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Origin of the Term Logarithm

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!


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


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

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.]


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   
Associated Topics:
High School Definitions
High School Logs
Middle School Definitions
Middle School Logarithms

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