what is playfair's axiom
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In geometry, Playfair's axiom is an axiom that can be used instead of the fifth postulate of Euclid: In a plane, given a line and a point not on it, at most one line parallel to the given line can be drawn through the point.
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The axiom which says that, given a point not on a given line, there is precisely one line through the point parallel to the line. It is equivalent to the axiom of Euclid's known as the parallel postulate. The name arises from its occurrence in a book by John Playfair (1748–1819), a British geologist and mathematician
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