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### Origin of the Term Logarithm

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Date: 10/27/1999 at 21:16:51
From: Suzanne
Subject: Where did the term "Logarithm" come from?

Dr. Math,

Hi. In my junior pre-calculus class, we have just recently started to
study logarithms. Some of my fellow classmates, as well as myself,
have been wondering where the term for logarithms came from. How did
the term "logarithm" come to represent logarithms? We've asked my
teacher, but she's not sure of the answer. Please help!

Sincerely,
Suzanne
```

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Date: 10/27/1999 at 21:38:45
From: Doctor Jaime
Subject: Re: Where did the term "Logarithm" come from?

Hello

The following is taken from Jeff Miller's page, Earliest Known Uses of
Some of the Words of Mathematics (L):

http://jeff560.tripod.com/l.html

LOGARITHM was coined in Latin as logarithmus by John Napier
(1550-1617) in 1614 in _Mirifici Logarithmorum Canonis descriptio_.
The word appears in English in a letter of March 10, 1615, from Henry
Briggs to James Ussher: "Napier, Lord of Markinston, hath set my Head
and Hands a Work with his new and admirable Logarithms. I hope to see
him this summer, if it please God, for I never saw a book which
pleased me better or made me more wonder."

In the _Constructio_, the phrase "artificial numbers" is used, rather
than "logarithms." Napier offered no explanation for the term
logarithm, but in the _Arithmetica logarithmica_ (1624), Briggs
explains that the name came from their inventor because they exhibit
numbers which preserve always the same ratio to one another. [Older
English-language dictionaries pronounce logarithm with an unvoiced th,
as in thick and arithmetic.]

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In _The Words of Mathematics_ - An Etymological dictionary of
Mathematical Terms Used in English, Steven Schwartzman's writes:

logarithm, often shortened to log (noun), logarithmic (adjective):
from Greek logos "reckoning, ratio," and arithmos "number." A
logarithm is literally a "reckoning number." The Indo-European root
underlying Greek logos is leg- "to collect," while that underlying
arithmos is ar- "to fit together," so that the word logarithm twice
contains the notion of putting things together... [p. 128]

Hope this helps.

- Doctors Jaime and Sarah, The Math Forum
http://mathforum.org/dr.math/
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Associated Topics:
High School Definitions
High School Logs
Middle School Definitions
Middle School Logarithms

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