Euclid and the Elements

Euclid and the Elements

Euclid was a Greek geometer who wrote the Elements, the world's most definitive text on geometry. The book synthesized earlier knowledge about geometry, and was used for centuries in Western Europe as a geometry textbook. The text began with definitions, postulates, and common opinions, and then proceeded to obtain results by thorough geometric proof. Euclid also proved what is generally known as Euclid's Second Theorem: the number of primes is infinite. The proof Euclid gave of this theorem is still commonly recognized to be one of the classic proofs of all times in terms of its shortness and simplicity. In the Elements, Euclid used the method of exhaustion and reduction ad absurdum. He also discussed the so-called Euclidean algorithm for finding the greatest common divisor of two numbers, and is credited with the well-known proof of the Pythagorean Theorem.

Euclid of Alexandria is the most prominent mathematician of antiquity best known for his treatise on mathematics The Elements. The lengthy nature of The Elements must make Euclid the leading mathematics teacher of all time. However, little is known of Euclid's life except that he taught at Alexandria in Egypt.

Even if we accept that Euclid was a historical character who wrote the Elements and the other works attributed to him then there is little doubt that he built up a vigorous school of mathematics at Alexandria. It definitely doesn’t prove that Euclid was a historical character since there are many similar references to Bourbaki by mathematicians who knew perfectly well that Bourbaki was fabricated.

Euclid's most famous work is his treatise on mathematics The Elements. The Elements begins with definitions and five postulates. Euclid's decision to make this a postulate led to Euclidean geometry. There are also axioms which Euclid calls 'common notions'. Zeno of Sidon, about 250 years after Euclid wrote the Elements, seems to have been the first to show that Euclid's propositions were not...

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