**Greek**

**mathematicians**. Very little is known about the life of Euclid. Both the dates and places of his birth and death are unknown. It is believed that he was educated at Plato\'s academy in Athens and s

Eratosthenes

Eratosthenes was born in Cyrene which is now in Libya in North Africa. His

teachers included the scholar Lysanias of Cyrene and the philosopher Ariston of

Chios who had studied under Zeno, the founder of the Stoic school of philosophy.

Eratosthenes also studied under the poet and scholar Callimachus who had also

been born in Cyrene. Eratosthenes then spent some years studying in Athens. The

library at Alexandria was planned by Ptolemy I Soter and the project came to

fruition under his son Ptolemy II Philadelphus. The library was based on copies

of the works in the library of Aristotle. Ptolemy II Philadelphus appointed one

of Eratosthenes\' teachers Callimachus as the second librarian. When Ptolemy III

Euergetes succeeded his father in 245 BC and he persuaded Eratosthenes to go to

Alexandria as the tutor of his son Philopator. On the death of Callimachus in

about 240 BC, Eratosthenes became the third librarian at Alexandria, in the

library in a temple of the Muses called the Mouseion. The library is said to

have contained hundreds of thousands of papyrus and vellum scrolls. One of the

important works of Eratosthenes was Platonicus which dealt with the mathematics

which underlie Plato\'s philosophy. Theon of Smyrna tells us that Eratosthenes\'

work studied the basic definitions of geometry and arithmetic, as well as

covering such topics as music. Eratosthenes also worked on prime numbers. He is

remembered for his prime number sieve, the \'Sieve of Eratosthenes\' which, in

modified form, is still an important tool in number theory research.

Eratosthenes made a surprisingly accurate measurement of the circumference of

the Earth. Details were given in his treatise On the measurement of the Earth

which is now lost. However, some details of these calculations appear in works

by other authors such as 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. Eratosthenes also measured the distance to the sun as

804,000,000 stadia and the distance to the Moon as 780,000 stadia. He computed

these distances using data obtained during lunar eclipses. Ptolemy tells us that

Eratosthenes measured the tilt of the Earth\'s axis with great accuracy obtaining

the value of 11/83 of 180, namely 23° 51’ 15". Eratosthenes made many other

major contributions to the progress of science. He worked out a calendar that

included leap years, and he laid the foundations of a systematic chronography of

the world when he tried to give the dates of literary and political events from

the time of the siege of Troy. He is also said to have compiled a star catalogue

containing 675 stars. Eratosthenes made major contributions to geography. He

sketched, quite accurately, the route of the Nile to Khartoum, showing the two

Ethiopian tributaries. He also suggested that lakes were the source of the

river. Many scholars before Eratosthenes had made a study of the Nile and they

had attempted to explain the rather strange behavior of the river, but most like

Thales were quite wrong in their explanations. Eratosthenes was the first to

give what is essentially the correct answer when he suggested that heavy rains

sometimes fell in regions near the source of the river and that these would

explain the flooding lower down the river. Another contribution that

Eratosthenes made to geography was his description of the region "Eudaimon

Arabia", now the Yemen, as inhabited by four different races. The situation

was somewhat more complicated than that proposed by Eratosthenes, but today the

names for the races proposed by Eratosthenes, namely Minaeans, Sabaeans,

Qatabanians, and Hadramites, are still used. Eratosthenes writings include the

poem Hermes, inspired by astronomy, as well as literary works on the theatre and

on ethics which was a favorite topic of the Greeks. Eratosthenes is said to have

became blind in old age and it has been claimed that he committed suicide by

starvation.

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