Proposition 3
Construction
To cut off from the longer of two given unequal line segments a part equal to the shorter.
Construction Steps
1. Let AB and CD be the given line segments and AB be the longer one.
2. ConstructAE such that ￜAE ￜ = ￜCD ￜ .
3. Construct the circle through the point E centered at A intersectingAB at F. AF has been cut off from the longer line segment AB equal to the shorter line segment CD .
2. Construct
3. Construct the circle through the point E centered at A intersecting
Original statement
δύο δοθϵισῶν ϵὐθϵιῶν ἀνίσων ἀπὸ τῆς μϵίζονος τῇ ἐλάσσονι ἴσην ϵὐθϵῖαν ἀϕϵλϵῖν.
English translation
Given two unequal straight lines, to cut off from the greater a straight line equal to the less.
