convex

Etymology

It is borrowed from Latin convexus (“vaulted, arched, rounded”),^{[2][3][4][5][6][7]} which Barnhart, Etymonline and Klein see as coming through Middle French convexe;^[8][9][10] Merriam-Webster gives the source as either.^[11] The origin of the Latin word is disputed.^[7][10] The OED, Etymonline and Ayto take it as an old past participle of convehō (“to bring together”), from com- (“together”) and vehō (“to carry”), because the ends of an arch are brought together to meet at the top;^{[2][9][7][12]} Etymonline traces vehō to Proto-Indo-European *wegh- (“to go, transport in a vehicle”).^[9][3] Klein, Skeat, Barnhart and Merriam-Webster instead connect -vexus with a root meaning "to bend, be curved", found also in vacillō (“to sway, waver”) and Old English wōh (“crooked”).^{[10][13][8][11]} The OED notes that Latin convexus could also include the sense "concave".^[2]

Earliest recorded meaning

Curved like the outside of a circle or sphere, and of glasses and mirrors of that shape: in L. Digges's Pantometria, published in 1571,^[2][8][11] which the OED dates to possibly before 1560.^[2]

Semantic evolution

The word came into English in geometry and optics, with convex lenses and mirrors among its first uses.^[2] In the 17th century it was also a noun for a convex surface or vault, and poets used it for the vault of the sky or of hell (1627–1715);^[2][11] Milton stressed the second syllable.^[2] Johnson (1755) defined it as "rising in a circular form; opposite to concave".^[14] Later senses are a convex lens (1705), a card cut slightly convex for cheating (1864), and in mathematics a figure or set that contains the straight line joining any two of its points (1858).^[2] Etymonline dates the phrase convex lens to 1822.^[9] The verb, to bend outwards, is recorded from 1805.^[2]

Timeline

• 1571 – curved like the outside of a sphere; of lenses and mirrors.^[2][8][11]
• 1626 – noun, a convex surface or vault (obsolete by 1796).^[2]
• 1627 – noun, in poetry, the vault of the sky (obsolete by 1715).^[2]
• 1705 – noun, a convex lens.^[2]
• 1805 – verb, to bend outwards.^[2]
• 1822 – convex lens.^[9]
• 1858 – in mathematics, of a figure or set.^[2]
• 1864 – a card cut convex for cheating.^[2]

Meanings

Adjective

1. Curving or bulging outwards, like the outside of a circle or sphere; the opposite of concave: a convex mirror at the corner of the street.^[15][11][2]
2. (physics) Of a lens, having one or both surfaces curved outwards.^[15][2]
3. (mathematics) Of a polygon, having no interior angle greater than 180 degrees; of a set, containing the straight line between any two of its points; of a function, having a graph that bends upwards.^[15][2][11]

Noun

1. (archaic) A convex surface or body, especially a vault or the vault of the sky seen from outside.^[11][2]

Verb

1. To make convex, or to bend outwards.^[15][11][2]

Word family

• convexly
• convexedness
• biconvex
• concavo-convex
• convexity
• plano-convex
• subconvex
• convex hull

Related words

• concave
• vacillate
• vehicle
• convey

References

1. ^ a b 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 Oxford English Dictionary Online (accessed March 2026), Oxford: Oxford University Press
3. ^ a b The American Heritage Dictionary of the English Language (online 2024), 5th ed., Boston: Houghton Mifflin Harcourt
4. ^ Stevenson, Angus, ed. (2010), Oxford Dictionary of English, 3rd ed., Oxford: Oxford University Press
5. ^ Hoad, T. F., ed. (1986), The Concise Oxford Dictionary of English Etymology, Oxford: Clarendon Press
6. ^ Shorter Oxford English Dictionary on Historical Principles (2002), 5th ed., ed. William R. Trumble and Angus Stevenson, Oxford: Oxford University Press
7. ^ a b c Ayto, John (2005), Word Origins: The Secret Histories of English Words from A to Z, 2nd ed., London: A & C Black
8. ^ a b c d Barnhart, Robert K. (1988), The Barnhart Dictionary of Etymology
9. ^ a b c d e Harper, Douglas. Online Etymology Dictionary, https://www.etymonline.com
10. ^ a b c Klein, Ernest. A Comprehensive Etymological Dictionary of the English Language. 2 vols. Amsterdam: Elsevier, 1966–1967.
11. ^ a b c d e f g h i Merriam-Webster Unabridged Dictionary (2024), online ed., Springfield, Mass.: Merriam-Webster
12. ^ Weekley, Ernest (1921), An Etymological Dictionary of Modern English, London: John Murray
13. ^ Skeat, Walter W. (1911), A Concise Etymological Dictionary of the English Language, new ed., Oxford: Clarendon Press
14. ^ Johnson, Samuel (1755), A Dictionary of the English Language, London; 4th ed. 1773; Johnson's Dictionary Online, ed. Beth Rapp Young et al.
15. ^ a b c d Collins English Dictionary (2023), Glasgow: HarperCollins