From ProofWiki
Jump to navigation Jump to search


Greek mathematician about whom little is known, apart from:

  • He taught in Alexandria (then a Macedonian colony, the hub of the Hellenic world);
  • He assembled the geometry text The Elements, possibly the most famous mathematics text book of all time.

There is controversy as to whether he did actually exist. It has been suggested that the name Euclid was a pseudonym for a team of mathematicians working as a team. (See Bourbaki for a modern example of this.)

Not to be confused with the Socratic philosopher Euclid of Megara.




  • Born: c. 325 BCE
  • Died: c. 265 BCE, Alexandria, Egypt

Theorems and Definitions

Several concepts are named after him, but they were so named because they possess properties inherited from concepts which Euclid introduced:

Results named for Euclid can be found here.

Definitions of concepts named for Euclid can be found here.


  • c. 300 BCE: The Elements
  • The Pseudaria (or Pseudographemata) (referred to by Proclus, believed irreparably lost): a more elementary primer on geometry
  • The Data: elementary exercises in analysis, supplementary to The Elements
  • On Divisions (of Figures) (mentioned by Proclus, lost in Greek but survived in Arabic): concerns dissection of geometric figures
  • The Porisms: a collection of theorems and problems in more advanced geometry
  • The Surface-Loci (mentioned by Pappus, now considered lost): may have concerned surfaces of revolution
  • The Conics: now lost, but according to Pappus may have been the basis of the work of the same name by Apollonius. It was well-known to Archimedes who quoted it extensively.
  • The Phaenomena: a work of astronomy and spherical geometry which still exists
  • The Optics
  • Elements of Music (but it is disputed as to whether he actually wrote this)


The laws of nature are but the mathematical thoughts of God.
This misattribution seems first to have appeared in A Mathematical Journey by Stanley Gudder ($1976$), p. xv.
It is suspected that it originated from Kepler.
Many sources have propagated this mistake, and many of those use it as an excuse to preach sermons on the subject.

Anecdotes (of questionable accuracy)

Ptolemy once asked Euclid if there was any shorter way to a knowledge of geometry than that of the Elements, and he replied that there is no royal road to geometry.
-- Proclus Lycaeus

Someone who had begun to read geometry with Euclid, when he had learned the first proposition, asked him: "What shall I get from learning these things?" Euclid called his slave and said, "Give this person a penny, since he must make a profit out of what he learns."
-- Stobaeus

Critical View

[Abraham Lincoln] studied and nearly mastered the six books of Euclid since he was a member of Congress.
He began a course of rigid mental discipline with the intent to improve his faculties, especially his powers of logic and language. Hence his fondness for Euclid, which he carried with him on the circuit till he could demonstrate with ease all the propositions in the six books; often studying far into the night, with a candle near his pillow, while his fellow-lawyers, half a dozen in a room, filled the air with interminable snoring.
-- Abraham Lincoln: Short Autobiography ($1860$)
-- Quoted in 1937: Eric Temple Bell: Men of Mathematics: They Say: What Say They? : Let Them Say

Also known as

In Greek: Εὐκλείδης (Eukleídēs), also known as Euclid of Alexandria.

Proounced: Yoo-klid.


Beware: the entry starts with the above misattributed quote, and then launches into a biography of Abraham Lincoln. The politically squeamish may wish to avoid this link.