Viewed from Alexandria (point A), at that same moment, the point E only overlapped point C on the Sun, about 1/5 solar diameter short of the edge --- which was why the eclipse there was not total. One-fifth of the Sun's diameter covers about 0.1 degrees in the sky, so the small angle $$\alpha$$ (alpha, Greek A) between the two directions measured about 0.1 degrees. That angle is the parallax (See the chapter “Parallax") of the edge of the Moon, viewed from the above two locations.
The latitude of the Hellespont (from a modern atlas) is about 4020′ (40 degrees and 20 minutes, 60 minutes per degree), while that of Alexandria is about 3120′, a difference of 9 degrees. We will also assume Alexandria is exactly due south. Furthermore, if $$r$$ is the radius of the Earth, then the circumference of the Earth is $$2\pi r$$. Since the circumference also spans 360 degrees, we get $AB\,=\,\frac{2\pi r}{360}\times 9$