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Mathematics
Measurement of the circumference of the Earth.Details of his calculations appear in works by Cleomedes, Theon of Smyrna and Strabo.
Eratosthenes compared the noon shadow at midsummer between Syene (now Aswan on the Nile in Egypt) and Alexandria. He assumed that the sun was so far away that its rays were essentially parallel, and then with a knowledge of the distance between Syene and Alexandria, he gave the length of the circumference of the Earth as 250,000 stadia.
His work on prime numbers led to the concept known as the 'Sieve of Eratosthenes' and is still a tool in number theory research. The sieve appears in the Introduction to Arithmetic by Nicomedes.
Science:
He developed a calendar that catered for leap years
He compiled a directory of some 675 stars.
History :
He developed a systematic chronography or timeline commencing at the time of the siege of Troy
Geography :
Mapped the route of the Nile and two of its tributaries in Ethiopia as well as developing an explanation for its regular flooding.
Proposed names for four of the races in "Eudaimon Arabia", now the Yemen. These are still used today and include the Minaeans, Sabaeans, Qatabanians, and Hadramites.
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