, or a circle in four equal parts. See the example following.

A geometric diagram showing a straight line AB intersected by a perpendicular line FCG, with an oval shape formed by two intersecting arcs.

The Second Chapter

How perpendicular or hanging lines are drawn from a point assigned to any straight line lying in the same plane surface.

Suppose C is the point from which I would let fall a perpendicular to the straight line AB. Open your compass wide enough that, when placing one foot in C, you can reach beyond the line AB. Draw an arc that intersects the line at two points, which in this figure are marked D and E. Now, placing one foot of your compass in E...