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Geometry by Jeremy J. Gray, Matthew F. Esplen, David A. Brannan

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0    Introduction: Geometryand Geometries

Geometry is the study of shape. It takes its name from the Greek1 belief that geometry began with Egyptian surveyors of two or three millennia ago measuring the Earth, or at least the fertile expanse of it that was annually flooded by the Nile.

It rapidly became more ambitious. Classical Greek geometry, called Euclidean geometry after Euclid2, who organized an extensive collection of theorems into a definitive text, was regarded by all in the early modern world as the true geometry of space. Isaac3 Newton used it to formulate his Principia, the book that first set out the theory of gravity. Until the mid-19th Century, Euclidean geometry was regarded as one of the highest points of rational thought, as ...

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