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Definition: Hyperbolic logarithm
, Hyperbolical \Hy`per*bol"ic*al\
[L. hyperbolicus, Gr. ?: cf. F. hyperbolique.]
1. (Math.) Belonging to the hyperbola; having the nature of
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.”
(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
. See Logarithm
(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
(l[o^]g"[.a]*r[i^][th]'m), n. [Gr.
lo`gos word, account, proportion + 'ariqmo`s number: cf. F.
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
and 3 is the logarithm of 1,000, because 10^3
Arithmetical complement of a logarithm
, the difference
between a logarithm and the number ten.
. See under Binary
, or Brigg's logarithms
, logarithms of
which the base is 10; -- so called from Henry Briggs, who
, 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.
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.
or Proportional logarithms
, See under