A way to defined geometry without talking about coordinates, i.e. like Euclid's Elements, notably Euclid's postulates, as opposed to Descartes's Real coordinate space.
There are 5: en.wikipedia.org/w/index.php?title=Euclidean_geometry&oldid=1036511366#Axioms, the parallel postulate being the most controversial/interesting.
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Euclid's Elements is a thirteen-book mathematical work organized through definitions, postulates and proofs. Its topics include plane and solid Euclidean geometry, proportions and number theory. For example, Book I ends with the Pythagorean theorem and its converse, while Book IX includes a construction of even perfect numbers. Its enduring feature is the attempt to derive many geometric statements from a small explicit base of assumptions. Modern axiomatizations make additional assumptions about order, continuity and incidence explicit.[ref]
Euclid's "Elements" is a comprehensive mathematical work composed by the ancient Greek mathematician Euclid around 300 BCE. It is one of the most influential works in the history of mathematics and serves as a foundational text in geometry. The "Elements" consists of 13 books that cover various topics in mathematics, including: 1. **Plane Geometry**: The first six books focus on the properties of plane figures, such as points, lines, circles, and triangles.