Flying Scrolls V: Tracing a Pentagram by Geometry

Let AB be any line of the length required for the distance between the points of Earth and Fire.

Bisect AB in O and from O draw OH perpendicular to AB. Cut off OC to equal AB.

Join B with C and produce the line BC to F making FC to equal OA. From centre B, with radius BF, draw the circle FDK, cutting OH at D.

D is then the Spirit angle of the Pentagram. With the centres B and D draw circles with a radius equal to AB, and they cut each other at E which will be the Water angle. In a similar way find G the Air angle. Join A, B, D, E, and G in the usual way.