Noun

1. The point in a perspective drawing at which parallel lines receding from an observer seem to converge.
   • 1884, Wm. M. Thornton, "Construction of Perspective Projections," The Annals of Mathematics, vol. 1, no 1, p. 13,

     These formulae . . . give for the vanishing point of a set of parallel lines whose common azimuth is α and declivity δ: η=d tan α, ζ=d tan δ sec α.

2. The situation in which, place where, or point in time when some object or phenomenon is no longer observable or notable.
   • 1762, Samuel Dunn, "Some Observations of the Planet Venus, on the Disk of the Sun, June 6th, 1761," Philosophical Transactions (1683-1775), vol. 52, p. 192,

     At 8h 35' 4", the least dent possible, quite black, appeared in the sun's limb. And at 8h 35' 6", the limb was restored to its perfect form, there having been a small trembling light, between the narrow watery border of Venus and the vanishing point of contact in the sun's limb for these two seconds of time.

   • 1923, "Tuberculosis at Bay," Time, 25 June,

     It might cut the tuberculosis deathrate to the vanishing point.

   • 2003, Sally B. Donnelly, "The Need for Speed," Time, 25 Aug.,

     It hit 100 m.p.h. with ease and sped toward the vanishing point down Highway 93A.