The Collaborative International Dictionary of English v.0.48:

Thirteenth \Thir"teenth`\ (th[~e]r"t[=e]nth`), a. [From
   Thirteen: cf. AS. [thorn]re['o]te['o][eth]a.]
   1. Next in order after the twelfth; the third after the
      tenth; -- the ordinal of thirteen; as, the thirteenth day
      of the month.
      [1913 Webster]

   2. Constituting or being one of thirteen equal parts into
      which anything is divided.
      [1913 Webster]

The Collaborative International Dictionary of English v.0.48:

Thirteenth \Thir"teenth`\, n.
   1. The quotient of a unit divided by thirteen; one of
      thirteen equal parts into which anything is divided.
      [1913 Webster]

   2. The next in order after the twelfth.
      [1913 Webster]

   3. (Mus.) The interval comprising an octave and a sixth.
      [1913 Webster]

WordNet (r) 3.0 (2006):

thirteenth
    adj 1: coming next after the twelfth in position [syn:
           thirteenth, 13th]
    n 1: position 13 in a countable series of things