Leading mathematicians, including Richard Dedekind and David Hilbert, attempted to add axioms to the Elements, such as an axiom of continuity and an axiom of congruence, to make Euclidean geometry more complete.

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A construction used in any of Euclid's proofs required a proof that it is actually possible.

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Scholars believe that Elements is largely a collection of theorems proved by earlier mathematicians in addition to some original work by Euclid.

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Euclid probably chose to describe results in number theory in terms of geometry because he could not develop a constructible approach to arithmetic.

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Euclid (also referred to as Euclid of Alexandria) (Greek: ?????????) (c. 325 B.C.E.

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At the same time, non-Euclidean geometries attracted the attention of contemporary mathematicians.

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Euclid’s most famous work, Elements, is thought to be one of the most successful textbooks in the history of mathematics.

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Mathematicians (Bertrand Russell, Alfred North Whitehead) and philosophers such as Baruch Spinoza have also attempted to use Euclid’s method of axiomatized deductive structures to create foundations for their own respective disciplines.

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Euclid's Elements (Greek: ????????) is a mathematical and geometric treatise, consisting of thirteen books, written around 300 B.C.E.

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Euclid's famous proof of the infinitude of prime numbers is in Book IX, Proposition 20.

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A marked ruler, used in neusis construction, is forbidden in Euclidian construction, probably because Euclid could not prove that verging lines meet.

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Euclid’s text provides some missing proofs, and includes sections on number theory and three-dimensional geometry.

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Little is known about Euclid outside of what is presented in Elements and his other surviving books.

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By the mid-nineteenth century, it was shown that no such proof exists, because one can construct non-Euclidean geometries where the parallel postulate is false, while the other postulates remain true.

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Euclid thus imposed a logical organization on known mathematical truths, by the disciplined use of logic.

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A version by a pupil of Euclid called Proclo was translated later into Arabic after being obtained by the Arabs from Byzantium and from those secondary translations into Latin.

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The success of the Elements is due primarily to its logical presentation of most of the mathematical knowledge available to Euclid.

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Today, however, it is often referred to as Euclidean geometry to distinguish it from other so-called non-Euclidean geometries which were discovered during the nineteenth century.

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Euclid's Book 1 begins with 23 definitions such as point, line, and surface—followed by five postulates and five "common notions" (both of which are today called axioms).

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Euclid's parallel postulate, treated above, has been a primary target of critics.

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Euclid also wrote works on perspective, conic sections, spherical geometry, and possibly quadric surfaces.

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Although Euclid is a famous mathematician, very little is known about his life. It is believed that he was a student of Plato. Euclid was born around 365 B.C. in Alexandria, Egypt and lived until about 300 B.C. Euclid's most famous work is his collection of 13 books, dealing with geometry, called The Elements.

Very little is known of the father of geometry, also known as Euclid. Records show that he lived somewhere around 300 B.C., but that date is sketchy. He was a Greek mathematician and is probably best known for his work Elements.

Euclid enters history as one of the greatest of all mathematicians and he is often referred to as the father of geometry. The standard geometry most of us learned in school is called Euclidian Geometry.