Sector by Aston and Mander, London
Galileo Galilei popularized the sector at the end of the 16th century.
The sector's vital feature is a pair of jointed legs, which carry paired geometrical scales.
In use, problems are set up using a pair of dividers to determine the appropriate opening of the jointed legs and the answer is taken off directly as a dimension using the dividers.
The sector may be used to calculate squares, cubes, reciprocals and tangents of numbers.
Galileo's design of the sector as a mathematical tool heralded the moment when calculation aids ceased to be based on counting and instead exploited the deeper relationships among numbers.
His invention was still in use as a navigation aid in the 20th century, 300 years later.