The term Napierian logarithm or Naperian logarithm, named after the Scottish mathematician John Napier (1550–1617), is often used to mean the natural logarithm. Napier did not introduce this natural logarithmic function, although it is named after him. However, if it is taken to mean the "logarithms" as originally produced by Napier, it is a function given by (in terms of the modern natural logarithm):
The Napierian logarithm satisfies identities quite similar to the modern logarithm, such as
or
In Napier's 1614 , he provides tables of logarithms of sines for 0 to 90°, where the values given (columns 3 and 5) are
Properties
Napier's "logarithm" is related to the natural logarithm by the relation
and to the common logarithm by
Note that
and
Napierian logarithms are essentially natural logarithms with decimal points shifted 7 places rightward and with sign reversed. For instance the logarithmic values
would have the corresponding Napierian logarithms:
For further detail, see history of logarithms.
References
. . .
External links Denis Roegel (2012) Napier’s Ideal Construction of the Logarithms, from the Loria Collection of Mathematical Tables.