Hence for every tension greater than the minimum tension there are two catenaries passing through A and B.
Since the tension is measured by the height above the directrix these two catenaries have the same directrix.
Now let us consider the surfaces of revolution formed by this system of catenaries revolving about the directrix of the two catenaries of equal tension.
14) be two catenaries having the same directrix and intersecting in A and B.
Draw Pp and Qq touching both catenaries, Pp and Qq will intersect at T, a point in the directrix; for since any catenary with its directrix is a similar figure to any other catenary with its directrix, if the directrix of the one coincides with that of the other the centre of similitude must lie on the common directrix.