History of geometry lost. He was brought to the university at Alexandria by Ptolemy I, King of Egypt. "The Elements" began with definitions of terms, fundamental geometric principles (called "axioms" or "postulates"), and general quantitative principles (called "common notions") from which all the rest of geometry could be logically deduced. Following are his five axioms, somewhat paraphrased to make the English easier to read. Concepts, that are now understood as algebra, were expressed geometrically by Euclid, a method referred to as Greek geometric algebra. Archimedes (287-212 BC), of Syracuse, Sicily, when it was a Greek city-state, is often considered to be the greatest
Reign of Cleopatra could be classified as Greeks if they abandoned their original cultures, received a Greek education, labeled their gods and goddesses with Greek names, and embraced the Greek lifestyle. Native Egyptians had been largely excluded from serving in the military by the reign of Ptolemy II, replaced by Greek and Jewish landholders called cleruchs. By the reign of Ptolemy IV in the late 3rd century BC they were reintroduced as phalangite soldiers. Large migrations of Greeks to Egypt ceased by the 2nd century BC, so that the Greek minority in Ptolemaic Egypt remained demographically small. Although Egyptian priests were often wealthy