The Collaborative International Dictionary of English v.0.48:

Seventeenth \Sev"en*teenth`\, a. [From Seventeen: cf. AS.
   seofonte['o][eth]a, seofonteoge[eth]a.]
   1. Next in order after the sixteenth; coming after sixteen
      others.
      [1913 Webster]

            In . . . the seventeenth day of the month . . . were
            all the fountains of the great deep broken up.
                                                  --Gen. vii.
                                                  11.
      [1913 Webster]

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

The Collaborative International Dictionary of English v.0.48:

Seventeenth \Sev"en*teenth`\, n.
   1. The next in order after the sixteenth; one coming after
      sixteen others.
      [1913 Webster]

   2. The quotient of a unit divided by seventeen; one of
      seventeen equal parts or divisions of one whole.
      [1913 Webster]

   3. (Mus.) An interval of two octaves and a third.
      [1913 Webster]

WordNet (r) 3.0 (2006):

seventeenth
    adj 1: coming next after the sixteenth in position [syn:
           seventeenth, 17th]
    n 1: position 17 in a countable series of things