Eudoxus

Eudoxus of Cnidus (c. 390–c. 337 BCE) was a Greek mathematician, astronomer, and philosopher from Cnidus in Ionia. He is regarded as a foundational figure in early Greek mathematics and astronomy, and his ideas influenced later traditions of geometry and celestial theory.

In mathematics, Eudoxus developed the Eudoxian theory of proportion, a rigorous framework for comparing magnitudes by means of ratio and multiples. This theory became the standard basis for the treatment of proportion in Euclid’s Elements (Book V). He also introduced the method of exhaustion, a geometric technique for proving limits by enclosing figures with shrinking sequences of inscribed and circumscribed figures; it anticipated ideas later formalized as limits and integral calculus. Through these methods, he contributed to the understanding of areas, volumes, and irrational numbers.

In astronomy, he proposed a mechanistic model of the heavens using concentric, homocentric spheres to account for the apparent motions of the planets and the Sun and Moon. Although later refinements replaced or extended his model, it represented a major early attempt to describe celestial motion with a unified geometrical framework.

Writings by Eudoxus have not survived; our knowledge comes from later commentators such as Aristotle, Proclus, and Pappus, who describe his theories and methods.

Disambiguation: The name Eudoxus can also refer to Eudoxus of Cyzicus, a Hellenistic geographer and explorer known for his voyage into the Indian Ocean.