Proof
Let be the given line and the given angle. At ,
construct (I.23). At , draw (I.11). At the midpoint of (I.10), draw
(I.11), meeting at . With as centre and
as radius (= by the perpendicular bisector property),
describe a circle. By III.32, the inscribed angle in the alternate
segment to on this circle equals .
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Full neighborhood
Depends on (4)
- 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…
- I.10Proposition I.10To bisect a given finite straight line.
- I.11Proposition I.11To draw a straight line at right angles to a given straight line from a given point on it.
- I.23Proposition I.23On a given straight line and at a point on it to construct a rectilineal angle equal to a given rectilineal angle.
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