Sentence Examples


  • The three subjects to which Smith's writings relate are theory of numbers, elliptic functions and modern geometry; but in all that he wrote an "arithmetical" made of thought is apparent, his methods and processes being arithmetical as distinguished from algebraic. He had the most intense admiration of Gauss.
  • Thus, 1 - x would represent the operation of selecting all things in the world except horned things, that is, all not horned things, and (1 - x) (1 - y) would give us all things neither horned nor sheep. By the use of such symbols propositions could be reduced to the form of equations, and the syllogistic conclusion from two premises was obtained by eliminating the middle term according to ordinary algebraic rules.
  • It was then proposed to arrange a detector so that it was affected by the algebraic sum of the two oscillations, and by swivelling round the double receiving antennae to locate the direction of the sending station by finding out when the detector gave the best signal.
  • An obituary notice by his friend Auguste Chevalier appeared in the Revue encyclopedique (1832); and his collected works are published, Journal de Liouville (1846), pp. 381-444, about fifty of these pages being occupied by researches on the resolubility of algebraic equations by radicals.
  • Energyequations, such as the above, may be operated with precisely as if they were algebraic equations, a property which is of great advantage in calculation.

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