6. A segment of a circle is the figure contained by a straight line and the circumference it cuts off.
7. The angle of a segment is that which is contained by the straight line and the circumference.
8. An angle in a segment is the angle contained by two straight lines drawn from any point in the circumference of the segment to the extremities of the straight line which is the base of the segment.
9. And an angle is said to insist or stand on the circumference Intercepted between the straight lines which contain the angle.
10. A sector of a circle is the figure contained by two straight lines drawn from the centre, and the circumference between them.
11. Similar segments of circles are those in which the angles are equal, or which contain equal angles.
[Note. In the following propositions, whenever the expression "straight lines from the centre," or "drawn from the centre," occurs, it is to be understood that the lines are drawn to the circumference.
Any portion of the circumference is called an arc.]
PROPOSITION 1. PROBLEM.
To find the centre of a given circle.
Let ABC be the given circle: it is required to find its centre.
