I once saw it claimed on the internet -- unfortunately, I can no longer find it -- that the following argument was used by European flat-earthers of the 1400s or so. (Obviously this would still have been a fringe position, as in that area the earth had been known to be round for a long time, but the claim was that there were still some flat-earthers making this argument.)

If the world were round, there would be a southern hemisphere. If there were a southern hemisphere, it would be populated, because God wouldn't waste all that space. If the southern hemisphere were populated, it would be possible for us to reach it, because God has mandated us to spread the gospels to all the people of the earth, and God would not assign us an impossible task. But to reach the southern hemisphere, you would have to cross the equator; and clearly anyone crossing the equator would burn up and die. Therefore, the earth must be flat.

(Supposedly, some other people who didn't accept all these premises instead just used this to argue that the southern hemisphere must be uninhabited.)

Now, I love this argument as an example for demonstrating the difference between [validity](https://en.wikipedia.org/wiki/Validity_(logic)) and soundness. The problem is, I can no longer find the source I got this from, and, well, I'm not confident that it's real.

So, is it? Did people make this argument, and if so who and when? Presumably if this is real, it must be from before any European had crossed the equator (which according to a quick search seems to have occurred in 1471?), or at least before such had become widely known. But was it really made?

Thank you!