325 B.C. ~ 265 B.C. (?)

The dates are not exact as little is known about Euclidâs life. It is generally believed that he studied under the students of Plato and it is known that he established a school of mathematics and taught at the library in Alexandria. His most well known work is *The Elements*, which is a wonderfully organized development of the plane and solid geometry, geometric algebra, theory of proportions, number theory, and the theory of incommensurate lengths (irrational numbers) known in his time. The work is divided into 13 books and contains 465 propositions. Beginning in Book I with five (5) postulates, five (5) common notions, and twenty three (23) definitions, Euclid develops the basic properties of plane geometry from the construction of an equilateral triangle in Proposition 1 to his beautiful proof of the Theorem of Pythagoras in Proposition 47 (the book closes with a proof of the converse of the Pythagorean Theorem in Proposition 48). In Book I we see the strong commitment to a logical development of ideas that Euclid used throughout the work. This "first mathematics text" set a standard for mathematics which has been followed to this day.

Even though little personal information exists about Euclid, two stories have survived. It is known that Ptolemy I was a student in Euclidâs school for quite some time and he is reported to have asked if there was an easier way to master geometry; Euclid responded that although the king could travel on royal roads, "there is no royal road to geometry." The second story concerns a student who, after his first lesson, asked what he would gain form learning such things; Euclid called his slave and said: "Give him a coin since he must make gain by what he learns."

Other works of Euclid include: *The Data*, for use in the solution of problems by geometrical analysis, *On Divisions* (of figures), *The Optics*, and *The Phenomena*, a treatise on the geometry of the sphere for use in astronomy. His lost *Elements of Music* may have provided the basis for the extant *Sectio Canonis* on the Pythagorean theory of music.

St. Andrew's History of Euclid