Sextant measurement can show that measurement using Polaris on globe doesn't depend on latitude and on flat does.
At 30 degrees north you will measure 1.4 arcminutes, at 45 degrees 1.0 and at 60 degrees 0.6.
On gobe at all latitudes it will be 1 arcminute.
To "show" what you state above requires some assumptions about astronomical objects.
Please "show" and then show all work, including assumptions.
I think you'll find that you run into the problem that you're begging the question. You'll be trying to prove something, and one of the assumptions used in your proof is what you're trying to prove (or at least a FE frequently-disputed assumption).
Ok, let me try to answer your question:
If you go to 60 degrees north in Flat model, Polaris is 3300 miles above the ground, and you will see it at angle of 56.5 degrees.
Using Polaris to measure tilt between two verticals at ends of north-south segment 1852 meters long you will get
1.25 arcminutes.
If you go to 45 degrees north in Flat model, Polaris is 3300 miles above the ground, and you will see it at angle of 46 degrees.
Using Polaris to measure tilt between two verticals at ends of north-south segment 1852 meters long you will get
1.0 arcminutes.
If you go to 30 degrees north in Flat model, Polaris is 3300 miles above the ground, and you will see it at angle of 37.7 degrees.
Using Polaris to measure tilt between two verticals at ends of north-south segment 1852 meters long you will get
0.85 arcminutes.
If you go to 60 degrees north in Globe model, Polaris is 434 light years above the ground, and you will see it at angle of 60 degrees.
Using Polaris to measure tilt between two verticals at ends of north-south segment 1852 meters long you will get
1.0 arcminutes.
If you go to 45 degrees north in Globe model, Polaris is 434 light years above the ground, and you will see it at angle of 45 degrees.
Using Polaris to measure tilt between two verticals at ends of north-south segment 1852 meters long you will get
1.0 arcminutes.
If you go to 30 degrees north in Globe model, Polaris is 434 light years above the ground, and you will see it at angle of 30 degrees.
Using Polaris to measure tilt between two verticals at ends of north-south segment 1852 meters long you will get
1.0 arcminutes.
We know, and it is easy to find, that nautical mile was defined as 1852 meters
becauseeverywhere in the world tilt between two verticals at opposite ends of one nautical mile is
1.0 arcminute. It was good and easy way for navigators (and others) to convert degrees into distances.
For example, measured angle of 3 degrees 17 minutes is 3 * 60 + 17 = 197 nautical miles.
In Flat Earth model it doesn't work as seen above.
One nautical mile wouldn't have measuring value as it would change with degrees of position.
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Now, this example, no matter how obvious, will be rejected by Flat Earthers not because "there could be errors".
Flat Earthers will either know that
there are no errors here, or they know too little to know what is this all about.
This will be rejected because it doesn't say what they
want to hear.
Majority of Flat Earthers will mostly disregard the whole process.
Maybe some of them will try to throw in some additional "facts" to "water down" the obvious part and draw attention somewhere else.
Several notorious Flat Earthers already reject facts an figures, no matter what they are.
But at least others, who aren't sure, will not fall into trap of Flat Earth deception.
If they measure by themselves using relatively affordable sextant, Flat Earthers will not be able to tell them "somebody 'indictrinated' you".
Just like nobody can tell me "Moon is 3000 miles up", because I measured it myself, using two different methods.
One by lunar paralax, another decades ago, using radio waves.