Arc (Lat. arcvs, a bow), the name of any portion of a curved line; thus, an arc of a circle is a portion of the circumference. To rectify an arc is to give the length of the straight line to which it would be equal if it were made to have the same length in a right direction which it now has in a curved. Two arcs are said to be equal when, being rectified, they have the same length; and similar when, being taken from different circles, they have the same number of degrees - that is, are equal fractions of their respective circumferences. The arcs of a circle serve to measure the angles (see Angle); if from the vertex of the angle as a centre, with whatever radius, a circumference be described, the number of degrees of the arc intercepted between the two lines which form the angle will be the measure of the angle. Thus, for instance, as the arc of 90° corresponds to a right angle, if we find that the intercepted arc contains 15°, we conclude that the angle is to a right angle in the ratio of 15° to 90°, or that it is the sixth part of a right angle.

The chord of an arc is the right line which joins its extremities; a segment is the area included between an arc and its chord; and a sector is the area included between an arc and the two radii going from its extremities to the centre of the circle.