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Definition: Binary logarithms
(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
, a. [L. binarius, fr. bini two by two, two at
a time, fr. root of bis twice; akin to E. two: cf. F.
Compounded or consisting of two things or parts;
characterized by two (things).
, that in which numbers are expressed
according to the binary scale, or in which two figures
only, 0 and 1, are used, in lieu of ten; the cipher
multiplying everything by two, as in common arithmetic by
ten. Thus, 1 is one; 10 is two; 11 is three; 100 is four,
etc. --Davies & Peck.
(Chem.), a compound of two elements, or of
an element and a compound performing the function of an
element, or of two compounds performing the function of
, a system of logarithms devised by Euler
for facilitating musical calculations, in which 1 is the
logarithm of 2, instead of 10, as in the common
logarithms, and the modulus 1.442695 instead of .43429448.
(Mus.), measure divisible by two or four;
(Nat. Hist.), nomenclature in which the
names designate both genus and species.
(Arith.), a uniform scale of notation whose
ratio is two.
(Astron.), a double star whose members have a
revolution round their common center of gravity.
(Chem.), the theory that all chemical
compounds consist of two constituents of opposite and