The reduction compass or proportional dividers is a geometry tool with asymmetric-length branches to allow performing

homothetic transformation In mathematics, a homothety (or homothecy, or homogeneous dilation) is a transformation of an affine space determined by a point ''S'' called its ''center'' and a nonzero number ''k'' called its ''ratio'', which sends point X to a point X' by the ...

s, reproducing a pattern while enlarging or reducing its size and conserving angles. It was invented by Fabrizio Mordente before 1567.

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. File:Reduction compass-MHS 1880-IMG 3829-gradient.jpg, Simple reduction compass on display at the

Musée d'Histoire des Sciences de la ville de Genève The ''Musée d'histoire des sciences de la Ville de Genève'' (Museum of the History of Science of the City of Geneva) is a small museum in Switzerland dedicated to the history of science. Location The museum is located in the ''Villa Bartholoni' ...

. File:Reduction compass-MHS 1914-IMG 3834-gradient.jpg, Sliding-pivot reduction compass by Nairne on London, 18th century. On display at the

. 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.

References

{{reflist Technical drawing tools Drawing aids Stonemasonry tools