What is Euclid's Axiom?

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2009-10-17 16:29:56

Euclid posited five axioms, statements whose truth supposedly

does not require a proof, as the foundation of his work, the

Elements. These still hold for plane geometry, but do not hold in

the higher non-euclidean systems. The five axioms Euclid proposed


  • Any two points can be connected by one, and only one, straight


  • Any line segment can be extended infinitely
  • For any point, and a line emerging from it, a circle can be

    drawn where the point is the centre and the line is the


  • All right angles are equal
  • Given a line, and a point not on the line, there is only line

    that goes through the point that does not meet the other line.

    (basically, there is only one parallel to any given


This last point is controversial as it has been argued effectively

that this is not in fact self evident. In fact, ignoring the fifth

axiom was the starting point for many Non-Euclidean geometries. For

this reason, it is probably this which is best known as Euclid's


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