How Euclid Has Been an Influence

Euclid of Alexandria: 325 B.C. ~ 265 B.C. (?) The dates are not exact as little is known about Euclid's 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 irrational numbers known then.

The work is divided into 13 books and contains 465 propositions. Beginning in Book I with 5 postulates, 5 common notions, and 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 the book one can 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 following it to this day, making him one of the largest influences of all. Even though little personal information exists about Euclid, two stories about him have survived.

It is known that Ptolemy was a student in Euclid's school for quite some time and he is reported to have asked if there was an easier way to master geometry; to this Euclid responded that although the king could travel on royal roads, "there is no royal road to geometry."; a clear insight into his apparent wisdom.

The second story concerns a student who, after his first lesson, asked what he would gain in life from learning such things as he was in the school; Euclid called his slave and said: "Give him a coin since he must make gain by what he learns." Arabian and Syrian writers have said Euclid's father was Naucrates, and his grandfather, Zenarchus. They also said he was a Greek who was born in Tyre and lived in Damascus. Unfortunately, most of this information has little evidence of validity.

Added perplexity began around 14th century when the Byzantine writer Theodorus Metochita (d. 1332) wrote "Euclid of Megara, the Socratic philosopher, contemporary of Plato." This Euclid, Euclid of Megara, lived around 400 B.C.E. And was actually a pupil of Socrates who founded a philosophical school, which Plato did not like. Nothing is known of Euclid's death. Other works of Euclid include: The Data,.