algebraic

Etymology

It is partly formed from English algebra + -ic,^[2][3][4][5] and partly borrowed from Middle French algébraïque (1585),^[2] which is from New Latin algebraicus, recorded from 1545 or earlier.^[2] The noun algebra goes back to algebra, a word of Arabic origin.^[2][3] The OED compares the later algébrique (1740) and German algebraisch (1600).^[2] The longer form algebraical is older, from the 1570s in Etymonline.^[3]

Earliest recorded meaning

Of or relating to algebra: 1653, in John Webster's Academiarum Examen.^[2] Etymonline dates the word to the 1660s,^[3] and Merriam-Webster gives 1571 as its first known use.^[6]

Semantic evolution

The word first described anything belonging to or used in algebra, including a sum taken with its plus or minus sign.^[2] From 1657 it was applied more narrowly to an expression built only from addition, multiplication, powers and their inverses,^[2] the sense in which mathematicians contrast it with transcendental.^[6][4] In 1912 it was extended to numbers that are roots of a polynomial with whole-number coefficients,^[2] and since 1853 it has also named the chess notation in which each square is identified by its file and rank.^[2]

Timeline

• 1570s – the longer form algebraical.^[3]
• 1653 – of or relating to algebra.^[2]
• 1657 – of an expression, using only a finite number of algebraic operations.^[2][6]
• 1853 – in chess, of the notation that names each square by coordinates.^[2]
• 1912 – of a number, being a root of a polynomial with integer coefficients.^[2]

Meanings

Adjective

1. Of, relating to, or using algebra: an algebraic formula.^[7][6][2]
2. (mathematics) Of an expression or equation, using only a finite number of operations such as addition, multiplication and taking roots, as opposed to transcendental.^[6][2][4]
3. (mathematics) Of a number, being a root of a polynomial with whole-number coefficients.^[2]
4. (chess) Of the notation that names each square by its file and rank.^[2]

Word family

• algebraically
• nonalgebraic
• subalgebraic
• algebraic function
• algebraic equation
• algebraic extension
• algebraic topology
• algebraic geometry

Related words

• algebraical
• algebra

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 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 Shorter Oxford English Dictionary on Historical Principles (2002), 5th ed., ed. William R. Trumble and Angus Stevenson, Oxford: Oxford University Press
5. ^ Dictionary.com Unabridged (2016), based on the Random House Unabridged Dictionary, New York: Random House
6. ^ a b c d e Merriam-Webster Unabridged Dictionary (2024), online ed., Springfield, Mass.: Merriam-Webster
7. ^ Collins English Dictionary (2023), Glasgow: HarperCollins