Between 300 and 270 BCE because the date is not certain, the Greek mathematician Euclid (fl .: 325-265 BC) wrote his famous Elements, a sum of 13 volumes (15 years French) dedicated to the geometry and mathematics. Books I to VI deal with plane geometry, books VII to IX of the theory of relations, book X of the theory of irrational numbers of Eudoxe, books XI to XIII of geometry in space.

The whole ends with the study of the properties of the five regular polyhedra and a demonstration of their existence. These works served as a foundation for the development of logic and science in the West. Unfortunately the oldest complete copy that we have left was written by the Greek mathematician Théon of Alexandria probably around 370 AD, author who also wrote comments on the Almagest of Ptolemy.

The Elements will be translated for the first time into English by Henry Billingsley in 1570 and by Isaac Barrow in 1650, a translation that Newton apparently consulted in 1663. The oldest French version was written in 1613 by Jacques Le Roy.

At the same time, Aristarchus of Samos (310-230 BC) determined by trigonometry the mean distances of the Sun and the Moon. In his logic, he also felt that the little planet Earth had to turn around the big Sun. If the stars seemed fixed, it was because they were extremely distant. Rightly Aristarchus was nicknamed the Copernicus of Antiquity. Unfortunately his works have been lost. We only know about it through a treatise written by Archimedes.

After having cried out Eureka while discovering the way to calculate the density of a body, this great mathematician attacked the problem of the Universe around 250 BC, when he wrote the Arénaire (Arena meaning sand). According to Aristarchus' theory, Archimedes suggested to his friend King Hiero II of Syracuse that the Universe could contain 1063 grains of sand.