Sentence Examples

  • And f(ae i a5, a 2, a3,...) becomes f+h(aoaai +2alaa2+3a2aa3+...) f, and hence the functions satisfy the differential equation.
  • And we may suppose such identities between the symbols that on the whole only two, three, or more of the sets of umbrae are not equivalent; we will then obtain invariants of two, three, or more sets of binary forms. The symbolic expression of a covariant is equally simple, because we see at once that since AE, B, Ce,...
  • There Is A Still More General Form Of Seminvariant; We May Have Instead Of 0, 0 Any Collections Of Nonunitary Integers Not Exceeding 0, 0 In Magnitude Respectively, (2 A2 3 A3 ...0 Ae)A(L S 2 G2 3 G3 ...0' Ge') B (12 A2 3 A3 ..0 Ab)A(1 S I 2 G2 3 G3 ...B Ge) B (1 22A23A3 ...0 Ae) A(1822 G2 3 G3 ...0' Ge ') B () 8 (1 8 2 A2 3 A3 ...19'°) A(2 G2 3 G3 ...0' ' ') B, Is A Seminvariant; And Since These Forms Are Clearly Enumerated By 1 Z.
  • Ae T 1 T ...
  • +a,,en =t ae, which we shall call extensiveuantities of the first species q f ?

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