He was born in Cyrene, the present city of Shahhat in Libya in the year 276 a. C.
He studied in Alexandria and Athens. He was a disciple of Ariston of Chios, Lisanias of Cyrene and Callimachus. He was also a great friend of Archimedes.
It had the nickname of Beta (as the second Greek letter) and also that of Pentatlos, the athlete who is able to be part of several specialties but maybe because of that he is not capable of being excellent in any of them, he always remains second, nickname very hard for a philosopher whose bases have served for later scientific findings.
From 236 a. C. and until the end of his life he worked in the Library of Alexandria. According to Suidas, Eratosthenes lost his sight and left himself to die of hunger when he was eighty years old, although according to Luciano he arrived at eighty-two.
It is attributed the invention of the armillary sphere that was still used in the seventeenth century. Probably he will use this instrument for his astronomical observations, but it is only known that thanks to this sphere he determined the obliquity of the ecliptic. He calculated that the interval between the tropics was 11/83 of the Earth’s circumference, so the result was 23º 51 ’19 “, a figure that Claudio Ptolemy later adopted. According to some, Eratosthenes actually obtained a figure of 24º, and it was Ptolemy who tuned up to 23º 51’19 “.
Observing the eclipses, he calculated that the distance to the Sun was 804,000,000 stadiums. If the stadium measured 185 meters, this gave 148,752,000 kilometers, a figure very close to the astronomical unit. He also calculated that the distance to the Moon was 780,000 stadiums, although in reality it is almost three times greater. He also calculated that the diameter of the Sun was 27 times greater than that of the Earth, although in reality it is 109 times larger.
He is credited with the work Katasterismoi, which includes the nomenclature of 44 constellations and 675 stars.
He studied the prime numbers. The “sieve of Eratosthenes” is still used, although modified.
To calculate the size of the Earth he invented a trigonometric method and the notions of latitude and longitude, although it seems that they had already been used previously.
Eratosthenes had read in a papyrus of the Library of Alexandria where he worked, that on June 21, summer solstice, when at noon, the sun is closer to the zenith than any other day of the year, this star passed exactly through the zenith on Syene, in Egypt (the current Aswan). This was easily demonstrable simply by sticking a vertical stick on the ground and observing that it did not cast any shadow. It was also demonstrated by the fact that the sunlight reached the bottom of the wells. If the same was done in Alexandria, 800 kilometers north of Syene, the stick cast a short shadow, which meant that in that city the midday sun was a little over 7 degrees south of the zenith.
The distance between the two cities could be taken from the caravans that traded between these cities, or perhaps obtained the data of one of the hundreds of thousands of papyri that existed in the Library of Alexandria. Some people say that perhaps he used a regiment of soldiers to count the steps between the two cities. Thus, he calculated that the distance was 5,000 stadiums, from which he could deduce that the circumference of the earth was 252,000 stadiums. If Eratosthenes used the Egyptian stadium, which is 52.4 cm, it gives a total of 39,614.4 kilometers, that is, an error of less than 1%.
Posidonius, 150 years later, returned to these calculations and obtained a slightly lower figure, amount that would adopt Ptolemy and on which Christopher Columbus based to demonstrate the viability of his trip to the West Indies. With the measures of Eratosthenes that trip might never have been made.
He also calculated the distance of the Earth to the Sun in 804 million stadiums, which gives a figure of 139,996,500 kilometers and the distance from the Earth to the Moon in 708,000 stadiums, 123,280.5 kilometers. These calculations were made using data obtained during lunar eclipses.
Ptolemy tells that Eratosthenes measured the inclination of the Earth’s axis with great accuracy, since it obtained a value of 11/83 of 180º, that is, 23º51’15 “.
The result of these works of geodesy left them in his book “On the measurements of the Earth”, lost at present, although other authors, like Cleomedes, Teón de Izmir and Strabón reflected in their works details of these calculations.
Eratosthenes contributed to the progress of science with many other works. He devised a calendar with leap years. He created a star catalog that contained 675 stars. He drew the route from the Nile to Khartoum with great precision, including the two Ethiopian tributaries of the Nile, suggesting that the lakes were the source of the river. Many other scholars previous to Eratosthenes had studied the Nile, in their eagerness to explain the behavior of the river, but even Thales was mistaken in his theory. It was Eratosthenes who first came up with the correct answer by deducting that it sometimes rained very hard in the river source regions and this could be the explanation for the flooding of the river later on.
De Eratosthenes is also one of the most beautiful maps of the ancient world, the first with a network of meridians and parallels.