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Euclid's most notable error lies in his fifth postulate, known as the parallel postulate. He assumed that through a point not on a given line, only one line can be drawn parallel to the given line, which led to the development of Euclidean geometry. However, this assumption is not universally true, as demonstrated by non-Euclidean geometries, where multiple parallel lines can exist through a single point. This limitation in his framework constrained the exploration of alternative geometrical systems until the 19th century.

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