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# Euclid

Euclid of Alexandria (Greek: ) (circa 365275 BC) was a Greek mathematician, now known as "the father of geometry". His most famous work is 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 partly inspiring) the axiomatic method of modern mathematics.

Although many of the results in Elements originated with earlier mathematicians, one of Euclid's major accomplishments was to present them in a single, logically coherent framework. In addition to providing some missing proofs, Euclid's text also includes sections on number theory and three-dimensional geometry.

The geometrical system described in 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. Most of these investigations centered around an attempt to prove Euclid's fifth postulate from his other postulates (what we would today call axioms); essentially, showing that the fifth postulate was in actual fact a theorem. The reason that such a proof was so highly sought after for so many years was because while Euclid's other postulates appeared simple, self evident, and intuitively obvious, the fifth postulate essentially described the intersection of lines at potentially infinite distances––the concept of infinity being at the time, at least mathematically, problematic. Thus, the fifth postulate appeared as something of a blemish on the otherwise seemingly flawless logical edifice that was Euclid's Elements.

While 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 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.

## Reference

• Heath, Thomas L. (1956). The Thirteen Books of Euclid's Elements, Vol. 1 (2nd ed.). New York: Dover Publications. ISBN 0-486-60088-2.
• Kline, Morris. (1980). "Mathematics: The Loss of Certainty", Oxford: Oxford University Press. ISBN 0-19-502754-X