Nonsense!
The mile was defined in Roman times as one thousand (Mille) double paces (i.e. right foot to right foot) of a Roman legionary. The empire was paced out and measured by the tramp of sandalled feet.
This, long before most people understood that there was such a thing as a second of Arc.
When Eratoshenes measured the Earth based on geometry of vertical and angular incidence of the sun at Alexandria and Syene, he measured the distance between them in terms of days' travel by camel, which he expressed in terms of Stadia, the greek unit of measure (about 5.4 km), so he understood about angular measure, but neither used miles nor defined distance in terms of arc seconds.
