hyperbolic logarithm

2 definitions found

hyperbolic logarithm - Collaborative International Dictionary of English v.0.48 :

  Hyperbolic \Hy`per*bol"ic\, Hyperbolical \Hy`per*bol"ic*al\, a.
     [L. hyperbolicus, Gr. ?: cf. F. hyperbolique.]
     1. (Math.) Belonging to the hyperbola; having the nature of
        the hyperbola.
        [1913 Webster]
  
     2. (Rhet.) Relating to, containing, or of the nature of,
        hyperbole; exaggerating or diminishing beyond the fact;
        exceeding the truth; as, an hyperbolical expression. "This
        hyperbolical epitaph." --Fuller.
        [1913 Webster]
  
     Hyperbolic functions (Math.), certain functions which have
        relations to the hyperbola corresponding to those which
        sines, cosines, tangents, etc., have to the circle; and
        hence, called hyperbolic sines, hyperbolic cosines,
        etc.
  
     Hyperbolic logarithm. See Logarithm.
  
     Hyperbolic spiral (Math.), a spiral curve, the law of which
        is, that the distance from the pole to the generating
        point varies inversely as the angle swept over by the
        radius vector.
        [1913 Webster]

  Logarithm \Log"a*rithm\ (l[o^]g"[.a]*r[i^][th]'m), n. [Gr.
     lo`gos word, account, proportion + 'ariqmo`s number: cf. F.
     logarithme.] (Math.)
     One of a class of auxiliary numbers, devised by John Napier,
     of Merchiston, Scotland (1550-1617), to abridge arithmetical
     calculations, by the use of addition and subtraction in place
     of multiplication and division.
  
     Note: The relation of logarithms to common numbers is that of
           numbers in an arithmetical series to corresponding
           numbers in a geometrical series, so that sums and
           differences of the former indicate respectively
           products and quotients of the latter; thus,
           0 1 2 3 4 Indices or logarithms
           1 10 100 1000 10,000 Numbers in geometrical progression
           Hence, the logarithm of any given number is the
           exponent of a power to which another given invariable
           number, called the base, must be raised in order to
           produce that given number. Thus, let 10 be the base,
           then 2 is the logarithm of 100, because 10^2 = 100,
           and 3 is the logarithm of 1,000, because 10^3 =
           1,000.
           [1913 Webster]
  
     Arithmetical complement of a logarithm, the difference
        between a logarithm and the number ten.
  
     Binary logarithms. See under Binary.
  
     Common logarithms, or Brigg's logarithms, logarithms of
        which the base is 10; -- so called from Henry Briggs, who
        invented them.
  
     Gauss's logarithms, tables of logarithms constructed for
        facilitating the operation of finding the logarithm of the
        sum of difference of two quantities from the logarithms of
        the quantities, one entry of those tables and two
        additions or subtractions answering the purpose of three
        entries of the common tables and one addition or
        subtraction. They were suggested by the celebrated German
        mathematician Karl Friedrich Gauss (died in 1855), and are
        of great service in many astronomical computations.
  
     Hyperbolic logarithm or Napierian logarithm or Natural logarithm
     , a logarithm (devised by John Speidell, 1619) of
        which the base is e (2.718281828459045...); -- so called
        from Napier, the inventor of logarithms.
  
     Logistic logarithms or Proportional logarithms, See under
        Logistic.
        [1913 Webster] Logarithmetic