Eratosthenes' method to calculate the
Earth's circumference has been lost; what has been preserved is the simplified version described by
Cleomedes to popularise the discovery.
[12] Cleomedes invites his reader to consider two Egyptian cities,
Alexandria and
Syene, modern
Aswan:
- Cleomedes assumes that the distance between Syene and Alexandria was 5,000 stadia (a figure that was checked yearly by professional bematists, mensores regii);[13]
- he assumes the simplified (but false) hypothesis that Syene was precisely on the Tropic of Cancer, saying that at local noon on the summer solstice the Sun was directly overhead;[14]
- he assumes the simplified (but false) hypothesis that Syene and Alexandria are on the same meridian.
Under the previous assumptions, says Cleomedes, you can measure the Sun's angle of elevation at noon of the summer solstice in Alexandria, by using a vertical rod (a
gnomon) of known length and measuring the length of its shadow on the ground;
[15] it is then possible to calculate the angle of the Sun's rays,
[16] which he claims to be 7° 12', 7.2°, or 1/50th the circumference of a circle.
[17] Taking the Earth as spherical, the Earth's circumference would be fifty times the distance between Alexandria and Syene, that is 250,000 stadia. Since 1 Egyptian stadium is equal to 157.5 metres, the result is 39,375 km, which is 1.4% less than the real number, 40,076 km.
A Greek named Eratosthenes measured the circumference of the Earth thereby proving that the Earth is spherical and curved not flat. If the Ancients accepted the Earth was not flat why can't a modern person like you? Even when we have more advanced ways to prove it.