The postulate about parallels plays an important role in the history of nonEuclidean geometry.

It [ nonEuclidean geometry ] would be ranked among the most famous achievements of the entire [nineteenth] century, but up to 1860 the interest was rather slight.
ivor grattanguinnessThe classical theorists resemble Euclidean geometers in a nonEuclidean world who, discovering that in experience straight lines apparently parallel often meet, rebuke the lines for not keeping straight as the only remedy for the unfortunate collisions which are occurring. Yet, in truth, there is no remedy except to throw over the axiom of parallels and to work out a nonEuclidean geometry.
john maynard keynesWe find in the history of ideas mutations which do not seem to correspond to any obvious need, and at first sight appear as mere playful whimsies such as Apollonius' work on conic sections, or the nonEuclidean geometries, whose practical value became apparent only later.
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