Gleason’s map is not a map of the flat earth but of a flattened globe and he knew it when he applied for the patent for his map.
“But while Gleason argued the earth is flat in his book, his application to the U.S. Patent Office for the map appears to contradict this. The application states that the map is extracted from the earth as a globe. Specifically, Gleason said: “The extortion of the map from that of a globe consists, mainly in the straightening out of the meridian lines allowing each to retain their original value from Greenwich, the equator to the two poles.”
Gleason did not publicly address the contradiction between his book and his patent application. The team at Boston Rare Maps (
here), which sold a rare copy of the map, said on their website they read the passage in the patent application, “as Gleason unwittingly fessing up that his map is, like any other, a projection of a globe or section thereof onto a flat surface.”
So when you start with a fake you finish with a fake.