Proposition 33b
Construction
On a given line segment to describe a segment of a circle which contains an angle equal to a given right angle.
Construction Steps
1. Let AB be the given line segment and ∠PDQ the given angle.
2. Take A as a vertex, construct∠BAC = ∠PDQ .
3. BisectAB at O.
4. Construct the circle through the points A, and B centered at O. Let E be any other point on the circle.
5. ConnectAE and BE , constructing ∠AEB . On the given line segment AB , ∠AEB has been constructed equal to the given angle ∠PDQ .
2. Take A as a vertex, construct
3. Bisect
4. Construct the circle through the points A, and B centered at O. Let E be any other point on the circle.
5. Connect
Original statement
ἐπὶ τῆς δοθϵίσης ϵὐθϵίας γράψαι τμῆμα κύκλου δϵχόμϵνον γωνίαν ἴσην τῇ δοθϵίσῃ γωνίᾳ ϵὐθυγράμμῳ.
English translation
On a given straight line to describe a segment of a circle admitting an angle equal to a given rectilinear angle.
