Equant

The equant is a point offset from the center of a planet’s deferent, from which the planet’s motion along the deferent appears uniform in angle.

Deferent and epicycle: A Ptolemaic model in which a planet moves on an epicycle whose center travels along a larger circle called the deferent. The equant modifies the deferent’s motion in this standard model of planetary paths.
Ptolemy: A second-century Greek mathematician and astronomer whose works systematized geocentric astronomy. Ptolemy developed the equant as part of his mathematical account of planetary motion.
Islamic astronomy: Astronomical scholarship developed across the medieval Islamic world, combining observation, mathematics, and inherited models. Astronomers scrutinized Ptolemaic devices, including the equant, and devised geometrical alternatives.
Epicycle: A small circle whose center moves along a larger circle in ancient models of planetary motion. Epicycles add circular components; the equant instead changes the point from which angular uniformity is measured.
Uniform circular motion: Motion at constant angular speed along a circle centered on the point used to measure that motion. The equant preserves uniform angular motion, but measures it from an offset point.
Hipparchus: A Greek astronomer of the second century BCE known for mathematical astronomy and star cataloging. His earlier planetary models helped establish the geometric tradition Ptolemy extended.
Nasir al-Din al-Tusi: A thirteenth-century Persian astronomer and mathematician associated with the Maragha observatory and the Tusi couple. His mathematical work formed part of a broader effort to reform inherited planetary models.
Eccentric circle: A circle used to model celestial motion whose center does not coincide with Earth. An eccentric shifts the circle’s center, whereas the equant shifts the point of uniform angular motion.
Ptolemaic system: An Earth-centered astronomical model that represents celestial motions with combinations of circles. The equant is one geometric device within this larger planetary model.
Ancient Greek astronomy: The mathematical study of celestial bodies developed by Greek scholars from antiquity through late antiquity. The equant emerged within Greek efforts to model planetary appearances geometrically.

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