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Euclidean geometry is a mathematical well-known system attributed to the Greek mathematician Euclid of Alexandria. Euclid's text Elements was the first systematic discussion of geometry. It has been one of the most influential books in history, as much for its method as for its mathematical content. The method consists of assuming a small set of intuitively appealing axioms, and then proving many other propositions (theorems) from those axioms. Although many of Euclid's results had been stated by earlier Greek mathematicians, Euclid was the first to show how these propositions could be fitted together into a comprehensive deductive and logical system.

*To draw a straight line from any point to any other.*

*To produce a finite straight line continuously in a straight line.*

*To describe a circle with any centre and distance.*

*That all right angles are equal to each other.*

*That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, if produced indefinitely, meet on that side on which are the angles less than the two right angles.*

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Euclid is known to almost every high school student as the author of *The Elements*, the long studied text on geometry and number theory. No other book except the *Bible* has been so widely translated and circulated. From the time it was written it was regarded as an extraordinary work and was studied by all mathematicians, even the greatest mathematician of antiquity -- Archimedes, and so it has been through the 23 centuries that have followed. It is unquestionably the best mathematics text ever written and is likely to remain so into the distant future.

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Non-Euclidean Geometry

A Sample Construction

John D. Norton

Department of History and Philosophy of Science

University of Pittsburgh

From the Eighteenth to the Nineteenth Century

Alternative Formulations of Euclid's Fifth Postulate

Exploring the Geometry of 5NONE

Circles and Triangles

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