The geometry we study at school is called Euclidean precisely because it is born from a book. Before entering into the theorems, it is worth getting to know the work that gave shape to the very idea of mathematical proof.
History — Euclid and the Elements
The geometry we study at school is called “Euclidean” because it comes from a book: the Elements (Stoicheîa) of Euclid, written in Alexandria in Egypt around 300 BC. They are thirteen books (actually thirteen papyrus “scrolls”) that, starting from just five postulates and five common notions, deduce in a rigorously chained way 465 propositions of plane geometry, number theory and solid geometry.
The Elements are the most read, copied and commented mathematics book of all time: after the Bible, it is probably the text that has had the most editions in European history. Their influence on the very idea of “mathematical proof” is immense: for over two thousand years, presenting an idea “more geometrico” (in the manner of the geometers) has meant presenting it with the rigour of Euclid. Newton too, in his Principia, and Spinoza, in his Ethics, chose this expository form (Boyer, A History of Mathematics, ch. 4); see also Netz, ch. 3, for a modern re-reading of the Greek context.
Links
Topics: Euclidean geometry
Concepts: Postulate · Theory
Skills: Proving
People: Euclid · Isaac Newton