Sentence Examples


  • This is the true standpoint from which the theorem should be regarded.
  • Thus the ternary quartic is not, in general, expressible as a sum of five 4th powers as the counting of constants might have led one to expect, a theorem due to Sylvester.
  • We may, by a well-known theorem, write the result as a coefficient of z w in the expansion of 1 - z n+1.
  • If we expand the symbolic expression by the multinomial theorem, and remember that any symbolic product ai 1 a2 2 a3 3 ...
  • Now the symbolic expression of the seminvariant can be expanded by the binomial theorem so as to be exhibited as a sum of products of seminvariants, of lower degrees if alai 0-2a2 +...+crea0 can be broken up into any two portions (alai -1-0-2a2-1-��� +asas) +(as+1as +1 +o-8+2as+2+��� +ooae), such that Q1 +a2+...