subtraction

Etymology

It is inherited from Middle English subtraccioun,^[2][3] partly borrowed from Anglo-Norman subtraccion,^[4][2] and partly borrowed from Late Latin subtractiō (“a withdrawal, taking away”),^{[4][5][6][2][7][8]} formed from the past participle of subtrahō (“to take away, draw off”), from sub- (“from under”) and trahō (“to pull, draw”).^[5][6][4] According to the OED the Latin noun occurs in the Vulgate, translating Ancient Greek ὑποστολή (hupostolḗ), and in mathematics from the 6th century.^[4] The French form is recorded from 1155, first of the elision of a syllable, and of the mathematical operation from the later 13th century.^[4] The modern French word is soustraction, which the OED links to the variant substraction.^[4]

Earliest recorded meaning

Withdrawal or removal of something from a place: before 1425, in a translation of Guy de Chauliac's Grande Chirurgie.^[4] Etymonline and Barnhart date the word to about 1400,^[6][5] Dictionary.com to 1350–1400,^[9] and Merriam-Webster to the 15th century.^[3]

Semantic evolution

The arithmetical sense appears almost at once, about 1425, in The Crafte of Nombrynge: "Þou most know þat subtraccion is drawynge of one nowmber oute of anoþer nomber".^[6][4][5] It outlived the general sense of removal, which the OED ends in 1525.^[4] From 1474 the word also meant withholding something useful or something owed, especially in law, for the withholding of a right such as rents, tithes or conjugal rights.^[4][3][7] From 1534 it was used more loosely of any deduction or taking away.^[4] The medical use for letting blood is entered in the MED.^[2] The verb subtract came later, in 1533, probably as a back-formation, and took on its arithmetical sense only in 1557.^[5] Johnson (1755) entered the noun with a cross-reference to substraction.^[10] Coleridge and later writers used it from 1812 to 1890 for detraction, rarely.^[4]

Timeline

• before 1425 – withdrawal or removal (obsolete by 1525).^[4]
• c. 1425 – in mathematics, taking one number from another.^[4][5][6]
• 1474 – withholding of something useful or owed.^[4][2]
• 1534 – figurative, deduction or taking away.^[4]
• 1812 – detraction (rare, obsolete by 1890).^[4]

Meanings

Noun

1. The arithmetic operation of finding the difference between two numbers or quantities: Children learn addition before subtraction.^[11][3][4]
2. The act or process of subtracting or taking something away.^[11][3][4]
3. In law, the withholding of a right or service to which someone is entitled.^[3][7][4]
4. In logic, the process of excepting one class from another that includes it.^[3]
5. Withdrawal or removal from a place (obsolete, before 1425–1525).^[4][7]

Related words

• subtract
• subtractive
• substraction
• tract

References

1. ^ Wiktionary, the free dictionary, https://en.wiktionary.org
2. ^ a b c d e Kurath, Hans; Kuhn, Sherman M.; Lewis, Robert E., eds. (1952–2001), Middle English Dictionary, Ann Arbor: University of Michigan Press; online edition ed. Frances McSparran et al. (2000–2018)
3. ^ a b c d e f g Merriam-Webster Unabridged Dictionary (2024), online ed., Springfield, Mass.: Merriam-Webster
4. ^ 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
5. ^ a b c d e f Barnhart, Robert K. (1988), The Barnhart Dictionary of Etymology
6. ^ a b c d e Harper, Douglas. Online Etymology Dictionary, https://www.etymonline.com
7. ^ a b c d Shorter Oxford English Dictionary on Historical Principles (2002), 5th ed., ed. William R. Trumble and Angus Stevenson, Oxford: Oxford University Press
8. ^ Klein, Ernest. A Comprehensive Etymological Dictionary of the English Language. 2 vols. Amsterdam: Elsevier, 1966–1967.
9. ^ Dictionary.com Unabridged (2016), based on the Random House Unabridged Dictionary, New York: Random House
10. ^ Johnson, Samuel (1755), A Dictionary of the English Language, London; 4th ed. 1773; Johnson's Dictionary Online, ed. Beth Rapp Young et al.
11. ^ a b Collins English Dictionary (2023), Glasgow: HarperCollins