Proposition 34
Construction
To cut off from a given circle a segment which contains an angle equal to a given angle.
Construction Steps
1. Let the circle through the point A centered at O be the given circle and ∠EFG be the given angle.
2. Draw a lineAD tangent to the circle at point A.
3. Find a point B on the circle such that∠BAD = ∠EFG .
4. Pick a point C on the circle such that C and D are on opposite sides of infinite lineAB .
5. JoinAC and BC . In the given circle, the angle ∠ACB has been constructed equal to the given angle ∠EFG .
2. Draw a line
3. Find a point B on the circle such that
4. Pick a point C on the circle such that C and D are on opposite sides of infinite line
5. Join
Original statement
ἀπὸ τοῦ δοθέντος κύκλου τμῆμα ἀϕϵλϵῖν δϵχόμϵνον γωνίαν ἴσην τῇ δοθϵίσῃ γωνίᾳ ϵὐθυγράμμῳ.
English translation
From a given circle to cut off a segment admitting an angle equal to a given rectilinear angle.
