# Euclid

**Type:** Person  
**Domain:** Geometry  
**Active:** c. 300 BCE  
**Location:** Alexandria, Egypt  
**Codex URL:** /mathematics/geometry/euclid/  
**Entry status:** Live — v1.0 (2026-05-27)

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## Summary

Greek mathematician, author of the *Elements* — the most influential mathematics textbook in history, used for over 2,300 years. Almost nothing is known of his personal life; known almost entirely through his work. Active in Alexandria under Ptolemy I Soter.

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## Key facts

- Author of *Elements* (13 books), *Data*, *Optics*, *Phaenomena*
- Main ancient source: Proclus's Commentary (c. 450 CE), written ~750 years after Euclid
- Credited with systematising work of Eudoxus (proportion theory) and Theaetetus (irrationals)
- Distinct from Euclid of Megara (philosopher, student of Socrates, different person)

## Historiography

Mainstream scholarly consensus (Heath, Knorr, Fowler, Netz): Euclid was a real individual whose biography is lost, not a collective pseudonym. Stylistic consistency across the Elements supports single authorship.

## Euclid's gaps and Hilbert's fix

Euclid's proofs contain implicit unstated assumptions (e.g. Pasch's axiom on betweenness). Hilbert's *Grundlagen der Geometrie* (1899) supplies 20 axioms making Euclidean geometry logically complete.

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## Sources

### Tier 1
- Heath, T.L. (1956). *Euclid: The Thirteen Books of the Elements*. Vol. 1. Dover.
- Netz, R. (1999). *The Shaping of Deduction in Greek Mathematics*. Cambridge University Press.

### Tier 2
- O'Connor, J.J. and Robertson, E.F. (1999). Euclid of Alexandria. MacTutor.
- Taisbak, C.M. (2003). *Euclid's Data*. Museum Tusculanum Press.

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*Mathematics Codex entry v1.0 — added 2026-05-27 — thecodex.expert/mathematics/*