arithmetic

Etymology

It is inherited from Middle English arsmetike, later arsmetrike,^[3][4][5][6] borrowed from Old French arismetique, also arsmetique,^{[7][4][3][8][9]} which the OED derives through Old Occitan arismetica or Late Latin arismetica, an altered form of Latin arithmētica,^[7][10][5] from Ancient Greek ἀριθμητική (arithmētikḗ), short for the phrase with τέχνη (tékhnē, “art”), the art of counting,^[7][3][5][6] the feminine of ἀριθμητικός (arithmētikós, “of or for reckoning”),^[3][10] from ἀριθμέω (arithméō, “to number, count, reckon”), from ἀριθμός (arithmós, “number”).^[7][6][4] The s of the French form renders the Greek letter theta.^[6][11] Etymonline traces arithmós to Proto-Indo-European *re- (“to reason, count”),^[3] and Klein to a base meaning "to count, number" that also gave Old English rīm (“number”) and Latin rītus (“religious custom, rite”);^[6] Barnhart takes it as cognate with ars (“art”).^[4] In Middle English the word was taken for Latin ars metrica (“the art of measure”), which gave the form arsmetrike, the usual one from the 14th to the 16th century.^[7][5][3][9] It was gradually brought back towards the Latin and Greek, through arismetrik in Caxton and arithmetricke in Thomas More, to arithmetyke in Robert Recorde in 1543.^[7][4] The adjective, recorded from the mid-17th century, is borrowed from French arithmétique, the OED allowing also Latin arithmēticus.^[7][9] Old English had its own word for the art, tælcræft (“tell-craft”).^[3][11]

Earliest recorded meaning

The art of computing with numbers: about 1250, as arsmetike, according to Barnhart, and to the mid-13th century in Etymonline;^[4][3] the OED's first quotation is from about 1305, in a life of St Edmund.^[7] Merriam-Webster dates the main sense to the 15th century.^[12]

Semantic evolution

Barnhart notes other spellings from French, such as aritmétique in the Roman de la Rose (1270), a poem Chaucer translated about 1370.^[4] The learned respelling of the 16th century made the English and the French words agree with the Greek again,^[3][6] although a form arsmetry is still recorded from the 1590s.^[3][7] From the "science of numbers" the word passed to arithmetical knowledge or reckoning itself (Shakespeare's Coriolanus, before 1616) and to a book on the subject (1623).^[7] The adjective, "of or according to arithmetic", came in the mid-17th century,^[9][7] giving terms such as arithmetic mean and arithmetic progression,^[9][12] and in 1947 the arithmetic unit of a computer.^[7] In current use the noun also means a calculation or the working out of figures in a particular case, as in the arithmetic of the budget.^[13][12]

Timeline

• c. 1250 – arsmetike, the art of computation.^[4][3]
• c. 1300 – the form arsmetrike, after ars metrica.^[4]
• c. 1305 – the science of numbers, the OED's first quotation.^[7]
• 1543 – the corrected spelling arithmetyke, in Recorde.^[7][4]
• 1551 – adjective, according to Merriam-Webster.^[12]
• before 1616 – arithmetical knowledge, reckoning, in Shakespeare's Coriolanus.^[7]
• 1623 – a treatise on computation.^[7]
• 1652 – noun, an arithmetician (now obsolete).^[7]
• 1673 – adjective, arithmetical.^[7]
• 1947 – arithmetic unit, in a computer.^[7]

Meanings

Noun

1. The branch of mathematics that deals with numbers and with calculations using them, chiefly addition, subtraction, multiplication and division.^[13][12][10]
2. A calculation or set of calculations, or the working out of the figures in a given case: The arithmetic of the deal never added up.^[13][12]
3. Skill or knowledge in calculating: Her mental arithmetic is quick.^[13][7]
4. A book or treatise on arithmetic.^[12][7]

Adjective

1. Of or relating to arithmetic; following its rules; also arithmetical.^[12][13][9]
2. Changing by equal steps, as in an arithmetic progression, where each term differs from the last by the same amount.^[12][9]

Word family

• arithmetically
• arithmetician
• arithmetic mean
• arithmetic progression
• arithmetical

Related words

• logarithm
• algorithm
• rhyme
• rite
• art

References

1. ^ a b Jones, Daniel (2011), Cambridge English Pronouncing Dictionary, 18th ed., ed. Peter Roach, Jane Setter and John Esling, Cambridge: Cambridge University Press
2. ^ Wiktionary, the free dictionary, https://en.wiktionary.org
3. ^ a b c d e f g h i j k Harper, Douglas. Online Etymology Dictionary, https://www.etymonline.com
4. ^ a b c d e f g h i j Barnhart, Robert K. (1988), The Barnhart Dictionary of Etymology
5. ^ a b c d Hoad, T. F., ed. (1986), The Concise Oxford Dictionary of English Etymology, Oxford: Clarendon Press
6. ^ a b c d e f Klein, Ernest. A Comprehensive Etymological Dictionary of the English Language. 2 vols. Amsterdam: Elsevier, 1966–1967.
7. ^ a b c d e f g h i j k l m n o p q r s t u Oxford English Dictionary Online (accessed March 2026), Oxford: Oxford University Press
8. ^ Stevenson, Angus, ed. (2010), Oxford Dictionary of English, 3rd ed., Oxford: Oxford University Press
9. ^ a b c d e f g Shorter Oxford English Dictionary on Historical Principles (2002), 5th ed., ed. William R. Trumble and Angus Stevenson, Oxford: Oxford University Press
10. ^ a b c The American Heritage Dictionary of the English Language (online 2024), 5th ed., Boston: Houghton Mifflin Harcourt
11. ^ a b Weekley, Ernest (1921), An Etymological Dictionary of Modern English, London: John Murray
12. ^ a b c d e f g h i Merriam-Webster Unabridged Dictionary (2024), online ed., Springfield, Mass.: Merriam-Webster
13. ^ a b c d e Collins English Dictionary (2023), Glasgow: HarperCollins