The sector, also known as a proportional compass or military compass, was a major calculating instrument in use from the end of the sixteenth century until the nineteenth century. It is an instrument consisting of two rulers of equal length joined by a hinge. A number of scales are inscribed upon the instrument which facilitate various mathematical calculations. It was used for solving problems in proportion, multiplication and division, geometry, and trigonometry, and for computing various mathematical functions, such as square roots and cube roots. Its several scales permitted easy and direct solutions of problems in gunnery, surveying and navigation. The sector derives its name from the fourth proposition of the sixth book of Euclid, where it is demonstrated that similar triangles have their like sides proportional. Some sectors also incorporated a quadrant, and sometimes a clamp at the end of one leg which allowed the device to be used as a gunner's quadrant. History The sector was invented, essentially simultaneously and independently, by a number of different people prior to the start of the 17th century. Fabrizio Mordente (1532 – ca 1608) was an Italian mathematician who is best known for his invention of the "proportional eight-pointed compass" which has two arms with cursors that allow the solution of problems in measuring the circumference, area and angles of a circle. In 1567 he published a single sheet treatise in Venice showing illustrations of his device. In 1585 Giordano Bruno used Mordente's compass to refute Aristotle's hypothesis on the incommensurability of infinitesimals, thus confirming the existence of the "minimum" which laid the basis of his own atomic theory. Credit for the invention is often given to either Thomas Hood, a British mathematician, or to the Italian mathematician and astronomer Galileo Galilei. Galileo, with the help of his personal instrument maker Marc'Antonio Mazzoleni, created more than 100 copies of his military compass design and trained students in its use between 1595 and 1598. Of the credited inventors, Galileo is certainly the most famous, and earlier studies usually attributed its invention to him. The scales The following is a description of the instrument as it was constructed by Galileo, and for which he wrote a popular manual. The terminating values are arbitrary and varied from manufacturer to manufacturer. The arithmetic lines The innermost scales of the instrument are called the arithmetic lines from their division in arithmetical progression, that is, by equal