Proposition 14
Construction
To construct a square equal to a given polygon.
Construction Steps
1. Let ◇ADCB be the given polygon.
2. Construct a rectangle◇EFGH such that it has the same area as polygon ◇ADCB .
3. ExtendEF to J such that ￜFJￜ = ￜFGￜ .
4. BisectEJ at K.
5. Construct the circle through the point J centered at K that intersects the extension ofGF at P.
6. Construct a square◇PFMN with FP as a side. The square ◇PFMN has been constructed equal (in area) to the given polygon ◇ABCD .
2. Construct a rectangle
3. Extend
4. Bisect
5. Construct the circle through the point J centered at K that intersects the extension of
6. Construct a square
Original statement
τῷ δοθέντι ϵὐθυγράμμῳ ἴσον τϵτράγωνον συστήσασθαι.
English translation
To construct a square equal to a given rectilinear figure.
