Euclid of Alexandria (Greek: Eukleides) (circa 365-275 BC) was a Greek mathematician who lived in the 3rd century BC in Alexandria. His most famous work is the Elements, widely considered to be history's most successful textbook. Within it, the properties of geometrical objects and integers are deduced from a small set of axioms, thereby anticipating (and partially inspiring) the axiomatic method of modern mathematics. Although many of the results in the Elements originated with earlier mathematicians, one of Euclid's major accomplishments was to present them in a single, logically coherent framework. He also provided some missing proofs. The text also includes sections on algebra, number theory, and three-dimensional geometry.
The geometrical system described in the Elements was long known simply as "the" geometry. Today, however, it is often referred to as Euclidean geometry to distinguish it from other so-called non-Euclidean geometries which developed in the 19th century. These new geometries grew out of more than two millennia of investigation into Euclid's fifth postulate, one of the most-studied results in all of mathematics. See the articles on Euclid's Elements and the Parallel postulate for more information.
While the Elements was used into the 20th century as a geometry textbook and has been considered a fine example of the formally precise axiomatic method, Euclid's treatment does not hold up to modern standards and some logically necessary axioms are missing. The first correct axiomatic treatment of geometry was provided by Hilbert in 1899.
Almost nothing is known about Euclid outside of what is presented in the Elements and his few other surviving books. What little biographical information we do have comes largely from commentaries by Proclus and Pappus of Alexandria: He was active at the great library in Alexandria and may have studied at Plato's Academe in Greece, but his exact lifespan and place of birth are unknown.
In the Middle Ages, writers sometimes referred to him as Euclid of Megara, confusing him with a Greek Socratic philosopher who lived approximately one century earlier.
Heath, Thomas L. (1956). The Thirteen Books of Euclid's Elements, Vol. 1 (2nd ed.). New York: Dover Publications. ISBN 0-486-60088-2.