Sentence Examples

  • = 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.
  • The people who finally abandoned the mainland and took their priests with them are the people who made the Venetian republic. But they were not as yet a homogeneous population.
  • Consider two binary equations of orders m and n respectively expressed' in non-homogeneous form, viz.
  • Forms adapted to terrestrial life and to aerial respiration occur in various divisions of Gastropods, and do not constitute a single homogeneous group. Thus the Helicinidae, which are terrestrial, are now placed among the Aspidobranchia.
  • In this he showed that a homogeneous fluid mass revolving uniformly round an axis under the action of gravity ought to assume the form of an ellipsoid of revolution.

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