*It is one of the oldest algorithms known and was included in Euclid's Elements. Euclid also discusses perfect numbers, infinite prime numbers, and Mersenne primes (the Euclid-Euler theorem).*

*It is one of the oldest algorithms known and was included in Euclid's Elements. Euclid also discusses perfect numbers, infinite prime numbers, and Mersenne primes (the Euclid-Euler theorem).*

More than one thousand editions have been printed throughout the decades.

Schools only stopped using the Elements in the early 1900s, some were still using it in the early 1980s, however, the theories continue to be those that we use today.

A departure from mathematical standards is then a mortal sin, whereas an error in history is venial. According to one, Hippasus was expelled for political insubordination, having headed a democratic move- ment against the conservative Pythagorean rule.

There is always the temptation in a class in history of mathematics to assume that the fundamental purpose of the course is to teach mathematics. The exact cause of the break is unknown, in part because of the rule of secrecy, but there are three suggested possibilities.

In a work of modest scope the author must exercise judgment in the selection of the materials to be included, reluctantly restraining the temptation to cite the work of every productive mathematician ; it will be an exceptional reader who will not note here what he regards as unconscionable omissions. They do not suffice, for example, to compare the diagonal of a square or a cube or a pentagon with its side.

Such an enterprise would call for the concerted effort of a team, similar to that which produced the fourth volume of Cantor's Vorlesungen uber Geschichte der Mathematik in 1908 and brought the story down to 1799. This was the discovery that within geometry itself the whole numbers and their ratios are inadequate to account for even simple fundamental properties.Euclid of Alexandria is considered to be the Father of Geometry.Very little is known about Euclid's life except that he taught in Alexandria, Egypt. There are references also to works in foreign languages, despite the fact that some students, hopefully not many, may be unable to read any of these. The latter remained to the end of his life deeply com- mitted to the Pythagorean veneration of number and geometry, and the supremacy of Athens in the mathematical world of the fourth century B. resulted primarily from the enthusiasm of Plato, the "maker of mathemati- cians." However, before taking up the role of Plato it is necessary to discuss the work of an earlier Pythagorean— an apostate by the name of Hippasus. Smaller college libraries may not be able to provide all of these sources, but it is well for a student to be aware of the larger realms of scholarship beyond the confines of his own campus. Nevertheless, the most important contribution of Archytas to mathematics may have been his intervention with the tyrant Dionysius to save the life of his friend, Plato.Many of them had been proposed by earlier mathematicians.Possibly the greatest value of Euclid's writings is that they present the ideas as a comprehensive, well-organized reference.In the 19th century, other types of geometry were described.Now, Euclid's work is called Euclidean geometry to distinguish it from the other methods.This text is organized chronologically and provides interesting information about the details of the mathematicians' lives.At the time, and for many centuries, Euclid's work was simply called "geometry" because it was assumed to be the only possible method of describing space and the position of figures.

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