Definition: 3.09: Angle Standing Upon An Arc
And when the straight lines containing an angle cut off some circumference, the angle is said to stand upon that (circumference).
We say that the inscribed angle $\alpha$ stands upon the arc $AB$, if it is contained by the straight lines joining the ends of the arc $AB$ with any point on the circumference of a segment of the circle.
Proofs: 1 2 3 4 5
Propositions: 6 7 8
Adapted from (subject to copyright, with kind permission)
- Fitzpatrick, Richard: Euclid's "Elements of Geometry"