Definition:Segment of a Circle
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Definition
As Euclid defined it:
- A segment of a circle is the figure contained by a straight line and a circumference of a circle.
(The Elements: Book III: Definition $6$)
Base
The base of a segment is the straight line forming one of the boundaries of the seqment.
Angle of a Segment
As Euclid defined it:
- An angle of a segment is that contained by a straight line and a circumference of a circle.
(The Elements: Book III: Definition $7$)
That is, it is the angle the base makes with the circumference where they meet.
It can also be defined as the angle between the base and the tangent to the circle at the end of the base:
Angle in a Segment
As Euclid defined it:
- An angle in a segment is the angle which, when a point is taken on the circumference of the segment and straight lines are joined from it to the extremities of the straight line which is the base of the segment, is contained by the straight lines so joined.
(The Elements: Book III: Definition $8$)
- And, when the straight lines containing the angle cut off a circumference, the angle is said to stand upon that circumference.
(The Elements: Book III: Definition $9$)
Such a segment is said to admit the angle specified.
Similar
As Euclid defined it:
- Similar segments of circles are those which admit equal angles, or in which the angles are equal to one another.
