Euclidean geometry Euclidean geometry Euclidean geometry is a mathematical system attributed to Alexandrian Greek mathematician Euclid, which he described 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 by earlier mathematicians, Euclid was the first to show how these propositions could fit into a comprehensive deductive and logical system. The "Elements" begins with plane geometry, still taught in secondary school (High School) as the first axiomatic system and the first examples of formal proof. It goes
Spherical geometry geometries exist; see elliptic geometry. The earliest mathematical work of antiquity to come down to our time is "On the rotating sphere" (Peri kinoumenes sphairas) by Autolycus of Pitane, who lived at the end of the fourth century BC. Spherical trigonometry was studied by early Greek mathematicians such as Theodosius of Bithynia, a Greek astronomer and mathematician who wrote the Sphaerics, a book on the geometry of the sphere, and Menelaus of Alexandria, who wrote a book on spherical trigonometry called "Sphaerica" and developed Menelaus' theorem. "The book of unknown arcs of a sphere" written by the Islamic mathematician Al-Jayyani