> To play devil's advocate - you would also need to prove that it is Earth's shadow on the moon and not the Sun's shadow. For an example, I made an HD image in paint [0].
Very nice! A great demonstration of how difficult it is to be explicit about all our assumptions.
That argument would prove the Earth is round - but not necessarily that it is spherical. A flat, round disc would also produce a curved shadow.
To play devil's advocate - you would also need to prove that it is Earth's shadow on the moon and not the Sun's shadow. For an example, I made an HD image in paint [0].
[0] https://vgy.me/8xRkJv.png