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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.
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.
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 ...
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 ...
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.
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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.)
Can we imagine ourselves back on that awful day in the summer of 2010, in the hot firefight that went on for nine hours? Men frenzied with exhaustion and reckless exuberance, eyes and throats burning from dust and smoke, in a battle that erupted after Taliban insurgents castrated a young boy in the village, knowing his family would summon nearby Marines for help and the Marines would come ...