You’re correct. I was thinking of an infinite plane.
I described a setting sun. The person on the ground would see the sunset before the person at the peak, and therefore wave their flag before the person at the top.
It would, of course, be opposite for a sunrise.
Agreed, which is why I mention using trigonometry and Huygens’s method. But, with that, you’d need telescopes. They didn’t come around until the early 1600s; though, grinding and polishing your own lenses wouldn’t be impossible.
Re: a Foucalt pendulum.
But the period of rotation changes with respect to latitude. You’d have to move it around and get different timings, but it would show that something was happening wrt latitude. The simplest explanation being a round Earth.
On a flat Earth, it would rotate at the same rate regardless of location. (With the rate being 0 for a fixed Earth.)
BTW: The ancient Greeks were also aware that sundials at different latitudes had to be locally calibrated. E.g., archaeologists found one in Alexandria the Farthest that had been badly “adjusted” due to having been originally located somewhere else.
Another, semi-practical proposal:
Step 1) Erect a tall enough tower to maximize the parallax effect on the raised platform. The large platform would have a bright red edge, and a bright green underside.
Step 2) Work out the angles over the decided distance, so that the platform would be seen edge on from POV1.
Step 3) From POV 1 (but really POV 2) observe under magnification (if necessary) whether or not the green underside of the platform can be seen.
If the earth is curved, an experiment like this can be performed over and over, so long as finding an adequately level surface of land, like the salt flats, is practical enough.
At 10 miles along the arc instead of the plane, the difference would only be 0.076 degrees. Can you make a board and paint it and have it that rigid and square?
Well but then how does the Sun rise and set?
You could use supports and braces from above the plane to keep it square I imagine.
I haven’t the time to work out the math, but how much distance would be feasible to put between yourself and the tower?
It is drawn by chariot on paths around the sky and under the earth. A better question is why it is not put out when it sets in the ocean.
A lot of these methods get frustrated by these small things and fine measurements. I would think that findings 10 miles of perfectly flat ground (that everyone involved would agree is perfectly flat) would be the major challenge. Maybe a large lake or a small strait would do.
There is at least one other thread on this site that discusses this issue at length.
I have no luck when I try to search up threads, though. 
This was my thought as well. I had wondered about about using barges on a large, calm sea somewhere, which might mitigate any margin of error.
What’s more, the further the distance, the more drastic the parallax. But of course, you’d lose resolve, unless you built a more massive structure.
Wind might be an issue too, but this can be mitigated by perforating the plane’s surface with holes.
Such as the Bedford Level.
Clever: 3 floating poles of equal length and a surveyor’s scope.
Can we bring a theodolite back in time?
If the world was flat wouldn’t there be equal amounts of day and night no matter how far north or south you were?
Why should it ? A flat Earth with the Sun sinking below its horizon is the same as, say, a die dropping from a table as observed with your eyes at table level. Lift your head and hey, you can see the die over the edge ! Same with the Sun and the cherry-picker, if we assume it to be (apparently) rotating around a flat-ish disc. Possibly supported by four elephants, themselves standing on the shell of a turtle.
This is pretty well covered by Carl Sagan in the first episode of Cosmos.
I used to see a different version of this when i was in the Navy. When I was onboard a carrier, I could use the height difference between the flight deck and the lower decks to change the angle of viewing another ship on the horizon. I could see the whole ship from the flight deck, but only the tops of the stacks from lower decks. Unfortunately, digital cameras didn’t exist then, so i could not get good shots of it.
You recognise of course, that you don’t need people with flags for this demonstration. Standing at the western base of any tall structure, you can easily observe that the top of the structure remains in sunlight well after the sun is below your own horizon. Of course this doesn’t demonstrate that the horizon is different for the base and the top.
You would need to locate your two observers, with their flags, as far away from you as possible to the west and to the east on a very flat plain. If you can demonstrate that the horizon varies for two observers at the same elevation you have demonstrated the curvature of the earth.
What no one has mentioned here (at least in my cursory scanning of the posts) is the observation (credited to Pythagoras, but who knows) that, during a lunar eclipse, the earth’s shadow is round. Again, this leaves the possibility open that the earth is a flat disk, but we’ve at least made it a flat circular disk.
I’ve always contended that the spherical earth is a concept that quickly becomes obvious to anyone who has regularly traveled more than 5-10 miles from their place of birth. It does require the propensity to make careful observations and to draw conclusions that differ from one’s own preconceptions.
Lunar eclipse shadow mentioned on first page
Huygens method, as described above, makes several assumptions that are untestable. The primary reason he is not usually given credit for measuring the value of an AU (though his value is close to the true one) is that his errors cancelled each other out. For instance, he assumed that Venus was the same size as earth to determine its actual distance. As it happens Venus is the only planet whose radius is close to the earth’s, so, lucky he didn’t use Mars or Jupiter.
Cassini and Richter measured the parallax of Mars from different latitudes, which didn’t require assuming the physical size of the planet, and came up with an measurement that was not as accurate as Huygens, but was limited only by measurement precision. The first accurate and precise measurement had to wait until data was available from the 1761 & 1769 transits of Venus, and was credited to Jerome Lalande. Since the 17th and 18th centuries all measurements have improved only as technology has allowed us to add decimal point to already accurate measurements.
