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“For every line l and for every point P not lying on a given line l, there exists a unique line m passing through P and parallel to l” is known as Playfair’s axiom.

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If a quantity B is a part of another quantity A, then A can be written as the sum of B and some third quantity C.

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The statements that are proved are called axioms.

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Two distinct intersecting lines cannot be parallel to the same line.

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Attempts to prove Euclid’s fifth postulate using the other postulates and axioms led to the discovery of several other geometries.