inverse

Etymology

It is borrowed from Latin inversus (“turned upside down, inverted; perverted”),^[2][3][4][5] the past participle of invertō (“to turn upside down, turn about, reverse”),^[2][3][6][7] from in- and vertō (“to turn”),^[8][4] from Proto-Indo-European *wer- (“to turn, bend”).^[4] In early use it was also written enverse.^[3] Skeat took it through Middle French invers,^[9] but the OED and most dictionaries take it straight from Latin; inverse is recorded only from 1611.^[2][3][4] The mathematical senses follow post-classical Latin, which used inversus in mathematics from at least the 16th century, as in inversa ratio.^[2] The verb, first recorded before 1425, is partly from the adjective and partly from Latin invers-.^[2]

Earliest recorded meaning

Turned upside down, inverted: about 1440, in a Middle English translation of Palladius's De re rustica.^[2][6] The verb, to invert, appears slightly earlier, in a translation of Guy de Chauliac's surgery.^[2] Etymonline dates the adjective to the mid-15th century.^[3]

Semantic evolution

From "upside down" the adjective widened to "reversed or turned in the opposite direction, having the contrary nature or effect" (1568).^[2] The mathematical use, in inverse proportion or inverse ratio, is recorded from 1660.^[2][6] Johnson (1755) defined it as inverted and as reciprocal, opposed to direct, and explained inverse proportion.^[10] Further mathematical senses followed: an inverse equation (1805), an inverse function (1813), the inverse square (1825) and points and curves related by geometric inversion (1843).^[2] The noun, the opposite or reverse of something, dates from 1630,^[2] or 1681 in Barnhart and Merriam-Webster.^[6][7] The old sense "upside down" is now rare or archaic.^[2][7][4]

Timeline

• before 1425 – verb, to invert.^[2]
• c. 1440 – adjective, turned upside down.^[2][6]
• 1568 – reversed, opposite in order or nature.^[2]
• 1630 – noun, the opposite or reverse.^[2]
• 1660 – inverse proportion, inverse ratio.^[2][6]
• 1813 – an inverse function.^[2]
• 1825 – inverse square.^[2]

Meanings

Adjective

1. Opposite or reversed in order, direction, nature or effect: the inverse of the usual sequence.^[4][11][7]
2. (mathematics) Of a relation between two quantities: such that one increases as the other decreases, as in inverse proportion.^[11][2]
3. (mathematics) Of or relating to an inverse function or an inverse element.^[4][11]
4. (archaic) Turned upside down; inverted.^[4][7][2]

Noun

1. Something that is the opposite of something else in order or character; the reverse.^[4][7][2]
2. (mathematics) An element that, combined with a given element under an operation, gives the identity element, as −x is the additive inverse of x.^[4][11]

Verb

1. (rare) To invert or reverse something.^[12][7][2]

Word family

• inversely
• inverse function
• additive inverse
• inverse cosine
• inverse sine
• inverse tangent
• multiplicative inverse

Related words

• inversion
• inversive
• reverse
• reversion
• invert
• converse
• obverse
• version

References

1. ^ Wiktionary, the free dictionary, https://en.wiktionary.org
2. ^ a b c d e f g h i j k l m n o p q r s t u v w Oxford English Dictionary Online (accessed March 2026), Oxford: Oxford University Press
3. ^ a b c d e Harper, Douglas. Online Etymology Dictionary, https://www.etymonline.com
4. ^ a b c d e f g h i j The American Heritage Dictionary of the English Language (online 2024), 5th ed., Boston: Houghton Mifflin Harcourt
5. ^ Klein, Ernest. A Comprehensive Etymological Dictionary of the English Language. 2 vols. Amsterdam: Elsevier, 1966–1967.
6. ^ a b c d e f Barnhart, Robert K. (1988), The Barnhart Dictionary of Etymology
7. ^ a b c d e f g Merriam-Webster Unabridged Dictionary (2024), online ed., Springfield, Mass.: Merriam-Webster
8. ^ Hoad, T. F., ed. (1986), The Concise Oxford Dictionary of English Etymology, Oxford: Clarendon Press
9. ^ Skeat, Walter W. (1911), A Concise Etymological Dictionary of the English Language, new ed., Oxford: Clarendon Press
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 c d Collins English Dictionary (2023), Glasgow: HarperCollins
12. ^ Shorter Oxford English Dictionary on Historical Principles (2002), 5th ed., ed. William R. Trumble and Angus Stevenson, Oxford: Oxford University Press