The sextant measures angles on a plane, the angular size of the Sun is 32 minutes and the definition of a mile is 1 minute. This is not proof that can be refuted by an inconclusive youtube video of a rusty ship wreck, it's direct measurement. If the Earth curved at a rate of 8 inches per mile squared the sextant would be rendered useless, the horizon would be 3 miles away, every navigation calculation would be in error and we're back to Gilligan's Island.