Reduction compass

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]

Late 19th-century reduction compass

Use and principleEdit

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.


  1. ^ "Reduction Compass". Epact. Museum of the History of Science, Oxford. Retrieved 10 January 2022.
  2. ^ "Reduction compass". Galileo Virtual Museum. Museo Galileo - Institute and Museum of the History of Science. Retrieved 10 January 2022.