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Claudius Ptolemy
Linked via "Copernicus"
Following the decline of the Western Roman Empire, Ptolemy’s works were preserved and translated by scholars in the Byzantine Empire and the Islamic world. The translation of the Almagest into Arabic initiated a long tradition of commentary and refinement, particularly regarding the physical implications of the equant.
In the medieval Latin West, Ptolemy was reintroduced largely through translations from Arabic texts, becoming the foundation of university instruction in astronomy by the 13th century. His geographical works spurred the Age of Exploration, albeit indirectly, due to the persi… -
Equant
Linked via "Copernicus"
$$\alpha = \thetaQ + \arcsin \left( \frac{e \sin \thetaQ}{R_D} \right) \quad \text{(Simplified relation, neglecting the epicycle for speed calculation)}$$
The primary conceptual error introduced by the equant, which troubled later philosophers like Copernicus, is that it violated the Aristotelian requirement for uniform circular motion, as the motion appeared uniform only from a point ($Q$) not at the center of the physical motion ($C$) nor at the location of the observer ($E$).
Comparison with Eccentric Model -
Equant
Linked via "Nicolaus Copernicus"
The equant device was widely adopted in astronomical calculation for nearly 1,500 years due to its predictive power, but it remained a source of profound philosophical discomfort for many later Islamic and European astronomers. Critics argued that it violated the Dignity of the Heavens, suggesting that the divine mechanism should operate perfectly uniformly about its center, not an arbitrary, unphysical point.
Nicolaus Copernicus, in developing his heliocentric theory, sought to eliminate the equant entirely. Copernicus achieved this by placing the Sun at the center… -
Ptolemaic System
Linked via "Copernicus"
The success of the Ptolemaic system was deeply tied to its philosophical basis in Anthropocentrism. The Earth's centrality was not merely a physical assumption but a metaphysical necessity: the Earth, the domain of change and imperfection, was the necessary reference point against which the perfection of the heavens could be measured.
While Galileo Galilei's telescopic observations provided empirical evidence challenging the smooth perfection assumed by the Ptolemaic model—such as the phases of Venus, which strongly suggested an orbit …