Sentence Examples

  • With Descartes the use of exponents as now employed for denoting the powers of a quantity becomes systematic; and without some such step by which the homogeneity of successive powers is at once recognized, the binomial theorem could scarcely have been detected.
  • Between 1886 and 1892 he published a series of papers on the foundations of the kinetic theory of gases, the fourth of which contained what was, according to Lord Kelvin, the first proof ever given of the Waterstdn-Maxwell theorem of the average equal partition of energy in a mixture of two different gases; and about the same time he carried out investigations into impact and its duration.
  • This paper is principally based on the following general theorem, which is a remarkable extension of Pascal's hexagram: "If a polygon move so that each of its sides passes through a fixed point, and if all its summits except one describe curves of the degrees m, n, p, &c., respectively, then the free summit moves on a curve of the degree 2mnp. ..
  • We therefore have the fundamental theorem that the angular velocity of the body around the centre of attraction varies inversely as the square of its distance, and is therefore at every point proportional to the gravitation of the sun.
  • Another curious theorem proposed by Bouilland in 1625 as a substitute for Kepler's second law is that the angular motion of the body as measured around the empty focus F' is (approximately) uniform.

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