## Tag Archives: Euclid

## What is “Euclid” ?

## Euclid

**Euclid**” is the anglicized version of the Greek name Εὐκλείδης, meaning “Good Glory”.

Little is known about *Euclid*‘s life, as there are only a handful of references to him. The date and place of *Euclid*‘s birth and the date and circumstances of his death are unknown, and only roughly estimated in proximity to contemporary figures mentioned in references. The few historical references to *Euclid* were written centuries after he lived, by Proclus and Pappus of Alexandria. Proclus introduces *Euclid* only briefly in his fifth-century Commentary on the Elements, as the author of Elements, that he was mentioned by Archimedes, and that when King Ptolemy asked if there was a shorter path to learning geometry than *Euclid*‘s Elements, “*Euclid* replied there is no royal road to geometry.” Although the purported citation of *Euclid* by Archimedes has been judged to be an interpolation by later editors of his works, it is still believed that *Euclid* wrote his works before those of Archimedes. In addition, the “royal road” anecdote is questionable since it is similar to a story told about Menaechmus and Alexander the Great. In the only other key reference to *Euclid*, Pappus briefly mentioned in the 4th century that Apollonius “spent a very long time with the pupils of *Euclid* at Alexandria, and it was thus that he acquired such a scientific habit of thought.”

Although many of the results in Elements originated with earlier mathematicians, one of **Euclid**‘s accomplishments was to present them in a single, logically coherent framework, making it easy to use and easy to reference, including a system of rigorous mathematical proofs that remains the basis of mathematics 23 centuries later.

There is no mention of **Euclid** in the earliest remaining copies of the Elements, and most of the copies tell they are “from the edition of Theon” or the “lectures of Theon”, while the text considered to be primary, held by the Vatican, mentions no author. The only reference that historians rely on of **Euclid** having written the Elements was from Proclus, who briefly in his Commentary on the Elements ascribes **Euclid** as its author.

Although best known for its geometric results, the Elements also includes number theory. It considers the connection between perfect numbers and Mersenne primes, the infinitude of prime numbers, **Euclid**‘s lemma on factorization, and the **Euclid**ean algorithm for finding the greatest common divisor of two numbers.

The geometrical system described in the Elements was long known simply as geometry, and was considered to be the only geometry possible. Today, however, that system is often referred to as **Euclid**ean geometry to distinguish it from other so-called non-**Euclid**ean geometries that mathematicians discovered in the 19th century.

In addition to the Elements, at least five works of **Euclid** have survived to the present day. They follow the same logical structure as Elements, with definitions and proved propositions.

Other works are credibly attributed to **Euclid**, but have been lost.

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