# Eudoxo of Cnido and the spheres

Eudoxo (408-355 a.C.) was a Greek mathematician and astronomer who was born and died in Cnido, son of Esquines and disciple of Plato. His family was composed of doctors and by his influence he studied medicine, a profession he practiced for some years in Greece. It is also known as Eudoxio de Cnidos.

At age 23 he went to Athens and entered the academy of Plato, where he studied philosophy. Years later he met the astronomical studies that were being carried out in Egypt. He organized his transfer to the city of Helipopolis sponsored and recommended by King Ageliseo. There he had access to the studies of the observations and theories of the priests of this city.

On his return to Greece he founded a school of Philosophy, Mathematics and Astronomy. Years later he wrote his first work called Phenomena, where he described the exit and concealment of the stars. He was the first Astronomer who established that the duration of the year was greater in 6 hours at 365 days.

In his second book, "The Speeds," he explained the movement of the Sun, the Moon and the Planets and introduced an ingenious system in which he assigns 4 spheres to each star to explain his movements.

In this model of the solar system the spherical Earth was in the center, around it rotated 3 concentric spheres, the outermost one carried the fixed stars and had a rotation period of 24 hours, the middle one rotated from east to west in a period that completed 223 moonings, the inner sphere possessed the moon and rotated in a period of 27 days 5 hours 5 minutes. Each of the 5 planets required 4 spheres that explained their movements and the sun and the moon 3 spheres each.

In geometry he influenced Euclid in an important way with his theory of proportions and the exhaustive method, which is why he is considered the father of integral calculus. The first was the oldest solution to irrational numbers, which cannot be expressed as a quotient of two integers. The exhaustive method allowed him to address the problem of calculating areas and volumes, such as the pyramid, whose volume is one third of a prism that has the same base.

Around 350 B.C. Eudoxo moved to the city of Cnido. There he met a newly established democratic regime and was commissioned to write the new constitution.

Eudoxo drew a map of the sky from an observatory he built on the banks of the Nile. He also studied various calendars and the record of seasonal changes, meteorological studies and the Nile.

He fought the horoscopes ardently by saying that: "When you think about making predictions about the life of a citizen with their horoscopes based on the date of their birth, we should not give any credit, since the influences of the stars are so complicated to calculate that there man on the face of the earth who can do it. "

The geometric conclusions that Eudoxo transmitted orally, were passed from generation to generation until today. Apparently Eudoxo does capture its results more than in the mind of its pupils, but with the burning of Alexandria and similar events any direct contribution from him has been lost. However, his work is known through quotes from other authors, such as the poet Arato, the influence in Book V of the elements of Euclid and the quadratures of circle and parabola described in "The method" by Arquimides.

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