One 7 1/2-inch brass sector by Anthonius Hoevenaer, Leiden, Holland, 1720-1760

Sectors were the ultimate instrument of proportion. Invented simultaneously by Galileo and Thomas Hood at the end of the 16th century, they enabled many calculations to do with scaling and ratios. While Galileo’s sector was aimed at military gentlemen, it included many lines that were not overtly useful. A preoccupation with Platonic solids is apparent. The lines marked with these figures give the length of side of the five regular solids that can be inscribed in the sphere S, and the length of sides necessary for all the solids to have the same volume.