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# Euclid

**Euclid** (325 BC to about 265 BC) became a prominent mathematician in Alexandria, Egypt during the rule of Alexander the Great, which later powers was transferred to the Ptolemaic dynasty upon his death. Most of what is known biographically about Euclid is from commentaries by Proclus and Pappus of Alexandria. Euclid was very active at the Library of Alexandria and quite possibly could have studied at Plato's Academy in Greece. Some writers living during the Middle Ages confused Euclid of Alexandria with Euclid of Megara who was a Greek Socratic philosopher that lived a century earlier. ^{[1]}

## Major Publications

The most fascinating aspect about Euclids mysterious life is that his writings, most of which have been lost with time have made a connection to them quite hard. Little is known about Euclid other than what can be deduced from his few writings that have survived.

### The Elements

Euclid of Alexandria's most substantial contribution to mathematics was entitled, *The Elements*. This massive collection of what is essentially a canon or mathematical treatise contains 13 books which outline definitions, starting assumptions or axioms as well as what would logically follow there after, theorems and constructions.

*The Elements* by Euclid was readily acceptable in society and due to its desk reference nature it became the primary mathematician's tool for nearly 2,000 years. Even more interesting is that it is clearly implied within the text that Euclid is borrowing concepts and ideas from earlier already established texts making traces of modern mathematics date back even further still.

Postulates put forth by Euclid such as number four which states that all right angles are equal and the parallel postulate that only one line can be drawn through a point parallel to a given line. It is through these very important postulates that a foundation for Euclidian geometry could be built upon. It was so stable, so dominant that it wasn't until the 19th century (1800-1900) that other forms of geometry were considered. ^{[2]}

Also found within his writing are various results in number theory such as the connection between perfect numbers and Mersenne primes as well as the proof of the infinitude of prime numbers. Euclid's lemma on factorization was also established which leads to the fundamental theorem of arithmetic on uniqueness of prime factorizations. The Euclidean algorithm for finding the greatest common divisor of two numbers can also be found within the *Elements*.

## References

## External Links

- Euclid Biography School of Mathematical and Computational Sciences for University of St Andrews
- Ptolemaic Egypt by Wikipedia
- Historical Mathmaticians Mr. Messier's Math Page