Proposition 33a
Construction
On a given line segment to describe a segment of a circle which contains an angle equal to a given acute 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 H be the intersection ofAE and the circle.
6. ConnectBH , constructing ∠AHB . On the given line segment AB , ∠AHB 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 H be the intersection of
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.
