Euclid's Extreme and Mean Proportion Constructions
Euclid VI.13 shows how to get a mean proportional to two other lines using a semicircle ADB.
Euclid II.11 shows how to cut a single line into extreme and mean proportion using squares AG and AH.
Sliding point D on the circle produces any number of three lines in extreme and mean proportion, but only when C coincides with M is the diameter cut in extreme and mean proportion.
Is there a way, using only the circle construction of VI.13, to find where pont M is such that the diameter AB is cut in extreme and mean proportion?