Proposition 33c
Construction
On a given line segment to describe a segment of a circle which contains an angle equal to a given obtuse 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. LetAE be perpendicular to AC at point A.
4. BisectAB at F. Find a point O on AE , such that OF ⊥ AB .
5. Construct the circle through the points A, and B centered at O. Let G be any other point on the circle.
6. ConnectAG and BG , constructing ∠AGB . On the given line segment AB , ∠AGB has been constructed equal to the given angle ∠PDQ .
2. Take A as a vertex, construct
3. Let
4. Bisect
5. Construct the circle through the points A, and B centered at O. Let G be any other point on the circle.
6. 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.
