Eratosthenes


Eratosthenes was born in Cyrene (in modern-day Libya) in 276 BC. He was the chief librarian of the Great Library of Alexandria and died in the capital of  Ptolemaic Egypt. He was never married.

Eratosthenes studied in Alexandria and claimed to have done so for some years in Athens. In 236 BC, he was appointed by Ptolemy III Euergetes I as librarian of the Alexandrian library, succeeding the first librarian, Apollonius of Rhodes, in that post. He made several important  contributions  to mathematics and science, and was a good friend to Archimedes. Around 255 BC, he invented the  armillary sphere , which was widely used until the invention of the  orrery  in the 18th century.

In 194 BC, Eratosthenes became blind, and he  supposedly  starved  himself to death a year later.

He is  credited  by Cleomedes in On the Circular Motions of the  Celestial  Bodies with having calculated the Earth's  circumference  around 240 BC, using knowledge of the angle of  elevation  of the sun at noon on the   summer solstice  in Alexandria and in the Elephantine Island near Syene (now Aswan, Egypt).

Eratosthenes knew that on the summer solstice at local noon in the Ancient Egyptian city of Swenet (known in Greek as Syene) on the  Tropic of Cancer , the sun would appear at the  zenith , directly  overhead . He also knew, from measurement, that in his  hometown  of Alexandria, the angle of elevation of the sun would be 1/50 of a full circle (7°12') south of the zenith at the same time.  Assuming  that Alexandria was due north of Syene, he  concluded  that the distance from Alexandria to Syene must be 1/50 of the total circumference of the Earth. His  estimated  distance between the cities was 5000 stadia (about 500  geographical or nautical miles  ). He rounded the result to a  final  value of 700 stadia per degree, which  implies  a circumference of 252,000 stadia. The exact size of the  stadion  he used is frequently argued. The common  Attic  stadion was about 185 m, which would imply a circumference of 46,620 km, i.e., 16.3% too large. However, if we assume that Eratosthenes used the "Egyptian stadion" of about 157.5 m, his measurement turns out to be 39,690 km, an  error  of less than 1%.

Although Eratosthenes'  method  was  well founded , the  accuracy  of his calculation was  inherently  limited. The accuracy of Eratosthenes' measurement would have been reduced by the fact that Syene is not  precisely  on the Tropic of Cancer, is not directly south of Alexandria, and the sun appears as a  disk  located  at a  finite  distance from the Earth instead of as a point  source  of light at an  infinite  distance. There are other sources of experimental error: the greatest limitation to Eratosthenes' method was that, in  antiquityoverland  distance measurements were not  reliable , especially for travel along the  non-linear  Nile, which was traveled  primarily  by boat. So the accuracy of Eratosthenes' size of the earth is surprising.

Eratosthenes' experiment was highly regarded at the time, and his estimate of the Earth’s size was accepted for hundreds of years afterwards. His method was used by Posidonius about 150 years later.

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