In the Wiki it is stated

https://wiki.tfes.org/Eratosthenes_on_Diameter

We can use Eratosthenes' shadow experiment to determine the diameter of the flat earth.

Syene and Alexandria are two North-South points with a distance of 500 miles. Eratosthenes discovered through the shadow experiment that while the sun was exactly overhead of one city, it was 7°12' south of zenith at the other city.

7°12' makes a sweep of 1/25th of the FE's total longitude from 90°N to 90°S (radius).

Therefore we can take the distance of 500 miles, multiply by 25, and find that the radius of the flat earth is about 12,250 miles. Doubling that figure for the diameter we get a figure of 25,000 miles.

However, I am confused about how this claim can be made.  Here is an simple diagram of the situation (no tto scale)



It is claimed, that on a flat earth, that if we know D, the distance between Syene and Alexandria, we know the angle of A, that we can compute De (diameter of the earth in a 'flat disc' model) 

However, I do not see how this can be done.  Without going into the geometry. Imagine extending De to any aribtrary length.  It will not change the angle A, nor the distance D.  Therefore, for any given A or D, maps to any De > D at least (which would be obvious)