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I know that Greenwich mean time was established in 1675, as an aid to navigation. Portuguese and Spanish navigators in the 15th century also appeared to be aware of the usefulness of timekeeping for longitudinal navigation, though they lacked sufficiently accurate clocks to implement the technique.
My question is this: when was the fundamental principle discovered? When did travelers first notice that, if you go to the west, the Sun rises and sets later?
Well, the potential for using time to measure longitude was certainly understood by Hipparchus in the second century BC.
He proposed that longitudes of distant places could be calculated by measuring the local solar time of lunar eclipses, which are visible over half the Earth's surface. However, the available means of timekeeping weren't sufficiently accurate for this to be useful.
Essentially when they understood that the Earth is round, and the Sun rotates about it with a period one day. Ancient Greeks credited this discovery to Pythagoras. Modern scientists consider Pythagoras a somewhat legendary figure, so the name of the first person who said this is unknown.
Anyway this was a common knowledge in the (educated) Hellenistic circles long before Hipparchus. The first attempt to measure the size of the Earth is associated with Eratosthenes (3d century b.c.), and at this time it was certainly clear (to educated people) that the local time depends on the longitude.
When the eight remaining crewmembers of Magellan's circumnavigation of the earth reached the Cape Verde Islands in July of 1522, they were puzzled by their apparent loss of one day with respect to the actual date on the islands.
https://www.staff.science.uu.nl/~gent0113/idl/idl_discovery.htm
So, the knowledge of change in sunrise time with longitude would appear to be after this date.
We can of course ignore Phileas Fogg's similar confusion in the late 1800s as Verne's dramatic license...
Its likely pretty much everyone who understood that the Earth was a sphere also understood this. All you'd need to see it is a sphere of your own to act as a model.
Eratosthenes in the third century BC not only understood this, but used it to calculate the circumference of the earth.
Basicly, he knew what day the sun was directly overhead at noon where he lived (Alexadria). So he had someone in another city a known distance away calculate the angle of the sun at noon on that same day, did a bit of trigonometry, and came up with an actual number (that wasn't off by a whole lot) for the circumference of the Earth.
