The proposition that if AA′‖BB′ then BB′‖AA′ appears at first sight so simple that it might be regarded as almost intuitive. This is because we already think of parallelism as a symmetrical relationship between two straight lines, in accordance with Euclid's definition of parallels as “straight lines which, being in the same plane and being produced indefinitely in both directions, do not meet one another in either direction.” If we take along with this definition Euclid's fifth postulate, or Playfair's equivalent, it defines a unique line through a given point parallel to a given line; but, without the postulate, it cannot be assumed to define more than a class of lines, and a stricter definition is required.