Euclid

Euclid was an ancient Greek mathematician whose Elements organized geometry and number theory through definitions, postulates, and deductive proofs.

Euclid's Elements: A thirteen-book mathematical treatise presenting geometry and number theory through definitions, postulates, and proofs. This is Euclid’s best-known work and the main source of his lasting mathematical influence.
Alexandria: An ancient Egyptian city founded by Alexander the Great that became a major center of Hellenistic scholarship. Euclid is traditionally associated with teaching mathematics in Alexandria under the Ptolemies.
Proclus: A fifth-century Neoplatonist philosopher whose commentary on Euclid’s first book preserves historical accounts of Greek geometry. Proclus is a major source for what later antiquity believed about Euclid and his predecessors.
Latin translations of Euclid: Medieval and early modern Latin versions of Euclid’s Elements, translated from Greek and Arabic sources. Latin editions carried Euclidean geometry into Western European schools and universities.
Euclidean geometry: The geometry of flat space developed from the postulates presented in Euclid’s Elements. Euclid’s name became attached to the geometric system organized in the Elements.
Ptolemaic Kingdom: A Hellenistic kingdom based in Egypt, ruled by the Ptolemaic dynasty from 305 to 30 BCE. Euclid’s career is commonly placed in Alexandria during the early Ptolemaic period.
Pappus of Alexandria: A fourth-century Greek mathematician whose surviving works discuss geometry, mechanics, and earlier mathematical texts. Pappus preserves later traditions about Euclid’s teaching and the mathematical culture of Alexandria.
Arabic mathematics: Mathematical scholarship written in Arabic across the medieval Islamic world and its neighboring regions. Arabic translators and commentators preserved, expanded, and transmitted Euclid’s mathematical works.
Euclidean algorithm: A procedure for finding the greatest common divisor of two integers by repeated division. Euclid’s Elements presents an early form of this algorithm for finding common measures.
Plato's Academy: A philosophical school founded by Plato in Athens, active from the fourth century BCE into late antiquity. Euclid’s mathematical environment inherited ideas shaped by the Academy’s engagement with geometry.

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