# Euclidean Geometry

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EUCLIDEAN GEOMETRY

Geometry was thoroughly organized in about 300 BC, when the Greek

mathematician Euclid gathered what was known at the time, added original work of his

own, and arranged 465 propositions into 13 books, called 'Elements'. The books covered

not only plane and solid geometry but also much of what is now known as algebra,

trigonometry, and advanced arithmetic.

Through the ages, the propositions have been rearranged, and many of the

proofs are different, but the basic idea presented in the 'Elements' has not changed. In the

work facts are not just cataloged but are developed in a fashionable way.

Even in 300 BC, geometry was recognized to be not just for mathematicians.

Anyone can benefit from the basic learning of geometry, which are how to follow lines of

reasoning, how to say precisely what is intended, and especially how to prove basic

concepts by following these lines of reasoning.

Taking a course in geometry is beneficial

for all students, who will find that learning to reason and prove convincingly is necessary

for every profession. It is true that not everyone must prove things, but everyone is

exposed to proof. Politicians, advertisers, and many other people try to offer convincing

arguments. Anyone who cannot tell a good proof from a bad one may easily be persuaded

in the wrong direction. Geometry provides a simplified universe, where points and lines

obey believable rules and where conclusions are easily verified. By first studying how to

reason in this simplified universe, people can eventually, through practice and

experience, learn how to reason in a complicated world.

Geometry in ancient times was recognized as...