Sector

Collier's New Encyclopedia (1921)

in geometry, that portion of the area of a circle included between two radii and an arc. The area of a sector is equal to the product of the are of the sector by half of the radius. If the angle at the center is given, the length of the arc of the sector may be found, since it is equal to x multiplied by the radius into the ratio of 180° to the number of degrees of the sector. A spherical sector or the sector of a sphere is a volume or solid that may be generated by revolving a sector of a circle about a straight line drawn through the vertex of the sector as an axis, or it is the conic solid whose vertex coincides with the center of the sphere, and whose base is a segment of the same sphere. In mathematics and surveying, a mathematical instrument used for laying down plans, measuring angles, etc. It has two legs, united by a rule-joint, and graduated. The scales put on sectors are divided into single and double; the former has a line with inches divided into eighths or tenths; a second, into decimals containing 100 parts; a third, into chords; the fourth has sines; the fifth, tangents; the sixth, rhombs; the seventh and eighth have latitudes, hours, etc. The double scale contains a line of lines; second, a line of chords; third, a line of sines; fourth, tangents to 45°; fifth, secants; sixth, tangents above 45°; seventh, polygons. In surveying, the inand the bob depending from the axis of strument is mounted on a leg or tripod, the rule-joint indicates the station exactly.