Celestial spheresThe 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, transparent fifth element (quintessence), like gems set in orbs. Since it was believed that the fixed stars did not change their positions relative to one another, it was argued that they must be on the surface of a single starry sphere.
Dandelin spheresIn geometry, the Dandelin spheres are one or two spheres that are tangent both to a plane and to a cone that intersects the plane. The intersection of the cone and the plane is a conic section, and the point at which either sphere touches the plane is a focus of the conic section, so the Dandelin spheres are also sometimes called focal spheres. The Dandelin spheres were discovered in 1822. They are named in honor of the French mathematician Germinal Pierre Dandelin, though Adolphe Quetelet is sometimes given partial credit as well.
Aix-en-ProvenceAix-en-Provence (UKˌɛks_ɒ̃_prɒˈvɒ̃s, USˌeɪks_ɒ̃_proʊˈvɒ̃s,ˌɛks-), or simply Aix (medieval Occitan: Aics), is a city and commune in southern France, about north of Marseille. A former capital of Provence, it is the subprefecture of the arrondissement of Aix-en-Provence, in the department of Bouches-du-Rhône, in the region of Provence-Alpes-Côte d'Azur. The population of Aix-en-Provence is approximately 145,000. Its inhabitants are called Aixois or, less commonly, Aquisextains.
Concentric spheresThe cosmological model of concentric (or homocentric) spheres, developed by Eudoxus, Callippus, and Aristotle, employed celestial spheres all centered on the Earth. 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. Eudoxus of Cnidus was the first astronomer to develop the concept of concentric spheres. He was originally a student at Plato's academy and is believed to have been influenced by the cosmological speculations of Plato and Pythagoras.
