use today. And neither Napier nor Bürgi
mentioned the concept of a logarithmic
base—something that Briggs presented.
By 1624 Briggs would write Arith-
metica logarithmica(The Arithmetic of
Logarithms), extending his common log
tables from 1 to 20,000 and from 90,000
to 100,000. But the work on logarithms
did not end with Napier, Briggs, or Bürgi.
Natural logarithms eventually evolved out
of Napier’s original work. Defining loga-
rithms as exponents was finally recog-
nized by English mathematician John
Wallis (1616–1703), who presented them
in his 1685 publication, De algebra trac-
tatus(Treatise of Algebra).
For what other inventionwas John
Napierknown?
Scottish mathematician John Napier may
have been known for his contributions to
logarithms, but he was also the inventor of a tool called Napier’s Bones (also known as
Napier’s Rods). These were multiplication tables inscribed on strips of animal bone or
wood. Wilhelm Schickard would eventually build the first calculating machine based on
Napier’s bones, a device that could add, subtract, and—with help—multiply or divide.
Napier was also the “instigator” in another discovery: In 1621 English mathemati-
cian and clergyman William Oughtred (1575–1660) used Napier’s logarithms as the basis
for the slide rule (a ruler-like instrument used long before hand-held calculators came
into vogue). Oughtred not only invented the standard rectilinear slide rule, but also the
circular slide rule, which was an extremely useful tool that remained in common usage
for more than three hundred years. (For more about Oughtred, see “Math Basics.”)
What are the properties of logarithms?
Logarithms have certain properties, depending on the interpretations of an equation.
The following lists some of the most common properties (these rules are the same for
all positive bases):
- loga 1 0, because a^0 1. For example, in the equation 14^0 1, the base is 14
and the exponent is 0. Because a logarithm is an exponent, this would mean the
equation can be written as a logarithmic equation, or log 141 0 (zero is the
146 exponent).
Slide rulers and calculating systems based on Napi-
er’s bones were used for centuries before the inven-
tion of today’s handy battery-operated and solar cal-
culators. Stone/Getty Images.
