Sentence Examples


  • But what was matter of immanent assumption with Erigena is in them an equating of two things which have been dealt with on the hypothesis that they are separate, and which, therefore, still retain that external relation to one another.
  • He first divides by the factor x -x', reducing it to the degree m - I in both x and x' where m>n; he then forms m equations by equating to zero the coefficients of the various powers of x'; these equations involve the m powers xo, x, - of x, and regarding these as the unknowns of a system of linear equations the resultant is reached in the form of a determinant of order m.
  • = 0, we find that, eliminating x, the resultant is a homogeneous function of y and z of degree mn; equating this to zero and solving for the ratio of y to z we obtain mn solutions; if values of y and z, given by any solution, be substituted in each of the two equations, they will possess a common factor which gives a value of x which, corn bined with the chosen values of y and z, yields a system of values which satisfies both equations.
  • X (1 +PD1+12D2+...+�8D8+...) fm, and now expanding and equating coefficients of like powers of /t D 1 f - Z(Difi)f2f3.
  • This can be verified by equating to zero the five coefficients of the Hessian (ab) 2 axb2.

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