Reduction compass explained

The reduction compass or proportional dividers is a geometry tool with asymmetric-length branches to allow performing homothetic transformations, reproducing a pattern while enlarging or reducing its size and conserving angles. It was invented by Fabrizio Mordente before 1567.^[1]

Use and principle

The reduction compass is made of two branches, with two points each. Several types exist, including the following:

• simple reduction compass: the pivot is fixed, and the enlargement factor is determined by the length difference between the small and long end of the branches;
• mobile-headed reduction compass: the pivot is mounted on a slide, and its position determines the enlargement factor.^[2]

The underlying principle is that of proportionality of the sides of two similar isosceles triangles.

The reduction compass was customarily used in geography to change the scale of maps.

Notes and References

1. Web site: Reduction Compass . Epact . Museum of the History of Science, Oxford . 10 January 2022.
2. Web site: Reduction compass . Galileo Virtual Museum . Museo Galileo - Institute and Museum of the History of Science . 10 January 2022.