Proposition 1
Construction
To construct an equilateral triangle on a given line segment.
Construction Steps
1. Let AB be the given line segment.
2. Construct the circle through the point B centered at A and the circle through the point A centered at B. These two circles intersect at C.
3. JoinCA , CB so that △ABC is constructed. △ABC is equilateral, and it has been constructed on the given line segment AB .
2. Construct the circle through the point B centered at A and the circle through the point A centered at B. These two circles intersect at C.
3. Join
Original statement
ἐπὶ τῆς δοθϵίσης ϵὐθϵίας πϵπϵρασμένης τρίγωνον ἰσόπλϵυρον συστήσασθαι.
English translation
On a given finite straight line to construct an equilateral triangle.
