Sure enough, the dictionary says the fathom is usually 6 ft, but sometimes defined as 1/100 of a cable, and the dictionary says that the cable is defined by the Admiralty as 1/10 of a minute of latitude.
Here is a paragraph that is included in the definition of cubit: "The Great Pyramid of Ghiza was measured in the 1880s by Flinders Petrie as having sides of length 230.24 to 230.4m. with a mean of 230.355m. Postulating them as being 250 points to a cubit of about 461mm and a fathom of about 1.84m. i.e. very close to today's international nautical mile, the length of one minute of latitude. In turn this indicates that the Ancient Egyptians nearly 5000 years ago, measured Earth's radius." p. 53
First, I think Fenna meant to say 500 points to a cubit instead of 250, since 230.355/.461 = 499.7. Also, given a fathom equal to four cubits, 500 cubits equals 125 fathoms, and 230.355/125 = 1.842m. 1842m is a little bit short for an average minute of latitude, but it is accurate for minutes of latitude at the equator. Given 125 fathoms per side, this gives 500 fathoms for the perimeter, equal to 1/2 minute of latitude at the equator, which has of course been pointed out before, although perhaps not to my knowledge in fathoms.
The half-minute of latitude is a measure of the circumference and Fenna does not explain how he gets from there to radius, and a half minute of equatorial latitude x 2 x 60 x 360 / 2pi is still a bit short even for the polar radius, because the equatorial degrees of latitude are so short, but regardless of how he got there, I agree with him that the Ancient Egyptians did know the measure of the earth's radius and I was surprised and happy to find this statement in the current Oxford dictionary of weights, measures and units.