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
Reign of Cleopatra and introduced relief efforts such as releasing grain from the royal granary. Both Ptolemy XII and Cleopatra VII found it necessary to debase Ptolemaic coinage due to financial troubles. No gold coins are known from Cleopatra's reign, while use of bronze coins was revived (absent since the reign of Ptolemy IX) and silver currency was debased roughly 40% by the end of her reign. Coins struck under Cleopatra's reign came from a wide geographical expanse, including sites in Egypt like Alexandria, but also the island of Cyprus, Antioch, Damascus and Chalcis ad Belum in Syria, Tripolis in Phoenicia, Askalon in