Euclid is one of the world’s most famous mathematicians, yet very little is known of his life. It is estimated he was born around 365 B.C. and died around 300 B.C. Euclid’s most famous work “The Elements”, a work and focused upon elementary geometry and other topics, exceeded all other works of its time, which are now known only by indirect reference. The Elements begins with definitions, postulates, and axioms, including the famous fifth, or parallel, postulate that one and only one line can be drawn through a point parallel to a given line. Euclid’s decision to make this postulate not demonstrable assumption led to Euclidean geometry. It was not until the 19th century that the fifth postulate was modified in order to develop non-Euclidean geometry.
The Elements are divided into 13 books. The first 6 are on geometry; 7, 8 and 9 are on number theory; and book number 10 is on Eudoxus’s theory of irrational numbers. Books 11, 12, and 13 all concern solid geometry, and end with a discussion of the properties of the five regular polyhedrons and proof that there can only be these five. Euclid’s Elements are remarkable for the clarity with which the theorems and problems are selected and ordered. The propositions proceed logically and concisely, with very few assumptions.