Page:LorentzStatement1920.djvu/16

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At this point Einstein intervened with a hypothesis which, apart altogether from subsequent verification, deserves to rank as one of the great monuments of human genius. After correcting Newton, it remained to correct Euclid, and it was in terms of non-Euclidean geometry that he stated his new theory. Non-Euclidean geometry is a study of which the primary motive was logical and philosophical; few of its promoters ever dreamed that it would come to be applied in physics. Some of Euclid's axioms were felt to be not "necessary truths," but mere empirical laws; in order to establish this view, self-consistent geometries were constructed upon assumptions other than those of Euclid. In these geometries the sum of the angles of