Reading: Euclid and deductive geometry

In 338 BC, Greece comes under Macedonian rule. Alexander the Great took Greek culture to the East and founded dozens of cities. One of them, Alexandria, in Egypt, would have an extraordinary role in the history of Mathematics. Ptolemy, who ruled Egypt after Alexander, created the Museum there, a research and teaching center maintained by the State. His library had close to 700 a thousand rolls of papyrus.

Claudius Ptolemy, later artistic representation.Justus van Gent or Pedro Berruguete · Wikimedia Commons · Public domain

One of the Museum’s first and most notable mathematicians was Euclid (c. 300 BC), about whose life almost nothing is known. It is said that when Ptolemy asked if there was a shorter way to learn geometry, he replied: “There is no real way in geometry.”

Euclid, Renaissance representation traditionally associated with Euclid or Archimedes.Rafael Sanzio · Wikimedia Commons · Public domain

His fame rests on The Elements, in thirteen books: the oldest complete text of Greek mathematics to reach us. Since the first printed edition, in 1482, there have been more than a thousand editions. From five common notions, five postulates and some definitions, Euclid deduced 467 theorems. For two millennia, The Elements were the model of good mathematics. Over time, logical flaws were found (for example, the use of continuity hypotheses that were never stated), but they little diminish the greatness and influence of the work.

Euler's Eyes

Reading: Euclid and deductive geometry

Further reading

On this page