When did Eratosthenes measure the circumference of the earth?

Answer 1

This was about 250 BC (c. 250BC) and is from the book:

("Science For The Citizen - A social educator based on the social background of scientific discovery"

by Lancelot Hogben (George Allen & Unwin 1944)

Exactly the same information can also be found in:

"Mathematics For The Million"

also by Lancelot Hogben (originally printed by George Allen & Unwin in 1936, revised 1968, and reprinted in 1997 by Merlin Press)

How he measured it:-

He "compared the sun's altitude at two [locations], one 500 miles due south of the other, on the summer solstice. ... [T]he noon sun was mirrored in a deep well near Syene.....on the tropic of Cancer. The noon sun was therefore at the zenith. On the same day in Alexandria, 500 miles due north, the obelisk shadow showed that the sun was 7 1/2degrees from the zenith. Since the sun's rays are parallel, this means that the arc, or...the difference of latitude between Syene and Alexandria is approximately 7 1/2 degrees, and

7 1/2 divided by 360 = 1/48 of the entire earth's circumference.

[Since] the difference between Alexandria and Syene is 500 miles...the earth's circumference is about 48 x 500 = 24,000 miles

.....The result agrees within 4% with modern determinations." [ Which is 24,902 miles.]

(Quote from 'Science for the Citizen', which I think would be safely out of copyright since it was written 64 (ie more than 50) years ago). It is also interesting to note that 2,250 years ago that Eratosthenes knew the earth was round and notflat, as is commonly arrogantly assumed by modern man of ancient(?) man, as did Tatius, Hipparchus, Poseidonius, and Strabo, who all likewise measured the circumference of the earth.

Answer 2

Eratosthenes measured the circumference of the earth around 240 BC. He did so by comparing the angles of the shadows cast by the sun at two different locations. This experiment led him to a relatively accurate estimation of the earth's size.