Etymology of 'Logarithm'Date: 03/19/99 at 18:31:08 From: Marco Filipetto Subject: About logarithms Why is a 'logarithm' called a 'logarithm'? Where did the term originate? Also, why is the inverse of the exponential function called a 'logarithm'? We thought that logarithms had to be tabled or 'logged' (as in Star Trek log) in charts, and thus the name 'logarithm'. Thanks. Date: 03/19/99 at 21:03:30 From: Doctor Rick Subject: Re: About logarithms The word 'logarithm' was coined by John Napier, the inventor of a form of logarithm, in 1614. See Earliest Known Uses of Some of the Words of Mathematics http://jeff560.tripod.com/mathword.html It comes from the Greek words 'logos' and 'arithmes'. The second word means 'number'. The first word has a broad range of meanings, starting from 'word' or 'speech' (thus our word 'dialog'), going into 'thought' and 'reason' (thus 'logical'), and on to 'proportion'. In this range of meanings, it resembles the Latin 'ratio', which means both 'reason' and 'proportion' (thus the two meanings of 'rational': reasonable, and expressable as a ratio or proportion of two integers). Thus, a 'logarithm' is a 'proportion number'. I suppose the thinking was that logarithms help in the calculation of proportions: instead of multiplying a number by a fraction, you just add or subtract the logarithm of the fraction to the logarithm of the number. The logarithm actually predates the exponential function, one of the oddities of math history. 'Exponent' is Latin for 'putting out'; I will have to think a bit about why it might be called that. I wondered briefly if 'log' as in logbook had to do with the logos part, at least -- but then I remembered the nautical origin of 'log'. To measure a ship's speed, sailors would heave a log, attached to a rope, into the water. The rope had knots in it, and a sailor would count the knots that passed through his hands in a certain amount of time. The record of speed and position came to include other information, but it was still called the log book. And you can guess that the unit of speed, a knot (nautical mile per hour), also came out of this practice. - Doctor Rick, The Math Forum http://mathforum.org/dr.math/ |
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