The sector, also known as a sector rule, 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.
A typical English sector, probably from the early 19th century, made of ivory with a brass hinge. This side has scales for lines of lines (L), secants (S), chords (C), and polygons (POL), along with a scale of 10ths of inches on the outer edges forming a straight 12-inch rule when the sector is fully opened, and a scale of 100ths of a foot marked along the side (only barely visible in this picture).
The other side of the same sector, with scales for a line of sines (S) and two lines of tangents (T), along with logarithmic Gunter's scales for numbers (N), sines (S), and tangents (T) on the outer edges.
De fabrica et usu menti ad omnia horarum genera describenda (1592), where Giovanni Paolo Gallucci is among the first to describe the sector
Clément Cyriaque de Mangin, Usage du compas de proportion, 1637
Guidobaldo del Monte, Marquis del Monte, was an Italian mathematician, philosopher and astronomer of the 16th century.
Guidobaldo del Monte
Cover of the book Mechanicorum Liber, 1577.
