logarithm

Etymology

It is borrowed from New Latin logarithmus,^{[2][3][4][5][6]} a word coined by the Scottish mathematician John Napier (1550–1617),^[3][7] who used it in 1614.^[2][8][7] He formed it from Ancient Greek λόγος (lógos, “word; proportion, ratio; reckoning”) and ἀριθμός (arithmós, “number”),^{[2][3][4][7][6]} so that it is usually understood as "ratio-number".^[2][3][7][9] The OED notes that Napier never explained what he meant by it, and that he may have used the first element simply for "reckoning, calculation", as in logistic.^[2] Barnhart derives the Greek noun from λέγω (légō, “to speak”).^[4] The American Heritage Dictionary refers the two Greek words to the roots Proto-Indo-European *leg- and *ar-,^[5] while Etymonline takes the number word from a suffixed form of *re- (“to reason, count”).^[3] The second element is also the source of arithmetic.^[10][11]

Earliest recorded meaning

One of the arithmetical functions that Napier invented and set out in tables to shorten calculation: 1616, in a letter of Henry Briggs printed in Richard Parr's life of James Usher (1686).^[2][12] The 1989 edition of the OED dated the word 1614,^[13] Barnhart 1615–16,^[4] Merriam-Webster about 1616^[14] and Dictionary.com 1605–15.^[15]

Semantic evolution

Napier published his first table in 1614; the kind of logarithm now chiefly used was worked out by his contemporary Henry Briggs (1561–1630), professor of geometry at Gresham College, London.^[3] In the modern definition a logarithm is the exponent to which a fixed base must be raised to give a number,^[14][5][16] and the American Heritage Dictionary names the common logarithm (base 10), the natural logarithm (base e) and the binary logarithm (base 2) as the kinds most used.^[5] Logarithms served above all to turn multiplication and division into addition and subtraction,^[17][16] and the word is often shortened to log.^[14][17]

Timeline

• 1616 – an arithmetical function invented by Napier and tabulated to shorten calculation.^[2][12]

Meanings

Noun

1. The exponent of the power to which a fixed number, the base, must be raised to give a particular number: The logarithm of 100 to the base 10 is 2.^[14][5][17]
2. Any of a series of such exponents set out in tables to simplify multiplication and division.^[16][17][2]

Word family

• logarithmic
• logarithmically
• cologarithm
• antilogarithm
• log
• Briggsian logarithm
• common logarithm
• natural logarithm

Related words

• logos
• arithmetic
• logic
• logistic

References

1. ^ a b Wiktionary, the free dictionary, https://en.wiktionary.org
2. ^ a b c d e f g h Oxford English Dictionary Online (accessed March 2026), Oxford: Oxford University Press
3. ^ a b c d e f Harper, Douglas. Online Etymology Dictionary, https://www.etymonline.com
4. ^ a b c d Barnhart, Robert K., ed. (1995), The Barnhart Concise Dictionary of Etymology, New York: HarperCollins
5. ^ a b c d e The American Heritage Dictionary of the English Language (online 2024), 5th ed., Boston: Houghton Mifflin Harcourt
6. ^ a b Stevenson, Angus, ed. (2010), Oxford Dictionary of English, 3rd ed., Oxford: Oxford University Press
7. ^ a b c d Klein, Ernest. A Comprehensive Etymological Dictionary of the English Language. 2 vols. Amsterdam: Elsevier, 1966–1967.
8. ^ Weekley, Ernest (1921), An Etymological Dictionary of Modern English, London: John Murray
9. ^ Skeat, Walter W. (1911), A Concise Etymological Dictionary of the English Language, new ed., Oxford: Clarendon Press
10. ^ Ayto, John (2005), Word Origins: The Secret Histories of English Words from A to Z, 2nd ed., London: A & C Black
11. ^ Hoad, T. F., ed. (1986), The Concise Oxford Dictionary of English Etymology, Oxford: Clarendon Press
12. ^ a b Kay, Christian; Roberts, Jane; Samuels, Michael; Wotherspoon, Irené, eds. (2009), Historical Thesaurus of the Oxford English Dictionary, Oxford: Oxford University Press; online edition (2024)
13. ^ Simpson, J. A.; Weiner, E. S. C., eds. (1989), The Oxford English Dictionary, 2nd ed., Oxford: Clarendon Press
14. ^ a b c d Merriam-Webster Unabridged Dictionary (2024), online ed., Springfield, Mass.: Merriam-Webster
15. ^ Dictionary.com Unabridged (2016), based on the Random House Unabridged Dictionary, New York: Random House
16. ^ a b c Shorter Oxford English Dictionary on Historical Principles (2002), 5th ed., ed. William R. Trumble and Angus Stevenson, Oxford: Oxford University Press
17. ^ a b c d Collins English Dictionary (2023), Glasgow: HarperCollins