Sector, in geometry, the portion of the area of a circle included between two radii and an arc. The instrument called by this name is used for solving mechanically numerous questions of proportions in geometry and trigonometry. It is called by the French the compass of proportion. It is made of two strips of ivory, wood, or metal, each of them 6 in. or a foot long, and is hinged in the centre like a carpenter's rule. The pivot represents the centre of the circle, and the lines drawn from it upon the two limbs the radii. Upon these lines are drawn the several scales specially adapted to the sector. Other scales not directly belonging to it may be placed in the blank spaces on the limbs. The scales for the radial lines are selected and arranged according to the particular uses for which the instrument is intended. They commonly consist of a line of chords by which we may protract an angle of any number of degrees, find the degrees corresponding to any arc, etc.; a scale of equal parts, which affords the means when the limbs are opened to the proper extent of finding with a pair of dividers a third proportional to two given lines, or a fourth to three given lines, etc.; also lines of sines, secants, tangents, and polygons.
The sector is a convenient instrument in plotting for giving without calculation angles and the lengths of required lines; but all instruments are necessarily imperfect, and since the introduction of logarithmic tables this one is little used. - An instrument called the astronomical or equatorial sector is used for taking the difference of right ascensions and declinations of stars; and the zenith sector is used in trigonometrical surveys to determine the zenith distances of stars whose declinations differ little from the latitude of the observer.