So if they invented radio on a flat earth; how did they ever discover line of sight, or associate it with distance?

I pulled up the coverage map of a TV station (WJXT Jacksonville FL) where the signal is divided roughly equally between a water path and over land, and notice that the signal decreases in strength the further out in the Atlantic you get, until about 70-75 miles out, it just drops off the cliff, so to speak.  Over land, you then have terrain considerations, viz. elevations blocking the line of sight, or creating a knife-edge signal as the case might be.  This station broadcasts on over-the-air channel 18 (494-500 mHz), even though it is "channel 4" on one's receiver (PSIP information, a system they devised to allow stations to retain their analog channel numbers from before the transition to digital, it's complicated and was done primarily to allow TV stations to keep their historical channel numbers).

I hear stuff like this all the time.
This clip was from Ham Radio Workbench #213 (around 2:54:00)
The man speaking became a ham in the 70's, so he has a lot of real world experience.
Funny how his inner scientist didn't get "triggered" by such a mystery. To his credit, he states the TRUTH matter of factly. But unfortunately, he completely fails to follow up and investigate HOW such an impossible thing can happen in this world.

One should NOT be able to communicate 700 miles using a LINE OF SIGHT frequency like 10 GHz (with 3 Watts of power) -- unless the earth is flat, of course.

And I would like to point out: no matter HOW MUCH you amplify a signal, catch it in a satellite dish, amplify it thousands of times stronger, etc. -- if you have ZERO signal to begin with, then zero times a billion is still zero. In other words, if the signal went off into outer space due to the "curve" of the "globe earth" -- the signal would be completely absent 700 miles away, or "zero" -- i.e., nothing left to amplify!

Once again, Flat Earth confirmed.

Gladly.  Knife-edge propagation can do freakish things.  The scenario I described puts the signal over almost-flat land.  In mountainous regions, you can have a viable knife-edge TV signal over 100 miles out.  WLOS in Asheville NC was legendary for having its transmitter atop Mount Pisgah, just shy of 6000 feet ASL (the tower itself is fairly short), and its signal reached locations all the way from southeastern Kentucky to central South Carolina on VHF channel 13.  WMTW in Poland Spring ME had an even larger coverage area from its transmitter atop Mount Washington on VHF channel 8.

If you follow the globe-earth paradigm, it would be curvature of the earth.

If you follow the flat-earth paradigm, it would be the point at which the line of sight from the tower reaches some point beyond which the signal cannot go. Think of a triangle and the vertex of the angle that touches the earth.

Keep in mind also that TV and radio broadcast signals are "flattened", i.e., they are suppressed at the top of the transmitter --- no use sending a signal straight up into the air, that's just wasted signal --- and "spray out" horizontally.  Think of shooting a cone of water vertically out of a garden hose squirter, then putting your hand an inch or so over the jet, allowing the water then to splatter horizontally in all directions (including all over you!), yet not shoot all the way up in the air.  It's an imperfect analogy but is the best way I can think of, to describe how broadcast signals work.  Another example might be a sprinkler system.  The water shoots out in a flat spray 360 degrees but doesn't shoot straight down, due to the placement of that little deflector on the sprinkler head:



I'm simply an amateur hobbyist in all of this.  I'll welcome more elegant technical explanations of how broadcast transmitters work.

Conditions such as humidity and rain do indeed interfere, also, the signal gets progressively weaker, the further out it is broadcast.  You finally reach a point where there is no signal, also, there is the signal-to-noise ratio, meaning that you may have a marginal signal, but it can't break through the various factors that would interfere with it.

As far as television is concerned, any signal beyond about 80 miles tops (and that's being generous as well) is basically unwatchable.  In analog broadcasting, the signal is weak and snowy, and in digital broadcasting, you either have the signal or you don't, and it starts "blocking", getting so choppy and intermittent that your receiver can't decode it.  For what little television I do watch, in addition to nearby stations, I have stations 80-90 miles away that may come in late at night, or in the early morning, but beyond that, they're not receivable.  I have high-gain rooftop antennas (Televes brand from Spain, they're excellent) on both of my houses that enable it, again, it's a hobby, not any great love for television itself.