Sentence Examples


  • The vanishing of this invariant is the condition for equal roots.
  • Locks (East London Advertiser, 1902); Philip Norman, London vanished and vanishing (1905); Records of the London Topographical Society; Monographs of the Committee for the Survey of the Memorials of Greater London.
  • We find that if the series of excitations of the muscle be prolonged beyond the short stage of initial improvement, the contractions, after being well maintained for a time, later decline in force and speed, and ultimately dwindle even to vanishing point.
  • This implies the vanishing of the discriminant of the original form.
  • The discriminant, whose vanishing is the condition that f may possess two equal roots, has the expression j 2 - 6 i 3; it is nine times the discriminant of the cubic resolvent k 3 - 2 ik- 3j, and has also the expression 4(1, t') 6 .