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Mathematics# Euclid

## Who was Euclid?

## Euclid biography

## Discoveries

## Contributions

#### Elements

#### The Euclid algorithm

#### Euclidean geometry

#### Demonstration

#### Axiomatic methods

## Works by Euclid

## Euclid postulates

## Phrases

In the history of geometry, **Euclid** of Alexandria is the main representative of this science. His contributions to humanity are invaluable and many of them remain today as universal premises. For many mathematicians and geometricians, he is known as the **father of geometry**. Euclid along with Archimedes and Apolonio of Perga is **part of the triad of mathematicians of Antiquity **and is one of the most illustrious and best known mathematicians of all time. His most renowned work is "**Elements**” and is composed of thirteen books that develop different geometric and arithmetic themes, and that have remained unchanged until the 19th century. This work has been as widespread as one of the most important written works of universal literature, as well as the Bible or Don Quixote.

**Personal information**

**When he was born**: 330 B.C.**Where he was born**: Unknown**When he died**: 285 B.C.**Where did he die**: Alexandria, Egypt

Euclid of Alexandria was a Greek **mathematician** and **geometrician born in Alexandria in the 330 B.C**. His best-known work is "**Elements**" which contains significant themes related to geometry and arithmetic. He is known as the **father of geometry** for his great contributions to the world of geometry and mathematics.

Little is known about Euclid’s life. **He was born in 330 B.C**., and he was the son of Naucratis. Some authors claim that he was born and **lived in Alexandria**, northern Egypt during **the reign of Ptolemy I**, while others claim that his birth was in Tyre Kingdom and that he lived in Damascus.

It is believed that **his education began in Athens**, where he was able to acquire, in **Plato’s** school, great knowledge of geometry and mathematics. He was a teacher at his own school in Alexandria, **founder of the Ptolemaic dynasty**, during the reign of Ptolemy I – the first Greek Pharaoh, who ruled Egypt from 305 BC to 285 BC.

In his life, he was able to develop several discoveries and compile in his works all the advances that existed on the geometry and arithmetic of his time.

*“ Elements“* is his best-known work and contains 465 propositions, 93 problems and 372 theorems in thirteen volumes. He also wrote other works related to thought,

According to research, **Euclid’s death occurred in 265 B.C**.

In his life, Euclid made several important discoveries in the **theory of numbers** as his well-known **algorithm for the calculation of the maximum common divisor of two numbers;** in the field of **geometry** with its **axioms and the set of books** that make up the work entitled “**Elements**“.

His work includes several contributions that have been of great importance for the development of the study of geometry: these are: “**Elements**“, the “**Euclidian Algorithm**“, the “**Euclidian Geometry**“, the “**Mathematics and Demonstration**” and the **Axiomatic Methods**.

It is **Euclid’s best-known contribution** and is made up of **465 propositions**, **93 problems** and 372 **theorems** that include the most important mathematical and geometric developments of his time. In this work, we find the 5 Euclidian postulates and the Euclidian algorithm.

**The books from I to VI develop themes of flat geometry**; the books from **VII to X deal with topics of arithmetic **by presenting the theory of numbers and irrational segments; the books from **XI to XIII explain spatial geometry**.

In this algorithm, Euclid **describes the method for finding the greatest common divisor between two numbers**. This work has been of great importance to mathematics and has been applied in other fields such as **economics**.

The contributions developed by Euclid’s in the field of geometry **have dominated the study of this science for almost two millennia**, especially in the areas of **flat geometry** and **spatial geometry**.

Euclidean geometry, besides being a valuable tool for deductive reasoning, has been used in other fields of knowledge such as **physics**, mathematics, astronomy, **chemistry** and different branches of engineering.

Euclid, like Archimedes and Apollonius, **perfected the process of mathematical demonstration**, as a chained argument, in such a significant way that today its use in modern mathematics is indispensable.

The axioms posed by Euclid in his work “**Elements**” pose a global perspective of the axiom that motivated the development of this fundamental area of modern mathematics.

**Euclid produced many treatises on geometry and other sciences.** However, his best-known work is called “**Elements**” and consists of 13 books that compile works by other authors and him and where they touch on the themes of flat or elementary geometry, theorems of numbers and spatial geometry. In addition to developing in arithmetic and geometry, Euclid has a work entitled “**Sophisms**” and writings on music and optics.

Euclid developed in the area of geometry a set of axioms that he later called postulates. These are five and we will present them below:

**Postulate 1:**“Given two points, a line can be drawn that joins them.”**Postulate 2**: “Any segment can be continuously prolonged in an unlimited line in the same direction.”**Postulate 3**: “A center circumference can be drawn at any point and any radius.”**Postulate 4:**“All right angles are equal.”**Postulate 5:**“If a straight line, when cutting two others, forms the internal angles of the same side smaller than two straight lines, those two straight lines prolonged indefinitely are cut from the side on which are the angles smaller than two straight lines. This axiom is also known as the axiom of parallels.

Here are some of Euclid’s best-known phrases. These are:

- What is asserted without proof, can be denied without proof
- Freedom is not an end; it is a means to develop our forces.
- Reason is a means to get to the truth
- Success is not for what they think they can do, but for those who do.
- There is no real way to Geometry

Written by Gabriela Briceño V.

Briceño V., Gabriela. (2019). *Euclid*. Recovered on 2 February, 2023, de Euston96: https://www.euston96.com/en/euclid/