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 Euclid 450 BC-404 BC - Alexandria 

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Euclid of Alexandria (Greek: Eukleides) (circa 365–275 BC) was a Greek mathematician. 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 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 axioms in all of mathematics.

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.

From Columbia Encyclopedia: Greek mathematician. Little is known of his life other than the fact that he taught at Alexandria, being associated with the school that grew up there in the late 4th cent. B.C. He is famous for his Elements, a presentation in thirteen books of the geometry and other mathematics known in his day. The first six books cover elementary plane geometry and have served since as the basis for most beginning courses on this subject. The other books of the Elements treat the theory of numbers and certain problems in arithmetic (on a geometric basis) and solid geometry, including the five regular polyhedra, or Platonic solids. The great contribution of Euclid was his use of a deductive system for the presentation of mathematics. Primary terms, such as point and line, are defined; unproved assumptions, or postulates, regarding these terms are stated; and a series of statements are then deduced logically from the definitions and postulates. Although Euclid’s system no longer satisfies modern requirements of logical rigor, its importance in influencing the direction and method of the development of mathematics is undisputed. One consequence of the critical examination of Euclid’s system was the discovery in the early 19th cent. that his fifth postulate, equivalent to the statement that one and only one line parallel to a given line can be drawn through a point external to the line, can not be proved from the other postulates; on the contrary, by substituting a different postulate for this parallel postulate two different self-consistent forms of non-Euclidean geometry were deduced, one by Nikolai I. Lobachevsky (1826) and independently by János Bolyai (1832) and another by Bernhard Riemann (1854). A few modern historians have questioned Euclid’s authorship of the Elements, but he is definitely known to have written other works, most notably the Optics

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