nth

Etymology

It is formed from English n + -th, from the use of the letter n in mathematics for an unspecified or variable number.^{[2][3][4][5][6]} Barnhart suggests it is probably a loan translation of French nième, formed from n and -ième.^[7]

Earliest recorded meaning

In mathematics, being number n in a series, where n is an unspecified or variable number: 1756, in the Philosophical Transactions of the Royal Society.^[2][4] Etymonline finds the phrase to the nth in algebra textbooks by 1717.^[5]

Semantic evolution

Equations and roots "of the nth degree" were spoken of in mathematics well before the figurative use: the Phrase Finder quotes The Monthly Review of 1794.^[8] The OED records a more general use from 1827, especially in the phrases to the nth (degree, power), to the utmost, without limit, and for the nth time;^[2] the 2003 Collegiate likewise dates the word to 1827.^[9] Barnhart and Etymonline date the figurative use to 1852,^[10][7][5] and the Phrase Finder places the rise of to the nth degree in the United States, quoting a newspaper of 1871.^[8]

Timeline

• 1756 – in mathematics, being number n in a series.^[2][4]
• 1827 – in general use, the latest of an indefinitely long series, and in to the nth, to the utmost.^[2][9]

Meanings

Adjective

1. (mathematics) Being number n in a series, where n is an unspecified or variable ordinal number: raise the value to the nth power.^[11][2][4]
2. (informal) Being the latest of a long series, or one of an indefinitely large number: I have told you for the nth time to close the gate.^[11][4][12]
3. Utmost, extreme; especially in to the nth degree, as far as possible.^[4][11][12]

References

1. ^ Wiktionary, the free dictionary, https://en.wiktionary.org
2. ^ a b c d e f Oxford English Dictionary Online (accessed March 2026), Oxford: Oxford University Press
3. ^ The American Heritage Dictionary of the English Language (online 2024), 5th ed., Boston: Houghton Mifflin Harcourt
4. ^ a b c d e f Merriam-Webster Unabridged Dictionary (2024), online ed., Springfield, Mass.: Merriam-Webster
5. ^ a b c Harper, Douglas. Online Etymology Dictionary, https://www.etymonline.com
6. ^ Dictionary.com Unabridged (2016), based on the Random House Unabridged Dictionary, New York: Random House
7. ^ a b Barnhart, Robert K. (1988), The Barnhart Dictionary of Etymology
8. ^ a b Martin, Gary, The Phrase Finder: Meaning and Origin of Phrases, Sayings, Clichés and Quotes, https://www.phrases.org.uk
9. ^ a b Merriam-Webster's Collegiate Dictionary (2003), 11th ed., Springfield, Mass.: Merriam-Webster
10. ^ Barnhart, Robert K., ed. (1995), The Barnhart Concise Dictionary of Etymology, New York: HarperCollins
11. ^ a b c Collins English Dictionary (2023), Glasgow: HarperCollins
12. ^ a b The American Heritage Dictionary of the English Language (1992), 3rd ed., Boston: Houghton Mifflin