Pantometria — A Geometrical Treatize of Measuring

A woodcut illustration showing a stone tower (labeled with points A, B, and G) being measured by an observer at point E. A vertical measuring staff is placed at point C, with point F marking the line of sight from E to the top of the tower B. In the background, two figures stand near a cluster of trees. Lines are drawn to demonstrate geometric proportions for calculating altitude.

The distance DC will always retain the same proportion to DE as BF does to AB. Therefore, if you measure BF, you may, by the Rule of Three Also known as the Golden Rule; a method of finding a fourth number proportional to three given numbers., obtain the height of AB; or conversely, if you know the altitude AB, you may proportionally learn the length FB. This method is more pleasant to practice than the former and is the most exact for altitudes. However, whereas some use this method for both lengths and distances, making the staff a common side for both the greater and lesser triangles, I do not approve of it. The angle made with the square and staff grows so acute and imprecise that the slightest mistake results in a great error.

A geometric diagram showing a tower on the right (A-B). A large triangle is formed with its vertex at point F on the ground. Within this large triangle, a smaller triangle (C-D-F) is formed by two tools labeled "Squire" and "Staff." Point E is also marked on the horizontal ground line.