Proof
Let and both stand on arc from points
, on the opposite arc. By III.20 each equals half the
central angle , so (Common
Notion 1: things equal to the same thing are equal).
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Depends on (3)
- III.20Proposition III.20In a circle the angle at the centre is double of the angle at the circumference, when the angles have the same…
- 1Common notion 1Things which are equal to the same thing are also equal to one another.
- III.8Definition III.8An angle in a segment is the angle which, when a point is taken on the circumference of the segment and straight lines…
Required by (dependents) (3)
- III.22Proposition III.22The opposite angles of quadrilaterals in circles are equal to two right angles.
- III.23Proposition III.23On the same straight line there cannot be constructed two similar and unequal segments of circles on the same side.
- III.32Proposition III.32If a straight line touch a circle, and from the point of contact there be drawn across, in the circle, a straight line…
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