1540s, "a goal, a guiding object," from French finalité, from Late Latin finalitatem (nominative finalitas) "state of being final," from Latin finalis "last, of or pertaining to an end" (see final). From 1833 as "quality or state of being final."
1650s, from Late Latin ultimatus, past participle of ultimare "to be final, come to an end," from Latin ultimus (fem. ultima) "last, final, farthest, most distant, extreme," superlative of *ulter "beyond" (from suffixed form of PIE root *al- "beyond"). As a noun from 1680s. Ultimate Frisbee is attested by 1972.