The first proposition constructs an equilateral triangle off a line segment AB. By definition, the distance unknown vertice C of the equilateral triangle and A must be equal to the distance between A and B. This means that C must lie on the circle with center A and radius AB, so constructing this circle is the first step. Likewise, the distance between C and B must equal to the distance between A and B, so we also know that C lies on the circle with center B and radius AB. After constructing this second circle, C can be found by taking one of the intersections between the two circles.