This text was written in 2013. In it, I presented a preliminary discussion of the changing interrelations between geometry and arithmetic in various versions Book II of Euclid's Elements throughout the centuries. It should be seen as a draft [not free of problems] dealing with an idea that is intended to be developed in more detailed in various forthcoming articles.

Meanwhile, I have published an article in Archive for History of Exact Sciences, dealing in detailed with the part corresponding to the period up to the late 14th century, before the first printed editions of the Elements started to appear.

The article can be reached here.

The preliminary draft, from p. 38 (not including the sections on Medieval math), can be reached here.