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### Euclid - Wikipedia, Euclid of alexandria essay

# Euclid of alexandria essay

In Euclid's method, deductions are made from premises or axioms. This deductive method, as modified by Aristotle , was the sole procedure used for demonstrating scientific certitude ("truth") until the seventeenth century.

Euclid's book the Elements also contains the beginnings of number theory. The Euclidean algorithm, which is often referred to as Euclid's algorithm, is used to determine the greatest common divisor (gcd) of two integers .

Book V shifts from plane geometry to expound a general theory of ratios and proportions that is attributed by Proclus (along with Book XII) to Eudoxus of Cnidus ( c. 395/390–342/337 bce ). While Book V can be read independently of the rest of the Elements , its solution to the problem of incommensurables ( irrational numbers ) is essential to later books. In addition, it formed the foundation for a geometric theory of numbers until an analytic theory developed in the late 19th century. Book VI applies this theory of ratios to plane geometry, mainly triangles and parallelograms, culminating in the “application of areas,” a procedure for solving quadratic problems by geometric means.

Copyright John D. Norton. December 28,
2006, February 28, 2007; February 2, 9, 14, September 22, 2008; February
2, 2010; January 1, 2013. February 13, 14, 2017.

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The philosopher Proclus of Athens (412-485 CE), who lived seven centuries later, said that Euclid "put together the Elements, collecting many of Eudoxus’s theorems, perfecting many of Theaetetus’s, and bringing to irrefragable demonstration things which were only somewhat loosely proved by his predecessors." The scholar Stobaeus lived at about the same time as Proclus. He collected Greek manuscripts that were in danger of being lost. He told a story about Euclid that has the ring of truth:

Another surviving work, the
*
Optics,
*
corrects the belief held at the time that the sun and other heavenly
bodies are actually the size they appear to be to the eye. This work
discusses the relationship between what the eye sees of an object and
what the object actually is. For example, the eye always sees less than
half of a sphere, and as the observer moves closer to the sphere, the
part of it that is seen is decreased, although it appears larger.

The * Elements* also includes works on perspective , conic sections, spherical geometry, and possibly quadric surfaces. Apart from geometry, the work also includes number theory . Euclid came up with the idea of * greatest common divisors* . They were in his * Elements* . The greatest common divisor of two numbers is the greatest number that can fit evenly in both of the two numbers.

The second type of information is that Euclid was born at Megara. This is due to an error on the part of the authors who first gave this information. In fact there was a Euclid of Megara, who was a philosopher who lived about 100 years before the mathematician Euclid of Alexandria. It is not quite the coincidence that it might seem that there were two learned men called Euclid. In fact Euclid was a very common name around this period and this is one further complication that makes it difficult to discover information concerning Euclid of Alexandria since there are references to numerous men called Euclid in the literature of this period.

· This is a biography of Euclid of Alexandria . All of the rules we use in Geometry today are based on the writings of Euclid , 'The Elements'.

Details about Euclid’s life are sparse – the main biographical information was not written until many centuries later, . Proclus c. 450 AD. Proclus writes about Euclid:

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The first Ptolemies created the learning center in the city. This center held a cult temple to Serapis (Serapeum or Sarapeion) with Alexandria's most important sanctuary, museion (museum) and a library. Which Ptolemy had the temple built is debatable. The statue was a draped figure on a throne with a sceptre and a Kalathos on his head. Cerberus stands beside him.

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Euclid | Biography, Contributions, & Facts | Britannica.com

Euclid of Alexandria - Elements and Mathematics

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euclid of alexandria essay

euclid of alexandria essay