SECTOR, in practical mechanics, an instrument of considerable utility in rough mathe matical drawing, consists of two strips of wood, ivory, or metal jointed together like a carpenter's foot-rule. It is absolutely necessary for the correctness of the instrument that the center of the axle of the joint should be accurately at the inner corner of each slip, so that it will always be the vertex of a triangle of which the inner edges (and con sequently any of the corresponding pairs of lines drawn from the joint obliquely along the rule) form the two sides. These oblique lines, which are drawn on both sides of the instrument, and converge front the extremities of the two strips to the center of the joint, are graduated in different ways, so as to give, on each limb, it line of equal parts, a scale of chords, scales of sines, tangents, and secants, a line of polygons, etc. (all of which are graduated from the center of the hinge, which is their zero point), besides a number of common scales on the blank portions of the sector. The special use of this instrument is in the finding of a fourth proportional to three given quantities, and the operation is performed as follows: If the fourth proportional to 18, 10, arid 81 is required, find the graduation indicating 18 on each limb; then obtain, by means of a pair of compasses, the length from 0 to 10, and open out the instrument till the two 18 points are as far apart as the distance given by the compasses; then, by measuring with the compasses the distance of the two graduations indicating 81, and applying the com passes to the scale, we obtain the fourth proportional required. It will he seen that this
instrument merely supplies a mechanical mode of constructing two similar isosceles tri angles, one of which has all its sides, and the other has only its equal sides given, the other side or base, which is formed by the sector, and read off by aid of the compasses and scale, being, from the very nature of similar triangles, the fourth proportion required. This instrument becomes more inaccurate as the angle formed by the limbs increases. The sector is said to have been invented by Guido Ubaldi about 1568, though Gasper of Antwerp describes it in 1584, and attributes its invention to hio brother Fabricius in 1554. It was described by several German and English writer* in the same century, and again by Galileo, who claimed to have invented it in 1604.