Sentence Examples


  • Some of the most important results of his discoveries were communicated to the Royal Society in two memoirs upon "Systems of Linear Indeterminate Equations and Congruences" and upon the "Orders and Genera of Ternary Quadratic Forms" (Phil.
  • He was also the author of important papers in which he extended to complex quadratic forms many of Gauss's investigations relating to real quadratic forms. After 1864 he devoted himself chiefly to elliptic functions, and numerous papers on this subject were published by him in the Proc. Lond.
  • It forms quadratic prisms, having a violet reflex and insoluble in boiling hydrochloric acid.
  • Tannery thinks that the solution of a complete quadratic promised by Diophantus himself (I.
  • Among the great variety of problems solved are problems leading to determinate equations of the first degree in one, two, three or four variables, to determinate quadratic equations, and to indeterminate equations of the first degree in one or more variables, which are, however, transformed into determinate equations by arbitrarily assuming a value for one of the required numbers, Diophantus being always satisfied with a rational, even if fractional, result and not requiring a solution in integers.

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