The work of Euclid , a paradigm of the mathematics of ancient Greece

Euclid of Alexandria is one of those among the mathematicians of ancient Greek culture about whom little biographically is known. The date and city of his birth are not preserved for posterity, although modern historians assign approximate dates based on the extant literature of the period in which he worked. Archimedes of Syracuse mentions Euclid during the reign of Ptolemy I of Egypt (306-283 B.C.E), giving the modern expositor some idea of Euclid's historical framework. i In the literature Proclus (circa 450 C.E) records Archimedes and Euclid as contemporaries, " He [Euclid] is therefore younger than the pupils of Plato, but older than Eratosthenes and Archimedes. For these men were contemporaries, as Eratosthenes somewhere says. " ii Archimedes lived from 287 until 212 B.C.E and Plato died in 347 B.C.E, fitting Euclid somewhere in the interval between the two, which also corresponds historically to the reign of Ptolemy I. iii Most historical references on Euclid are reconstructed from the historical period—it is hypothesized that Euclid studied at Plato's Academy in Athens due to the great body of geometric thought and study which existed in the city at the time. iv Euclid of Alexandria is sometimes confused with Euclid of Megara (circa 400 B.C.E) who was a contemporary of Plato v and a student of Socrates. vi Ptolemy I gained political control of Egypt after the Macedonian empire collapsed following the death of Alexander the Great in 323 B.C.E. As a royal act Ptolemy I enabled the existence of a royal institution, the Museum (circa 300 B.C.E), for the advancement of his royal prestige and the general body of knowledge at the time. It is known that Euclid taught mathematics at the Museum of Alexandria vii and because of this the title Euclid of Alexandria is given to him by historians to distinguish him from other historical Euclids. Pappus (circa 310