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Eudoxus, son of Aeschines, was born and died in Cnidus (also transliterated Knidos), a city on the southwest coast of Anatolia. [3] The years of Eudoxus' birth and death are not fully known but Diogenes Laërtius gave several biographical details, mentioned that Apollodorus said he reached his acme in the 103rd Olympiad (368– 365 BC), and claimed he died in his 53rd year.
The cosmological model of concentric (or homocentric) spheres, developed by Eudoxus, Callippus, and Aristotle, employed celestial spheres all centered on the Earth. [1] [2] In this respect, it differed from the epicyclic and eccentric models with multiple centers, which were used by Ptolemy and other mathematical astronomers until the time of Copernicus.
The celestial spheres, or celestial orbs, were the fundamental entities of the cosmological models developed by Plato, Eudoxus, Aristotle, Ptolemy, Copernicus, and others. In these celestial models, the apparent motions of the fixed stars and planets are accounted for by treating them as embedded in rotating spheres made of an aetherial ...
According to Eudoxus, there were only 27 spheres in the heavens, while there are 55 spheres in Aristotle's model. Eudoxus attempted to construct his model mathematically from a treatise known as On Speeds (Ancient Greek: Περί Ταχών) and asserted the shape of the hippopede or lemniscate was associated with planetary retrogression ...
Aristotle elaborated on Eudoxus' system. In the fully developed Aristotelian system, the spherical Earth is at the center of the universe, and all other heavenly bodies are attached to 47–55 transparent, rotating spheres surrounding the Earth, all concentric with it. (The number is so high because several spheres are needed for each planet.)
Callippus was born at Cyzicus, and studied under Eudoxus of Cnidus at the Academy of Plato. He also worked with Aristotle at the Lyceum, which means that he was active in Athens prior to Aristotle's death in 322 BC. He observed the movements of the planets and attempted to use Eudoxus' scheme of connected spheres to account for their movements.
Eudoxus emphasised that this is a purely mathematical construct of the model in the sense that the spheres of each celestial body do not exist, it just shows the possible positions of the bodies. [23] His model was later refined and expanded by Callippus. Geocentric celestial spheres; Peter Apian's Cosmographia (Antwerp, 1539)
Eudoxus, a student of Plato, was born around 400 BC. [4] A mathematician and an astronomer, he generated one of the earliest sphere-centric models of the planet systems, based on his background as a mathematician. Eudoxus's model was geocentric, with the Earth being a stationary sphere at the center of the system, surrounded by 27 rotating ...