Ancient scientist
Country: Greece

  1. Biography of Euclid
  2. Euclid in Alexandria
  3. Content of the "Elements"
  4. Euclid's Contributions

Biography of Euclid

Euclid, a renowned ancient scholar, was born in an unknown location and time. Little is known about his life, with the first commentator on his work, Proclus, unable to provide any information on his birth or death. However, some biographical details have been preserved in a 12th-century Arabic manuscript. According to this manuscript, Euclid, also known as the "Geometer," was the son of Naucrates and hailed from Tyre. While his origins were Greek, he resided in Syria.

Euclid in Alexandria

Euclid was invited to Egypt by King Ptolemy I, who established the Museion, a temple dedicated to scholars and poets. In Alexandria, the capital of Egypt, Euclid founded a mathematical school and wrote his fundamental work, collectively known as "Elements," for his students. This work was completed around 325 BC. The "Elements" consisted of thirteen books, all structured according to a unified logical framework. Each book began with the definition of concepts such as points, lines, planes, and figures, followed by the construction of an entire geometric system based on a small number of fundamental principles, including five axioms and five postulates, which were accepted without proof.

Content of the "Elements"

Books I-IV of the "Elements" covered geometry, drawing influence from the teachings of the Pythagorean school. Book V developed the theory of proportions, while books VII-IX delved into the study of numbers, drawing from Pythagorean sources. Books X-XII explored the measurement of areas in both plane and solid figures (stereometry), as well as the theory of irrational numbers, particularly in Book X. Book XIII contained investigations into regular solids. Euclid's "Elements" constituted the foundation of what is now known as Euclidean geometry, describing the metric properties of space, which modern science refers to as Euclidean space. Euclid gave mathematical clarity to the atomistic idea of empty space in which atoms move. According to Euclid, the simplest geometric object is a point, which he defined as something indivisible. In other words, a point is an atomic unit of space.

Euclid's Contributions

Euclid's teachings on parallel lines and his famous fifth postulate, often referred to as the parallel postulate ("If a straight line falling on two straight lines makes the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles"), defined the properties of Euclidean space and its geometry, setting it apart from non-Euclidean geometries. Throughout the centuries, the "Elements" were published 2,500 times, with an average of 6-7 editions per year. Until the 20th century, the book remained the primary textbook for geometry in schools and universities.

Euclid also authored partially preserved and subsequently reconstructed mathematical treatises. He introduced an algorithm for finding the greatest common divisor of two arbitrary natural numbers and devised the algorithm known as the "Sieve of Eratosthenes" for finding prime numbers. Euclid laid the foundations of geometric optics, as discussed in his works "Optics" and "Catoptrics." He also described the monochord, a single-stringed instrument used to determine the pitch of a string and its divisions. The invention of the monochord was significant in the development of music, eventually leading to the creation of keyboard instruments such as the harpsichord and piano.

While the discovery of all the peculiarities of Euclidean space was not immediate, the work of scientific thought over many centuries was built upon the foundation established by Euclid's "Elements." Knowledge of the basics of Euclidean geometry is now considered an essential component of general education worldwide.