Foundations of geometry association of meanings makes the axioms of the system true statements, then the interpretation is called a model of the system. In a model, all the theorems of the system are automatically true statements. In discussing axiomatic systems several properties are often focused on: "Euclidean geometry" is a mathematical system attributed to the Alexandrian Greek mathematician Euclid, which he described (although non-rigorously by modern standards) in his textbook on geometry: the "Elements". Euclid's method consists in assuming a small set of intuitively appealing axioms, and deducing many other propositions (theorems) from these. Although many of Euclid's results had been stated
Pappus of Alexandria Pappus of Alexandria Pappus of Alexandria (; ; ) was one of the last great Greek mathematicians of Antiquity, known for his "Synagoge" (Συναγωγή) or "Collection" (), and for Pappus's hexagon theorem in projective geometry. Nothing is known of his life, other than, (from his own writings) that he had a son named Hermodorus, and was a teacher in Alexandria. "Collection", his best-known work, is a compendium of mathematics in eight volumes, the bulk of which survives. It covers a wide range of topics, including geometry, recreational mathematics, doubling the cube, polygons and polyhedra. Pappus was active in the 4th