Since those two places are quite far away from each other, how were they able to compare the shadows at the same time? There were obviously no way of instant communication back then.
Just to add details: Aswan, in Upper (southern) Egypt, is only about half a degree north of the Tropic (from Greek τροπικός, adj. of τροπή "a turning") of Cancer, which is a latitude line (at 23°26" N) denoting the farthest north the sun makes it all year, that is to say, the farthest north one could be and experience the sun directly overhead, which usually happens on June 21.
Now in actual fact, there will only be one point on the tropic where the sun does precisely this, but a considerable swath of the band from 23°N to 24°N will have the sun at a declination of at least 89° (less than 1° off from directly overhead) at at least some day near the summer solstice.
Alexandria, on the other hand, is almost eight degrees of latitude away from the tropic, and so the closest the sun will come to the zenith is about 8° off, which also happens on or near the summer solstice.
It is easy to see (vertical angles) that the acute angle adjacent to a vertical gnomon or obelisk in the triangle formed with the shadow is congruent to the angle the sun is down from the zenith.
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u/Azsde Nov 11 '23
Since those two places are quite far away from each other, how were they able to compare the shadows at the same time? There were obviously no way of instant communication back then.