Hyperbolic logarithm

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.
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   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.
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   {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.
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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.
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   {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