x. Similar segments of circles are those that contain equal angles.
xi. A sector of a circle is formed of two radii and the arc included between them.
To a pair of radii may belong either of the two conjugate arcs into which their ends divide the circle.—Newcomb.
xii. Concentric circles are those that have the same centre.
xiii. Points which lie on the circumference of a circle are said to be concyclic.
xiv. A cyclic quadrilateral is one which is inscribed in a circle.
xv. It will be proper to give here an explanation of the extended meaning of the word angle in Modern Geometry. This extension is necessary in Trigonometry, in Mechanics—in fact, in every application of Geometry, and has been partly given in I. Def. ix.
Thus, if a line OA revolve about the point O, as in figures 1, 2, 3, 4, until it comes into the position OB, the amount of the rotation from OA to OB is called an angle. From the diagrams we see that in fig. 1 it is less than two right angles; in fig. 2 it is equal to two right angles; in fig. 3 greater than two right angles, but less than four; and in fig. 4 it is greater than four right angles. The arrow-heads denote the direction or sense, as it is technically termed, in which the line OA turns. It is usual to call the direction indicated in the above figures positive, and the opposite negative. A line such as OA, which turns about a fixed point, is called a ray, and then we have the following definition:—