Euclidean geometry of a modern formulation in terms of constructive type theory. This development has implications for pedagogy as well. 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
Ptolemy IV Philopator Ptolemy IV Philopator Ptolemy IV Philopator (, "Ptolemaĩos Philopátōr" "Ptolemy, lover of his Father"; 245/4–204 BC), son of Ptolemy III and Berenice II, was the fourth Pharaoh of Ptolemaic Egypt from 221 to 204 BC. The decline of the Ptolemaic dynasty began under the reign of Ptolemy IV. Among the children of Ptolemy IV Philopator and his sister-wife Arsinoe III of Egypt was Ptolemy V Epiphanes, who married Cleopatra I Syra, daughter of Antiochus III the Great and Laodice III. Ptolemy IV's reign was inaugurated by the murder of his mother, and he was always under the dominion of favourites,