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Euclid (325 BC- 265 BC). Scientist and Mathematician, of Greco-Roman origin, considered the brightest of his time. **He is also known as the father of Geometry.**

His work Los Elementos is the most important and recognized treatise on geometry and mathematics in the scientific world, **which contains valuable definitions and is a written testimony on the history of Greek Mathematics,** which is still in force today, thus being considered one of the most influential works in history.

## Hypothesis about its existence

Little is known of his life in the historical sense, except for what Is Referred to by Proclo in his summary of the famous Greek mathematicians. **He is believed to have lived in Alexandria, northern Egypt, **

during the tenure of Ptolemy I, who ruled this country between 323 BC and 285 BC. However, some historians doubt its existence, **while others are inclined to think that it can be more of a group of people than an individual as such.**

**At least three hypotheses are handled on the existence of Euclid. **

The first points out that Euclid was indeed a historical character, by mathematical profession, who wrote in his handwriting The Elements, **as well as other works that bear his signature. **

A second theory, states that Euclid was the head of a group of mathematicians, who worked in Alexandria, **and those who wrote the complete works of Euclid together,** signing them all with his name.

And thirdly, there is another thesis, which states that the complete works of Euclid were actually written by a group of mathematicians from Alexandria,** who signed it under that pseudonym, based on the philosopher Euclid de Megara,** contemporary of Plato, who had lived a century before.

## The Elements of Euclid

His work The Elements formally presents the study of the properties of regular geometric shapes and numbers.

According to some historians, Euclid did not reach for the first time the results presented in his treatise, but the outlining and presentation of his results, give him great merit, **thus becoming one of the most important scientific texts in the world and a compilation of the knowledge imparted in Greece at the time.**

It is mistakenly believed that The Elements only encompasses Geometry, **because only the first four books of the work are usually taken into account,** which develop definitions of elementary geometry.

In his first book, foundational, Euclid develops 23 definitions such as that a point has a dimension equal to zero, that a line has only length, **its dimension being equivalent to 1; that a surface has only two dimensions:** wide and long, while a solid body has three: long, wide, and height.

Euclid raises five unproven assumptions, called axioms, along with five proven assumptions he called common notions. **Likewise, book I exposes several elementary theorems and ends with the Pythagorean Theorem.**

Book II exposes knowledge of geometric algebra, **as well as contains a section on the “section” renamed in the Renaissance as the “golden section”,** as well as the application of the Pythagorean theorem for arbitrary triangles.

**Book III** studies the properties of circles, **while the IV** delves into the construction of regular polygons, placing special emphasis on the pentagon. Book V theorizes about the relationships and proportions of three-dimensional figures, attributed to Eudoxo de Cnido (390 BC- 350 BC). Book **VI** applies the theory of proportions to the figures of flat geometry, especially triangles and parallelograms.

For his part, according to the philosopher Proclo, **books VII, VIII and IX of Euclid’s work delve into the Theory of Positive Integers**. They include 22 definitions, including unit, even, odd, as well as methods for finding the various properties of these.

For example, Book VII describes t**he Euclid Algorithm, with which you can find the maximum common divider** of two or more numbers.

Book VIII studies what **is now known as geometric sequences, while the IX demonstrates an infinite** number of prime numbers. Books X, XI, XII and XIII would concern the work of Pythagoras Teeteto (417 BC – 369 BC) and the study of three-dimensional figures.

Due to the inequality between the different books, as well as the multiple levels of mathematics found in the work, **some historians are inclined to think of a fourth hypothesis tha**t places Euclid as a kind of ancient publisher of studies and discoveries made by other mathematicians, however it could not be known exactly which studies are of him and which of his predecessors.

July 28, 2019