Excerpt from Non-Euclidean Geometry

The axioms of Geometry were formerly regarded as laws of thought which an intelligent mind could neither deny nor investigate. Not only were the axioms to which we have been accustomed found to agree with our experience, but it was believed that we could not reason on the supposition that-any of them are not true. It has been Shown, however, that it is possible to take a set of axioms, wholly or in part contradicting those of Euclid, and build up a Geometry as consistent as his.

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